History of mathematics

8200:

that Bhaskara II may claim to be 'the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus' (Bag 1979, 294).... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285))... It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian 'discovery of the principle of the differential calculus' somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential 'principle' was not generalized to arbitrary functions – in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here

1026:. From this derives the modern-day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 × 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. It is thought the sexagesimal system was initially used by Sumerian scribes because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, and for scribes (doling out the aforementioned grain allotments, recording weights of silver, etc.) being able to easily calculate by hand was essential, and so a sexagesimal system is pragmatically easier to calculate by hand with; however, there is the possibility that using a sexagesimal system was an ethno-linguistic phenomenon (that might not ever be known), and not a mathematical/practical decision. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a place-value system, where digits written in the left column represented larger values, much as in the 2693: 13064: 4089: 3946: 13398: 1952: 964: 5576:"The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius." – Pierre Simon Laplace 3018: 11604: 5215: 2386: 220: 5608:, 6th Edition, "After Pappus, Greek mathematics ceased to be a living study, ..." p. 185; "The Athenian school struggled on against growing opposition from Christians until the latter finally, in A.D. 529, obtained a decree from Emperor Justinian that closed the doors of the school forever." p. 186; "The period starting with the fall of the Roman Empire, in the middle of the fifth century, and extending into the eleventh century is known in Europe as the Dark Ages... Schooling became almost nonexistent." p. 258. 3142:, accepting square roots and fourth roots as solutions and coefficients to quadratic equations. He also developed techniques used to solve three non-linear simultaneous equations with three unknown variables. One unique feature of his works was trying to find all the possible solutions to some of his problems, including one where he found 2676 solutions. His works formed an important foundation for the development of algebra and influenced later mathematicians, such as al-Karaji and Fibonacci. 2707: 4677: 4592: 2267: 3345: 1837: 14185: 13791: 11616: 4278: 2676: 13779: 2610: 5038: 4176: 13768: 1770: 1637: 1536: 2312: 11640: 1244: 1436: 11628: 1007: 2815: 7452:, Encyclopaedia Britannica, Quote: "The 1, 4, and 6 are found in the Ashoka inscriptions (3rd century BC); the 2, 4, 6, 7, and 9 appear in the Nana Ghat inscriptions about a century later; and the 2, 3, 4, 5, 6, 7, and 9 in the Nasik caves of the 1st or 2nd century AD – all in forms that have considerable resemblance to today’s, 2 and 3 being well-recognized cursive derivations from the ancient = and ≡." 4319: 2734:(dated variously between the 8th century BC and the 2nd century AD), appendices to religious texts which give simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and others. As with Egypt, the preoccupation with temple functions points to an origin of mathematics in religious ritual. The Sulba Sutras give methods for constructing a 3589: 3773: 2811:) showing strong Hellenistic influence. They are significant in that they contain the first instance of trigonometric relations based on the half-chord, as is the case in modern trigonometry, rather than the full chord, as was the case in Ptolemaic trigonometry. Through a series of translation errors, the words "sine" and "cosine" derive from the Sanskrit "jiya" and "kojiya". 3620: 3690:, Oresme made a more detailed general analysis in which he demonstrated that a body will acquire in each successive increment of time an increment of any quality that increases as the odd numbers. Since Euclid had demonstrated the sum of the odd numbers are the square numbers, the total quality acquired by the body increases as the square of the time. 2746:. All of these results are present in Babylonian mathematics, indicating Mesopotamian influence. It is not known to what extent the Sulba Sutras influenced later Indian mathematicians. As in China, there is a lack of continuity in Indian mathematics; significant advances are separated by long periods of inactivity. 2322:

followed by the symbol for "100", then the symbol for "2" followed by the symbol for "10", followed by the symbol for "3". This was the most advanced number system in the world at the time, apparently in use several centuries before the common era and well before the development of the Indian numeral system.

5194:

There are many observable trends in mathematics, the most notable being that the subject is growing ever larger as computers are ever more important and powerful; the volume of data being produced by science and industry, facilitated by computers, continues expanding exponentially. As a result, there

3571:

proposed that speed (V) increases in arithmetic proportion as the ratio of force (F) to resistance (R) increases in geometric proportion. Bradwardine expressed this by a series of specific examples, but although the logarithm had not yet been conceived, we can express his conclusion anachronistically

3130:

which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of

862:

or a six-month lunar calendar. Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has

8199:

It is not unusual to encounter in discussions of Indian mathematics such assertions as that 'the concept of differentiation was understood from the time of Manjula (... in the 10th century)' , or that 'we may consider Madhava to have been the founder of mathematical analysis' (Joseph 1991, 293), or

1046:

accurate to five decimal places. The Babylonians lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. By the Seleucid period, the Babylonians had developed a zero symbol as a placeholder for empty positions; however it was

1030:

system. The power of the Babylonian notational system lay in that it could be used to represent fractions as easily as whole numbers; thus multiplying two numbers that contained fractions was no different from multiplying integers, similar to modern notation. The notational system of the Babylonians

8121:

the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava's mathematics are being distorted as they are

3670:

Heytesbury and others mathematically determined the distance covered by a body undergoing uniformly accelerated motion (today solved by integration), stating that "a moving body uniformly acquiring or losing that increment will traverse in some given time a completely equal to that which it would

1632:

for expressing very large numbers. While he is also known for his contributions to physics and several advanced mechanical devices, Archimedes himself placed far greater value on the products of his thought and general mathematical principles. He regarded as his greatest achievement his finding of

1673:

is one of the best known and preserved mathematical works from antiquity, and in it he derives many theorems concerning conic sections that would prove invaluable to later mathematicians and astronomers studying planetary motion, such as Isaac Newton. While neither Apollonius nor any other Greek

1142:

became the written language of Egyptian scholars. Archaeological evidence has suggested that the Ancient Egyptian counting system had origins in Sub-Saharan Africa. Also, fractal geometry designs which are widespread among Sub-Saharan African cultures are also found in Egyptian architecture and

4568:

The 20th century saw mathematics become a major profession. By the end of the century, thousands of new Ph.D.s in mathematics were being awarded every year, and jobs were available in both teaching and industry. An effort to catalogue the areas and applications of mathematics was undertaken in

3925:

During the Renaissance the desire of artists to represent the natural world realistically, together with the rediscovered philosophy of the Greeks, led artists to study mathematics. They were also the engineers and architects of that time, and so had need of mathematics in any case. The art of

2321:

Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten. Thus, the number 123 would be written using the symbol for "1",

8270:, "The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwārizmī's exposition that his readers must have had little difficulty in mastering the solutions." 1096: 30: 8113:, in the 1830s, it was heralded as the Indians' discovery of the calculus. This claim and Mādhava's achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the 10847:(John J. O'Connor and Edmund F. Robertson; University of St Andrews, Scotland). An award-winning website containing detailed biographies on many historical and contemporary mathematicians, as well as information on notable curves and various topics in the history of mathematics. 2897:. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, all of which evolved from the 1333:, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the 9030:

Howard Eves, An Introduction to the History of Mathematics, 6th edition, 1990, "In the nineteenth century, mathematics underwent a great forward surge ... . The new mathematics began to free itself from its ties to mechanics and astronomy, and a purer outlook evolved." p.

1154:

of about 2000–1800 BC. It is an instruction manual for students in arithmetic and geometry. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, including

1696:. The 3rd century BC is generally regarded as the "Golden Age" of Greek mathematics, with advances in pure mathematics henceforth in relative decline. Nevertheless, in the centuries that followed significant advances were made in applied mathematics, most notably 4588:. These problems, spanning many areas of mathematics, formed a central focus for much of 20th-century mathematics. Today, 10 have been solved, 7 are partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not. 3200:

was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable for determining the general formula for the sum of any integral powers. He performed an integration in order to find the volume of a

4138:

to stand for the ratio of a circle's circumference to its diameter. He made numerous contributions to the study of topology, graph theory, calculus, combinatorics, and complex analysis, as evidenced by the multitude of theorems and notations named for him.

3427:

Medieval European interest in mathematics was driven by concerns quite different from those of modern mathematicians. One driving element was the belief that mathematics provided the key to understanding the created order of nature, frequently justified by

8283:

i, pp. 263–77: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of

1674:

mathematicians made the leap to coordinate geometry, Apollonius' treatment of curves is in some ways similar to the modern treatment, and some of his work seems to anticipate the development of analytical geometry by Descartes some 1800 years later.

8257:, "Arabic became the language of scholarship in science and philosophy in the 9th century when the ‘translation movement’ saw concerted work on translations of Greek, Indian, Persian and Chinese, medical, philosophical and scientific texts", p. 811. 4076:, attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite. In some sense, this foreshadowed the development of 10906: 9021:, p. 379, "... the concepts of calculus... (are) so far reaching and have exercised such an impact on the modern world that it is perhaps correct to say that without some knowledge of them a person today can scarcely claim to be well educated." 3122:" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which al-Khwārizmī originally described as 8108:

One example I can give you relates to the Indian Mādhava's demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by

2286:

An analysis of early Chinese mathematics has demonstrated its unique development compared to other parts of the world, leading scholars to assume an entirely independent development. The oldest extant mathematical text from China is the

8690: 1077:. However, as with Egyptian mathematics, Babylonian mathematics shows no awareness of the difference between exact and approximate solutions, or the solvability of a problem, and most importantly, no explicit statement of the need for 3685:

independently provided graphical demonstrations of this relationship, asserting that the area under the line depicting the constant acceleration, represented the total distance traveled. In a later mathematical commentary on Euclid's

2425:, the full title of which appeared by AD 179, but existed in part under other titles beforehand. It consists of 246 word problems involving agriculture, business, employment of geometry to figure height spans and dimension ratios for 1417:. The former allowed the calculations of areas and volumes of curvilinear figures, while the latter enabled subsequent geometers to make significant advances in geometry. Though he made no specific technical mathematical discoveries, 2644:

Japanese mathematics of this period is inspired by Chinese mathematics and is oriented towards essentially geometric problems. On wooden tablets called sangaku, "geometric enigmas" are proposed and solved; That's where, for example,

1581:, in a manner not too dissimilar from modern calculus. He also showed one could use the method of exhaustion to calculate the value of π with as much precision as desired, and obtained the most accurate value of π then known, 3712:

were intertwined. While there is no direct relationship between algebra and accounting, the teaching of the subjects and the books published often intended for the children of merchants who were sent to reckoning schools (in

940:. The majority of Babylonian mathematical work comes from two widely separated periods: The first few hundred years of the second millennium BC (Old Babylonian period), and the last few centuries of the first millennium BC ( 1896:

in Alexandria had her stripped publicly and executed. Her death is sometimes taken as the end of the era of the Alexandrian Greek mathematics, although work did continue in Athens for another century with figures such as

9216: 1880:

is a major source of knowledge on Greek mathematics as most of it has survived. Pappus is considered the last major innovator in Greek mathematics, with subsequent work consisting mostly of commentaries on earlier work.

994:

from 3000 BC that was chiefly concerned with administrative/financial counting, such as grain allotments, workers, weights of silver, or even liquids, among other things. From around 2500 BC onward, the Sumerians wrote

830:

societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two.

4657:(also called the "enormous theorem"), whose proof between 1955 and 2004 required 500-odd journal articles by about 100 authors, and filling tens of thousands of pages. A group of French mathematicians, including 9258: 4947:. The speed and data processing abilities of computers also enabled the handling of mathematical problems that were too time-consuming to deal with by pencil and paper calculations, leading to areas such as 1271:

in 529 AD. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language. Greek mathematics of the period following

1665:, showing that one can obtain all three varieties of conic section by varying the angle of the plane that cuts a double-napped cone. He also coined the terminology in use today for conic sections, namely 2841:, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology. It is in the 2410:

other than officially sanctioned ones be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics before this date. After the

863:

been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10." The Ishango bone, according to scholar

8691:

https://www.scientificlib.com/en/Mathematics/Biographies/AdamRies.html#:~:text=Adam%20Ries%20is%20generally%20considered%20to%20be%20the,more%20structured%20Arabic%20numerals%20to%20a%20large%20extent

2567:. Korean and Japanese mathematics were heavily influenced by the algebraic works produced during China's Song dynasty, whereas Vietnamese mathematics was heavily indebted to popular works of China's 1398:(c. 390 - c. 340 BC), came. Plato also discussed the foundations of mathematics, clarified some of the definitions (e.g. that of a line as "breadthless length"), and reorganized the assumptions. The 2989:

at the time and, as a result, directly influenced later European developments in analysis and calculus. However, other scholars argue that the Kerala School did not formulate a systematic theory of

2518:

with coefficients of binomial expansions through the eighth power, though both appear in Chinese works as early as 1100. The Chinese also made use of the complex combinatorial diagram known as the

867:, may have influenced the later development of mathematics in Egypt as, like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2; this however, is disputed. 481:. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Contemporaneous with but independent of these traditions were the mathematics developed by the 8117:, in which Whish's article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series 5127:

As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: by the end of the century, there were hundreds of specialized areas in mathematics, and the

1933:. Nevertheless, Byzantine mathematics consisted mostly of commentaries, with little in the way of innovation, and the centers of mathematical innovation were to be found elsewhere by this time. 8670:

Nicole Oresme ... was the first to prove the divergence of the harmonic series (c. 1350). His results were lost for several centuries, and the result was proved again by Italian mathematician

3375:

during the 1st millennium AD developed a unique tradition of mathematics that, due to its geographic isolation, was entirely independent of existing European, Egyptian, and Asian mathematics.

2481:

to seven decimal places (between 3.1415926 and 3.1415927), which remained the most accurate value of π for almost the next 1000 years. He also established a method which would later be called

2928:, who lived in southern India, wrote extensively on all then known branches of mathematics. His work contains mathematical objects equivalent or approximately equivalent to infinitesimals, 1909:. Although Proclus and Simplicius were more philosophers than mathematicians, their commentaries on earlier works are valuable sources on Greek mathematics. The closure of the neo-Platonic 1496:

was known to all educated people in the West up through the middle of the 20th century and its contents are still taught in geometry classes today. In addition to the familiar theorems of

4935:. In the preceding centuries much mathematical focus was on calculus and continuous functions, but the rise of computing and communication networks led to an increasing importance of 3826:(Italian: "Details of Calculation and Recording"). It was written primarily for, and sold mainly to, merchants who used the book as a reference text, as a source of pleasure from the 2545:

carried mathematical ideas back and forth between the two cultures from the 16th to 18th centuries, though at this point far more mathematical ideas were entering China than leaving.

3565:

The 14th century saw the development of new mathematical concepts to investigate a wide range of problems. One important contribution was development of mathematics of local motion.

9573: 1329:. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the 13083: 3493: 3106: 3023: 4879:

to deal with larger and larger amounts of data to facilitate mass production and distribution and communication, and new areas of mathematics were developed to deal with this:

4673:", attempted to exposit all of known mathematics as a coherent rigorous whole. The resulting several dozen volumes has had a controversial influence on mathematical education. 1283:

Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of

2981:. It has been argued that certain ideas of calculus like infinite series and taylor series of some trigonometry functions, were transmitted to Europe in the 16th century via 12280: 12245: 4990:

At the same time, deep insights were made about the limitations to mathematics. In 1929 and 1930, it was proved the truth or falsity of all statements formulated about the

13498: 1047:

only used for intermediate positions. This zero sign does not appear in terminal positions, thus the Babylonians came close but did not develop a true place value system.

1711:–120 BC) is considered the founder of trigonometry for compiling the first known trigonometric table, and to him is also due the systematic use of the 360 degree circle. 5525:, Dover, p. 1: "In the case of mathematics, it is the Greek contribution which it is most essential to know, for it was the Greeks who first made mathematics a science." 1789:

Following a period of stagnation after Ptolemy, the period between 250 and 350 AD is sometimes referred to as the "Silver Age" of Greek mathematics. During this period,

2366:

described various aspects of many fields associated with physical science, and provided a small number of geometrical theorems as well. It also defined the concepts of

3558:

in 1202 (updated in 1254) introducing the technique to Europe and beginning a long period of popularizing it. The book also brought to Europe what is now known as the

3067:, since much like the status of Greek in the Hellenistic world, Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time. 897:

in their design. All of the above are disputed however, and the currently oldest undisputed mathematical documents are from Babylonian and dynastic Egyptian sources.

13072: 8309:

presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word

4490:, which enabled the rigorous treatment of the notion of infinity and has become the common language of nearly all mathematics. Cantor's set theory, and the rise of 850:

years old and consists of a series of marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either a

10922: 9042: 4136: 8030:

Almeida, D. F.; J. K. John and A. Zadorozhnyy (2001). "Keralese mathematics: its possible transmission to Europe and the consequential educational implications".

2893:. It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as 1214:, which were apparently intended as entertainment. One problem is considered to be of particular importance because it gives a method for finding the volume of a 6408: 3213:. He thus came close to finding a general formula for the integrals of polynomials, but he was not concerned with any polynomials higher than the fourth degree. 8588:

Singh, Parmanand (1985). "The So-called Fibonacci numbers in ancient and medieval India", Historia Mathematica, 12 (3): 229–44, doi:10.1016/0315-0860(85)90021-7

13118: 5172:

Most mathematical journals now have online versions as well as print versions, and many online-only journals are launched. There is an increasing drive toward

1488:

and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. Although most of the contents of the

5148: 3971:

was first exposed to and seriously interacted with the topic of planetary motion. Kepler's calculations were made simpler by the contemporaneous invention of

12487: 12432: 10669: 3017: 5402:

Friberg, J. (1981). "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations",

1762:–168), a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Ptolemy is also credited with 8865:"The First Explanation of Decimal Fractions and Measures (1585). Together with a History of the Decimal Idea and a Facsimile (No. XVII) of Stevin's Disme" 7533: 2224:), but its design seems to have been lost until experiments were made during the 15th century in Western Europe. Perhaps relying on similar gear-work and 13910: 3480:. His works were theoretical, rather than practical, and were the basis of mathematical study until the recovery of Greek and Arabic mathematical works. 1633:

the surface area and volume of a sphere, which he obtained by proving these are 2/3 the surface area and volume of a cylinder circumscribing the sphere.

3114:). He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots, and he was the first to teach algebra in an 1325:

and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to

11982: 9992: 8820: 4452:. Mathematicians had vainly attempted to solve all of these problems since the time of the ancient Greeks. On the other hand, the limitation of three 3842:

was also the first known book printed in Italy to contain algebra. Pacioli obtained many of his ideas from Piero Della Francesca whom he plagiarized.

10994: 10609: 9749: 1394:, became the mathematical center of the world in the 4th century BC, and it was from this school that the leading mathematicians of the day, such as 983:, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework. 826:. Modern studies of animal cognition have shown that these concepts are not unique to humans. Such concepts would have been part of everyday life in 5106:

of a mathematician. This describes the "collaborative distance" between a person and Erdős, as measured by joint authorship of mathematical papers.

5098:

published more papers than any other mathematician in history, working with hundreds of collaborators. Mathematicians have a game equivalent to the

2583:

for solving them, followed by numerical answers. Mathematics in Vietnam and Korea were mostly associated with the professional court bureaucracy of

2537:, European and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline from the 13th century onwards. 276:

and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the

13828: 10330: 8441: 8049: 2308:(although ancient Babylonians had ones with a base of 60), is dated around 305 BC and is perhaps the oldest surviving mathematical text of China. 12779: 12257: 14060: 13895: 13473: 11064: 3012: 2670: 9741: 2473:

accurate to 5 decimal places (i.e. 3.14159). Though more of a matter of computational stamina than theoretical insight, in the 5th century AD

1726:

for finding the area of a scalene triangle and with being the first to recognize the possibility of negative numbers possessing square roots.

12470: 9421: 5371:

The approximate values for π are 4 x (13/15) (3.0044...), 25/8 (3.125), 900/289 (3.11418685...), 1156/361 (3.202216...), and 339/108 (3.1389)

5336: 3967:

had gathered a large quantity of mathematical data describing the positions of the planets in the sky. By his position as Brahe's assistant,

247: 13349: 11678: 5885: 3071: 2148:, a discrepancy that was solved by adding an extra month into the calendar after the 23rd of February. This calendar was supplanted by the 2081:

of allotted lands and territories. Aside from managing trade and taxes, the Romans also regularly applied mathematics to solve problems in

1917:

in 529 AD is traditionally held as marking the end of the era of Greek mathematics, although the Greek tradition continued unbroken in the

478: 5744:

Abstraction & Representation: Essays on the Cultural Evolution of Thinking (Boston Studies in the Philosophy & History of Science)

13523: 13518: 13488: 13478: 13468: 12412: 12304: 4110:

problem to standardizing many modern mathematical terms and notations. For example, he named the square root of minus 1 with the symbol

13528: 13513: 13508: 13493: 12517: 12199: 10552:

Volkov, Alexei (2009), "Mathematics and Mathematics Education in Traditional Vietnam", in Robson, Eleanor; Stedall, Jacqueline (eds.),

4681: 3322: 2950: 2168:

every four years in a 365-day cycle. This calendar, which contained an error of 11 minutes and 14 seconds, was later corrected by the

14214: 14101: 13204: 12479: 12374: 4240: 2421: 2390: 2187: 465:

and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium AD in

4467:

Abel and Galois's investigations into the solutions of various polynomial equations laid the groundwork for further developments of

4042:", followed from the second half of the 20th century, and into the 21st. Leibniz has been called the "founder of computer science". 2692: 12427: 9413: 9384: 6094: 4577: 4212: 3028: 2419:(202 BC–220 AD) produced works of mathematics which presumably expanded on works that are now lost. The most important of these is 2412: 17: 3059:

in the 8th century made significant contributions towards mathematics. Although most Islamic texts on mathematics were written in

14127: 8472: 4193: 2727:

basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.

1073:, a remarkable achievement for the time. Tablets from the Old Babylonian period also contain the earliest known statement of the 1050:

Other topics covered by Babylonian mathematics include fractions, algebra, quadratic and cubic equations, and the calculation of

10124:"Journal of Humanistic Mathematics - an online-only, open access, peer reviewed journal | Current Journals | Claremont Colleges" 5203:

estimating (in 2018) that "employment of mathematical science occupations is projected to grow 27.9 percent from 2016 to 2026."

2232:, the odometer of Vitruvius featured chariot wheels measuring 4 feet (1.2 m) in diameter turning four-hundred times in one 1150:(sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BC but likely a copy of an older document from the 14005: 13125: 12437: 10957: 4654: 3484: 3422: 3153:, where he extends the methodology to incorporate integer powers and integer roots of unknown quantities. Something close to a 505: 13561: 10978: 9357: 4526: 4440:, a Frenchman, proved that there is no general algebraic method for solving polynomial equations of degree greater than four ( 4219: 1368:, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the 13738: 13503: 13427: 12957: 10794: 10772: 10632: 10561: 10542: 10473: 10455: 10430: 10412: 10351: 10315: 10297: 10279: 10256: 10237: 9975: 9679: 9367: 9199: 8976: 8927: 8663: 8336: 7683: 7516: 7361: 5861: 5688: 5434: 10853:(David E. Joyce; Clark University). Articles on various topics in the history of mathematics with an extensive bibliography. 8313:

is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation."

5716:

Thom, Alexander; Archie Thom (1988). "The metrology and geometry of Megalithic Man", pp. 132–51 in Ruggles, C. L. N. (ed.),

4346:, where uniqueness of parallels no longer holds. In this geometry the sum of angles in a triangle add up to less than 180°. 3729:

in Italy), where they learned the skills useful for trade and commerce. There is probably no need for algebra in performing

1766:

for deriving trigonometric quantities, and the most accurate value of π outside of China until the medieval period, 3.1416.

13821: 11427: 11003: 6768: 5740:"The Development of Arithmetical Thinking: On the Role of Calculating Aids in Ancient Egyptian & Babylonian Arithmetic" 3412: 1516:, including proofs that the square root of two is irrational and that there are infinitely many prime numbers. Euclid also 183: 13063: 10859:(David R. Wilkins; Trinity College, Dublin). Collections of material on the mathematics between the 17th and 19th century. 4444:). Other 19th-century mathematicians used this in their proofs that straight edge and compass alone are not sufficient to 1782: 14122: 13883: 13437: 13422: 13372: 11952: 10965: 6293: 3416: 1372:). The association of the Neopythagoreans with the Western invention of the multiplication table is evident in its later 1314:. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests. 4226: 14055: 14020: 13044: 13008: 12861: 11572: 11057: 11013: 10729: 5346: 5299: 5128: 5065: 979:, knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s. Written in 12983: 11036: 10919: 9639: 8122:

buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution.

6415: 6125: 5002:

found that this was not the case for the natural numbers plus both addition and multiplication; this system, known as

13387: 12512: 12463: 12422: 11932: 11644: 10750: 10706: 9675: 9018: 8606: 7903: 7836: 7707: 6775: 6559: 6365: 6344: 6223: 6151: 5725: 4259: 3764: 2932:

and the derivative of the sine function although he did not develop the notion of a derivative. In the 14th century,

1892:) as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the 240: 14163: 11025: 3562:(known to Indian mathematicians for hundreds of years before that) which Fibonacci used as an unremarkable example. 2240:

that turned a second gear responsible for dropping pebbles into a box, each pebble representing one mile traversed.

14151: 14032: 13985: 13342: 13003: 12926: 11671: 11108: 8328: 7508: 5284: 5229: 4208: 2933: 2498: 1893: 843: 269: 6076: 5112:

has been described by many as the most important woman in the history of mathematics. She studied the theories of

3403:

had to be inferred in the mathematics of many contemporary cultures, the Maya developed a standard symbol for it.

2506:(1249–1314), dealing with the solution of simultaneous higher order algebraic equations using a method similar to 14209: 14188: 14117: 13927: 13814: 13685: 13287: 12172: 11522: 10694: 8559: 7569: 5259: 5089: 4900: 4888: 3572:

by writing: V = log (F/R). Bradwardine's analysis is an example of transferring a mathematical technique used by

3091: 2890: 2255: 523:

in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an

462: 4146:, who did pioneering work in number theory, algebra, differential calculus, and the calculus of variations, and 3838:

for the first time in a printed book, symbols that became standard notation in Italian Renaissance mathematics.

13978: 13966: 13723: 13629: 13417: 12962: 12921: 12906: 12407: 12022: 11776: 11620: 10686: 9939: 7548: 6497: 6005: 5751: 4546: 4534: 4308: 4197: 2113:, created illusionist geometric patterns and rich, detailed scenes that required precise measurements for each 10198:"Big data adds up to opportunities in math careers : Beyond the Numbers: U.S. Bureau of Labor Statistics" 8635:

The Rise and Development of the Application of Mathematics in Fourteenth Century Philosophy and Theology", in

8213: 6175:

Bernal, Martin (2000). "Animadversions on the Origins of Western Science", pp. 72–83 in Michael H. Shank, ed.

4354:; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed 4107: 4088: 14132: 13961: 13900: 13097: 11816: 11695: 11050: 10738: 9667: 4538: 4530: 4335: 4045:

Science and mathematics had become an international endeavor, which would soon spread over the entire world.

3815: 3610: 3267: 3006: 8992: 8817: 8575:

Beaujouan, Guy. "The Transformation of the Quadrivium", pp. 463–87 in Robert L. Benson and Giles Constable,

3628:

is known as the "father of modern calculating" because of his decisive contribution to the recognition that

2326:

allowed the representation of numbers as large as desired and allowed calculations to be carried out on the

1035:, and its power allowed it to achieve remarkable computational accuracy; for example, the Babylonian tablet 14081: 13695: 13657: 13412: 12784: 12774: 12718: 12456: 12397: 11632: 10172: 8805:

L'opera "De corporibus regularibus" di Pietro Franceschi detto della Francesca usurpata da Fra Luca Pacioli

5050: 3863: 2261: 1865: 1386:(428/427 BC – 348/347 BC) is important in the history of mathematics for inspiring and guiding others. His 1287:, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used 233: 13397: 12502: 10874: 3850: 2958: 2664: 2132:

also necessitated basic mathematics. The first calendar allegedly dates back to 8th century BC during the

379:

seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.

13794: 13690: 13647: 13335: 13219: 12417: 12402: 11664: 11547: 11103: 8530: 4522: 1861: 1829:(that of dividing a square into two squares). Diophantus also made significant advances in notation, the 1669:("place beside" or "comparison"), "ellipse" ("deficiency"), and "hyperbola" ("a throw beyond"). His work 1100: 367: 76: 3945: 2470: 13538: 13189: 13168: 12916: 12886: 12663: 12577: 11912: 11118: 5326: 5200: 5154: 4791: 4623: 4515: 4475:. In the 20th century physicists and other scientists have seen group theory as the ideal way to study 4445: 3667:... it were moved uniformly at the same degree of speed with which it is moved in that given instant". 2564: 2523: 2098: 1802: 1414: 357: 12542: 10877:(John Aldrich, University of Southampton) Discusses the origins of the modern mathematical word stock. 7971:"Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhāṣā" 5577: 3926:

painting in perspective, and the developments in geometry that were involved, were studied intensely.

2492:

The high-water mark of Chinese mathematics occurred in the 13th century during the latter half of the

13993: 13782: 13377: 12871: 12623: 11922: 11532: 11504: 11141: 8467: 5279: 5158: 4928: 4908: 4312: 4307:, leaving aside his many contributions to science. He also gave the first satisfactory proofs of the 4011: 3949: 3899:('the art of tenths'), first published in Dutch in 1585, contained the first systematic treatment of 3525: 3075: 2868: 2757: 2720: 2496:(960–1279), with the development of Chinese algebra. The most important text from that period is the 1306:(c. 582–c. 507 BC). Although the extent of the influence is disputed, they were probably inspired by 532: 198: 188: 178: 8968: 8962: 7635: 5464: 4358:, which unifies and vastly generalizes the three types of geometry, and he defined the concept of a 4233: 2901:. Each of the roughly dozen major scripts of India has its own numeral glyphs. In the 10th century, 2236:(roughly 4590 ft/1400 m). With each revolution, a pin-and-axle device engaged a 400-tooth 13922: 13594: 13382: 12942: 12901: 12769: 12653: 12212: 12078: 11927: 11577: 8477: 5311: 5254: 5173: 5073: 4747: 4619: 4441: 4035: 3955:

The 17th century saw an unprecedented increase of mathematical and scientific ideas across Europe.

3777: 2872: 2482: 2008:(106–43 BC), an influential Roman statesman who studied mathematics in Greece, believed that Roman 1822: 823: 409:) and expanded the subject matter of mathematics. Although they made virtually no contributions to 12628: 10024: 8655:

The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

5912:"The Antecedents of Old Babylonian Place Notation and the Early History of Babylonian Mathematics" 3552:

of Hindu–Arabic numerals was much more efficient and greatly facilitated commerce. Leonardo wrote

2183:), virtually the same solar calendar used in modern times as the international standard calendar. 13956: 13944: 13915: 13841: 13733: 13637: 13619: 13452: 13447: 13311: 13306: 13296: 12603: 12598: 12338: 12220: 11811: 11462: 11452: 11422: 11356: 11091: 9612: 8305:

mean, but the usual interpretation is similar to that implied in the translation above. The word

7859:

was translated into Arabic, and it was not long afterwards (ca. 780) that Ptolemy's astrological

5897: 5351: 5341: 5321: 5269: 5061: 4984: 4726:

etc. As mathematicians do, the concept of an abstract structure was itself abstracted and led to

4570: 4186: 4023: 3753: 3748: 3119: 2946: 2161: 2021: 1337:, though the statement of the theorem has a long history, and with the proof of the existence of 1203: 1151: 819: 516:, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in 410: 10360:

Joyce, Hetty (July 1979), "Form, Function and Technique in the Pavements of Delos and Pompeii",

7895: 7887: 5882: 2738:, which imply several different approximations of the value of π. In addition, they compute the 2293:(周髀算經), variously dated to between 1200 BC and 100 BC, though a date of about 300 BC during the 1951: 14076: 14010: 13871: 13700: 13642: 13609: 13442: 13235: 12911: 12896: 12830: 12759: 12359: 12286: 11560: 11457: 11437: 11432: 11361: 9449: 8767: 7926:, ed. I. Grattan. Guinness, Johns Hopkins University Press, Baltimore and London, 1994, p. 126. 7630: 7500: 5680: 5674: 5289: 5027: 5019: 5007: 4964: 4715: 4643: 4410: 4394: 4390: 4327: 4292: 4014:, developed calculus and much of the calculus notation still in use today. He also refined the 3915: 3598: 3360: 3286: 3262:

computed the value of π to the 16th decimal place. Kashi also had an algorithm for calculating

3251: 3158: 2997:, and that there is not any direct evidence of their results being transmitted outside Kerala. 2954: 2337: 1810: 1794: 1738: 1727: 1678: 1342: 1311: 1055: 1000: 906: 430: 426: 346: 193: 168: 14158: 12099: 9189: 8653: 7936: 7922:, Penguin Books, London, 1991 pp. 298–300; Takao Hayashi, "Indian Mathematics", pp. 118–30 in 7828: 5739: 5635: 5162: 4758:

was developed in the late 19th and early 20th centuries. Applications of measures include the

3454:

provided a place for mathematics in the curriculum in the 6th century when he coined the term

2961:, whose first 21 terms he used to compute the value of π as 3.14159265359. Madhava also found 382:

The study of mathematics as a "demonstrative discipline" began in the 6th century BC with the

14170: 14025: 14000: 13932: 13878: 13771: 13677: 13662: 13614: 13432: 13049: 12876: 12840: 12216: 12208: 11710: 11587: 11517: 11394: 11318: 11257: 11242: 11237: 11214: 11096: 10743:

The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth

10620: 10443: 10197: 8043: 7368: 5316: 5244: 5189: 5023: 4968: 4837: 4687: 4585: 4418: 4143: 4039: 4019: 3992: 3935: 3782: 3740: 3652: 3318: 3271: 3126:. His algebra was also no longer concerned "with a series of problems to be resolved, but an 2877: 2773: 2571:(1368–1644). For instance, although Vietnamese mathematical treatises were written in either 2315: 2298: 2294: 2271: 2229: 2037: 1997: 1902: 1798: 1689: 1625: 1399: 1176: 873:

of the 5th millennium BC pictorially represented geometric designs. It has been claimed that

203: 117: 12448: 10892: 10865:(Jeff Miller). Contains information on the earliest known uses of terms used in mathematics. 10448:

Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth

5195:

is a corresponding growth in the demand for mathematics to help process and understand this

4714:

changed the kinds of questions that could be answered by mathematical methods. All kinds of

2625:(1603-1887) is independent of Western mathematics; To this period belongs the mathematician 2579:

script, all of them followed the Chinese format of presenting a collection of problems with

401:

greatly refined the methods (especially through the introduction of deductive reasoning and

14050: 13949: 13748: 13743: 13667: 13556: 13546: 13214: 13163: 13039: 13018: 12891: 12799: 12298: 12009: 11977: 11567: 11447: 11442: 11366: 11267: 10948: 10491: 9814: 9530: 9314: 9164: 8827:(Accounting, Business & Financial History Conference, Cardiff, September 2007) pp. 1–2. 8649: 8075: 6501: 5488: 5331: 5304: 5132: 5121: 4995: 4952: 4936: 4892: 4884: 4635: 4631: 4304: 4288: 4281: 4147: 3910:

Driven by the demands of navigation and the growing need for accurate maps of large areas,

3827: 3798: 3786: 3277:

Other achievements of Muslim mathematicians during this period include the addition of the

3225: 3166: 3131:

solving a problem, but is specifically called on to define an infinite class of problems."

2918: 2914: 2680: 2584: 2548: 2515: 2442: 2305: 2144:

of the Republican era contained 355 days, roughly ten-and-one-fourth days shorter than the

1922: 1869: 1857: 1845: 1763: 1742: 1701: 1578: 1566: 1540: 1472: 1428:) contributed significantly to the development of mathematics by laying the foundations of 1406: 1365: 1307: 1090: 996: 976: 963: 362: 163: 122: 91: 39: 10466:

Science and Civilization in China: Physics and Physical Technology: Mechanical Engineering

5705:

The Roots of Civilization: the Cognitive Beginning of Man's First Art, Symbol and Notation

4653:

Mathematical collaborations of unprecedented size and scope took place. An example is the

4121: 3737:, a basic knowledge of arithmetic was mandatory and knowledge of algebra was very useful. 8: 14091: 13939: 13890: 13861: 13753: 13718: 13710: 13599: 13589: 13184: 13111: 12633: 12537: 12364: 12333: 12141: 12127: 12064: 11957: 11902: 11897: 11851: 11801: 11582: 11492: 11414: 11313: 11247: 11204: 11194: 11174: 10896: 10681: 10265: 10147: 8463: 8362:

Encyclopaedia of the history of science, technology, and medicine in non-western cultures

7816: 7583: 6358:

History of Mathematics, Volume I: General Survey of the History of Elementary Mathematics

6337:

History of Mathematics, Volume I: General Survey of the History of Elementary Mathematics

5264: 5249: 5117: 5034:'s dream of making all of mathematics complete and consistent needed to be reformulated. 4932: 4849: 4795: 4783: 4743: 4461: 4449: 4355: 4343: 4155: 4049: 3699: 3678: 3656: 3577: 3549: 3510: 2962: 2864: 2846: 2824: 2743: 2735: 2556: 2438: 2249: 2056: 2017: 1889: 1809:, a collection of 150 algebraic problems dealing with exact solutions to determinate and 1712: 1651: 1640: 1451:

In the 3rd century BC, the premier center of mathematical education and research was the

1350: 1334: 1303: 1288: 1284: 1273: 1248: 1222: 1135: 1074: 990:, who built the earliest civilization in Mesopotamia. They developed a complex system of 957: 474: 450: 418: 376: 12572: 10495: 10095: 9818: 9534: 9318: 8079: 6236:

Kurt Von Fritz (1945). "The Discovery of Incommensurability by Hippasus of Metapontum".

5492: 5169:(who declined to accept an award, as he was critical of the mathematics establishment). 1504:

was meant as an introductory textbook to all mathematical subjects of the time, such as

1492:

were already known, Euclid arranged them into a single, coherent logical framework. The

1402:

is ascribed to Plato, while a formula for obtaining Pythagorean triples bears his name.

1003:

problems. The earliest traces of the Babylonian numerals also date back to this period.

14096: 13856: 13728: 13584: 13566: 13551: 13358: 13316: 13271: 13245: 13194: 12835: 12713: 12648: 11866: 11687: 11608: 11527: 11467: 11399: 11389: 11328: 11303: 11179: 11136: 11131: 10820: 10599: 10511:

Straffin, Philip D. (1998), "Liu Hui and the First Golden Age of Chinese Mathematics",

10503: 10385: 10377: 10340: 9921: 9860: 9804: 9714: 9498: 9338: 9095: 8900: 8892: 8422: 8236: 8154: 8099: 8091: 7993: 7743: 7656: 7603: 6311: 6268: 5504: 5452: 5426: 5416: 5294: 5239: 5220: 5113: 4948: 4916: 4865: 4861: 4856:

which include infinitesimal and infinite quantities. An even larger number system, the

4807: 4799: 4767: 4739: 4699: 4695: 4611: 4596: 4542: 4491: 4406: 4371: 4367: 4331: 4061: 3904: 3846: 3682: 3648: 3644: 3568: 3559: 3434: 3310: 3298: 3255: 3232: 3210: 3154: 3139: 3127: 3115: 3087: 2929: 2910: 2658: 2572: 2507: 2385: 2169: 2086: 2024:

and geometry that were prized by the Greeks. It is unclear if the Romans first derived

1926: 1849: 1723: 1529: 1497: 1481: 1346: 1338: 1326: 1292: 1277: 1226: 1115: 1078: 1066: 933: 894: 864: 815: 524: 466: 454: 406: 402: 372: 223: 127: 9762: 9490: 8562:, "Translations and Translators", pp. 421–62 in Robert L. Benson and Giles Constable, 6389: 6387: 6052: 4521:

The 19th century saw the founding of a number of national mathematical societies: the

4437: 3671:

traverse if it were moving continuously through the same time with the mean degree ".

3177:

of mathematics, F. Woepcke, praised Al-Karaji for being "the first who introduced the

2742:

of 2 to several decimal places, list Pythagorean triples, and give a statement of the

527:

that continues through the present day. This includes the groundbreaking work of both

14086: 13778: 13483: 13261: 13240: 12678: 12567: 12369: 12251: 12071: 11846: 11841: 11715: 11603: 11323: 11308: 11252: 11199: 10790: 10768: 10746: 10725: 10702: 10628: 10557: 10538: 10469: 10451: 10426: 10408: 10398: 10389: 10347: 10324: 10311: 10293: 10275: 10269: 10252: 10233: 10225: 10077: 10069: 10000: 9971: 9913: 9852: 9671: 9593: 9554: 9546: 9471: 9363: 9330: 9280: 9239: 9195: 9099: 9087: 9014: 8972: 8923: 8904: 8884: 8659: 8602: 8599:

Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages

8342: 8332: 7997: 7899: 7832: 7821: 7703: 7679: 7648: 7607: 7512: 7449: 7357: 6894: 6771: 6555: 6361: 6340: 6315: 6219: 6147: 6001: 5857: 5747: 5721: 5684: 5440: 5430: 5214: 4960: 4920: 4815: 4779: 4759: 4735: 4723: 4647: 4433: 4382: 4347: 4073: 3984: 3734: 3514: 3498: 3488: 3364: 3302: 3247: 3052: 2849: 2646: 2638: 2634: 2450: 2173: 2122: 2082: 2033: 2013: 1617: 1395: 1299: 1264: 1238: 1188: 1111: 870: 847: 513: 482: 398: 219: 13806: 10880: 9518: 9466: 9434: 9275: 8103: 7660: 7495:

Puttaswamy, T.K. (2000). "The Accomplishments of Ancient Indian Mathematicians". In

6251:

Choike, James R. (1980). "The Pentagram and the Discovery of an Irrational Number".

5026:

and geometry), truth necessarily outruns proof, i.e. there are true statements that

5022:

is that in any mathematical system that includes Peano arithmetic (including all of

4875:, at first mechanical analog machines and then digital electronic machines, allowed 4751: 4680:

Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star, with

4658: 4322:

Behavior of lines with a common perpendicular in each of the three types of geometry

3988: 2198:

traveled, the Roman model first described by the Roman civil engineer and architect

1291:. The Greeks used logic to derive conclusions from definitions and axioms, and used 1103:. The problem includes a diagram indicating the dimensions of the truncated pyramid. 13973: 13604: 13139: 13013: 12988: 12693: 12673: 12582: 12562: 12547: 12085: 11967: 11937: 11907: 11537: 11512: 11384: 11232: 11169: 10975: 10954: 10594: 10524: 10520: 10499: 10369: 10061: 9963: 9905: 9844: 9758: 9733: 9585: 9538: 9461: 9430: 9342: 9322: 9270: 9231: 9122: 9079: 8876: 8847: 8763: 8675: 8414: 8228: 8188: 8146: 8083: 7985: 7747: 7739: 7735: 7640: 7595: 6384: 6301: 6260: 5849: 5588: 5508: 5496: 5274: 5234: 5166: 5099: 5085: 5003: 4904: 4876: 4853: 4841: 4787: 4707: 4670: 4507: 4472: 4426: 4422: 4414: 4405:, in which the only numbers were 0 and 1. Boolean algebra is the starting point of 4378: 4351: 4296: 4053: 4003: 3900: 3884: 3872: 3868: 3858: 3606: 3602: 3259: 3162: 3056: 2789: 2785: 2769: 2753: 2559:

are traditionally viewed as stemming from Chinese mathematics and belonging to the

2225: 2118: 2110: 1918: 1910: 1818: 1752: 1485: 1387: 1268: 1192: 1156: 980: 458: 12050: 11821: 8449:

Indian Institute of Social Reform & Research International Journal of Research

7843:

By 766 we learn that an astronomical-mathematical work, known to the Arabs as the

6064: 5030:

within the system. Hence mathematics cannot be reduced to mathematical logic, and

3959:

observed the moons of Jupiter in orbit about that planet, using a telescope based

1476:, widely considered the most successful and influential textbook of all time. The 13300: 13292: 13199: 12952: 12815: 12734: 12618: 12292: 12239: 12167: 12113: 11962: 11831: 11477: 11404: 11333: 11126: 11007: 10982: 10961: 10893:

Notes for MAA minicourse: teaching a course in the history of mathematics. (2009)

10782: 10651: 10625:

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

10532: 9966:(1981), "In Memory of Emmy Noether", in Brewer, James W; Smith, Martha K (eds.), 9706: 9617: 8824: 7351: 5889: 5420: 4848:

approach to calculus, which had fallen into disrepute in favour of the theory of

4727: 4691: 4457: 4402: 3968: 3876: 3633: 3506: 3372: 3282: 3240: 3060: 2894: 2552: 2289: 2149: 2064: 2051:

Using calculation, Romans were adept at both instigating and detecting financial

1562: 1184: 1164: 1062: 827: 490: 145: 11871: 11791: 11000: 9114: 7720: 5841: 5103: 4339: 3266:

th roots, which was a special case of the methods given many centuries later by

3161:

appears in a book written by Al-Karaji around 1000 AD, who used it to prove the

2845:

that the decimal place-value system first appears. Several centuries later, the

2756:. His notation was similar to modern mathematical notation, and used metarules, 13132: 13104: 12845: 12744: 12739: 12688: 12557: 12527: 12263: 12183: 12120: 12043: 12029: 11947: 11942: 11876: 11720: 11555: 11482: 11189: 10988: 10900: 10830:, BBC Radio 4 discussion with Robert Kaplan, Jim Bennett & Jackie Stedall ( 10760: 10439: 10404: 9299: 9140: 9126: 8671: 8389:

Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi

8134: 7847:, was brought to Baghdad from India. It is generally thought that this was the 5911: 5853: 5136: 5077: 5042: 4991: 4976: 4912: 4857: 4771: 4755: 4603: 4511: 4499: 4111: 4099: 4092: 4077: 3960: 3854: 3835: 3744: 3629: 3537: 3440: 3396: 3336:

from the 15th century, the development of Islamic mathematics became stagnant.

3333: 3329: 3306: 3236: 3197: 3170: 2938: 2898: 2588: 2434: 2426: 2279: 2153: 2141: 2129: 2029: 2025: 1989: 1946: 1662: 1644: 1629: 1521: 1513: 1369: 1354: 1260: 1199: 1180: 1168: 1119: 1070: 1051: 1023: 508:

from the 12th century onward, leading to further development of mathematics in

442: 438: 414: 387: 285: 173: 11771: 9777: 9589: 9542: 9235: 7644: 7599: 6306: 3580:

to quantify the nature of compound medicines to a different physical problem.

3460:

to describe the study of arithmetic, geometry, astronomy, and music. He wrote

2925: 2576: 14203: 12947: 12866: 12507: 12343: 12275: 12204: 12106: 11343: 11275: 11227: 11019: 10871:(Jeff Miller). Contains information on the history of mathematical notations. 10850: 10534:

Delos, Carthage, Ampurias: the Housing of Three Mediterranean Trading Centres

10073: 10004: 9917: 9856: 9597: 9550: 9475: 9334: 9284: 9243: 9091: 8888: 8836: 8760:

On the curious historical coincidence of algebra and double-entry bookkeeping

8063: 8029: 7652: 7496: 6533: 6531: 5031: 5011: 4980: 4972: 4940: 4924: 4845: 4607: 4581: 4557: 4503: 4065: 4057: 4048:

In addition to the application of mathematics to the studies of the heavens,

4015: 3983:. Kepler succeeded in formulating mathematical laws of planetary motion. The 3722: 3674: 3594: 3392: 3391:

system used by most modern cultures. The Maya used mathematics to create the

3376: 3349: 3294: 3278: 2970: 2886: 2781: 2777: 2637:), are almost simultaneous with contemporary European mathematicians such as 2626: 2604: 2403: 2367: 2323: 2157: 2133: 2045: 1693: 1505: 1172: 1147: 498: 470: 336: 293: 98: 12820: 11766: 11730: 10827: 10423:

The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook

9737: 8346: 8254: 7924:

Companion History of the History and Philosophy of the Mathematical Sciences

5385: 5383: 5095: 4999: 4662: 4627: 3980: 3632:

are unpractical and to their replacement by the considerably more practical

2749: 2633:(traditional Japanese mathematics), and whose discoveries (in areas such as 12978: 12794: 12552: 12310: 12148: 12092: 12036: 11856: 11836: 11761: 11285: 11280: 11184: 10844: 10641: 10081: 10049: 9558: 9043:"Bernhard Riemann Laid the Foundations for Einstein's Theory of Relativity" 8943: 8193: 8176: 7450:

Development Of Modern Numerals And Numeral Systems: The Hindu-Arabic system

5444: 5109: 5081: 5015: 4944: 4811: 4731: 4719: 4615: 4483: 4468: 4398: 4386: 4103: 3999: 3922:

in 1595. Regiomontanus's table of sines and cosines was published in 1533.

3911: 3890: 3793: 3314: 3217: 3048: 3044: 2966: 2819: 2808: 2731: 2568: 2542: 2519: 2493: 2106: 2090: 2078: 2001: 1993: 1956: 1942: 1930: 1873: 1841: 1745:. The most complete and influential trigonometric work of antiquity is the 1697: 1517: 1330: 1252: 1160: 1011: 937: 912: 859: 835: 528: 383: 341: 277: 11042: 10862: 9382: 8851: 7989: 6528: 5199:. Math science careers are also expected to continue to grow, with the US 5149:

List of unsolved problems in mathematics § Problems solved since 1995

4803: 4676: 4591: 3476:, also derived from Greek sources; and a series of excerpts from Euclid's 3344: 2977:

consolidated many of the Kerala School's developments and theorems in the

1447:

and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.

13090: 13034: 12789: 12754: 12683: 12316: 12269: 12057: 12003: 11786: 11740: 11487: 11151: 11074: 11030: 10868: 10582: 10468:, vol. 4 (reprint ed.), Cambridge: Cambridge University Press, 10123: 8172: 8110: 7861: 7621:

Kadvany, John (2008-02-08). "Positional Value and Linguistic Recursion".

7477: 7475: 7473: 7471: 7380: 7378: 7376: 7306: 7304: 7302: 7172: 7170: 7168: 5380: 5069: 4880: 4831: 4775: 4711: 4553: 3976: 3964: 3730: 3705: 3554: 3529: 3353: 3040: 2974: 2860: 2837: 2739: 2724: 2534: 2474: 2458: 2416: 2347:

The oldest extant work on geometry in China comes from the philosophical

2266: 2094: 1836: 1444: 1373: 1362: 1061:. The tablets also include multiplication tables and methods for solving 1032: 1019: 921: 885:, dating from the 3rd millennium BC, incorporate geometric ideas such as 517: 509: 434: 332: 265: 136: 62: 10856: 10230:

A Biographical Dictionary of Later Han to the Three Kingdoms (23–220 AD)

9801:

Ramanujan's formula for the logarithmic derivative of the gamma function

8016:

Divakaran, P. P. (2007). "The first textbook of calculus: Yukti-bhāṣā",

4456:

in geometry was surpassed in the 19th century through considerations of

2706: 12998: 12825: 12698: 12668: 12643: 12638: 12015: 11972: 11826: 11806: 11781: 11472: 11351: 11146: 9925: 9893: 9864: 9832: 9083: 8426: 8297:, "The Arabic Hegemony" p. 229) "It is not certain just what the terms 8240: 8158: 6272: 6126:"Egyptian Mathematical Papyri – Mathematicians of the African Diaspora" 5054: 4823: 4763: 4487: 4277: 4200: in this section. Unsourced material may be challenged and removed. 4159: 4027: 3895: 3803: 3733:

operations, but for complex bartering operations or the calculation of

3709: 3605:

in the foreground, was the first to offer a mathematical proof for the

3541: 3465: 3456: 3206: 3202: 3193: 2990: 2882: 2675: 2622: 2503: 2454: 2407: 2336:

is not certain, but the earliest written mention dates from AD 190, in

2233: 2145: 1790: 1551: 1456: 1358: 1183:(namely, that of the number 6). It also shows how to solve first order 986:

The earliest evidence of written mathematics dates back to the ancient

944:

period). It is named Babylonian mathematics due to the central role of

301: 273: 141: 131: 10920:

A Bibliography of Collected Works and Correspondence of Mathematicians

10381: 8896: 8864: 8095: 7970: 7468: 7373: 7299: 7165: 5135:

were published and, by the end of the century, the development of the

4287:

Throughout the 19th century mathematics became increasingly abstract.

3100:

is derived from the Latinization of his name, Algoritmi, and the word

1565:, widely considered the greatest mathematician of antiquity, used the 13327: 12993: 12881: 12749: 12708: 12658: 12613: 12608: 12532: 12134: 11796: 11756: 11656: 10787:

The History of Statistics: The Measurement of Uncertainty before 1900

10065: 9809: 9326: 9067: 8844: 8177:"The 'Error' in the Indian "Taylor Series Approximation" to the Sine" 6563: 5500: 4956: 4827: 4666: 4453: 4142:

Other important European mathematicians of the 18th century included

3972: 3625: 3521: 3384: 3189: 3174: 3146: 3135: 3096: 3036: 2902: 2832: 2761: 2609: 2580: 2560: 2430: 2199: 2137: 2102: 2069: 1965: 1914: 1805:

is a significant area of research to this day. His main work was the

1418: 1225:(c. 1800 BC) shows that ancient Egyptians could solve a second-order 1131: 1123: 991: 967:

Geometry problem on a clay tablet belonging to a school for scribes;

949: 917: 446: 422: 325: 321: 9909: 9848: 8418: 8232: 8150: 6360:, New York: Dover Publications (a reprint of the 1951 publication), 6339:, New York: Dover Publications (a reprint of the 1951 publication), 6264: 5037: 4448:, to construct the side of a cube twice the volume of a given cube, 4350:

was developed later in the 19th century by the German mathematician

4175: 4098:

The most influential mathematician of the 18th century was arguably

3887:

that could appear in Cardano's formula for solving cubic equations.

3483:

In the 12th century, European scholars traveled to Spain and Sicily

2985:

missionaries and traders who were active around the ancient port of

12764: 12703: 12522: 11917: 11881: 11861: 11376: 11295: 11222: 10886: 10373: 10247:

Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (2004),

10100: 8880: 8087: 7505:

Mathematics Across Cultures: The History of Non-western Mathematics

6289: 6021:

Eglash, R. (1995). "Fractal Geometry in African Material Culture".

6000:. New Brunswick, N.J.: Rutgers University Press. pp. 89, 141. 5822: 5820: 5806: 5804: 5802: 5788: 5786: 5784: 5782: 5578:

http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html

5196: 4872: 4819: 4703: 4476: 4432:

Also, for the first time, the limits of mathematics were explored.

4359: 4300: 4151: 4069: 4031: 4007: 3807: 3714: 3573: 3545: 3451: 3290: 3185: 3118:

and for its own sake. He also discussed the fundamental method of "

3083: 2994: 2527: 2457:(78–139) approximated pi as 3.1724, as well as 3.162 by taking the 2371: 2237: 2214: 2195: 2191: 2165: 2121:

pieces on average measuring eight millimeters square and the finer

2060: 2009: 1974: 1970: 1960: 1906: 1769: 1747: 1666: 1636: 1574: 1410: 1322: 1318: 1036: 941: 882: 874: 855: 536: 317: 313: 309: 113: 103: 10909:. Pictorial (moving) re-construction of Vitusius' Roman ododmeter. 9191:

The Rainbow of Mathematics: A History of the Mathematical Sciences

8920:

The Rainbow of Mathematics: A History of the Mathematical Sciences

6765:

Complex numbers: lattice simulation and zeta function applications

3235:. He was also the first to find the general geometric solution to 2449:, which Chinese mathematicians originally approximated as 3 until 1206:

period, dated to c. 1890 BC. It consists of what are today called

13652: 13209: 11735: 11161: 9878: 9640:"An enormous theorem: the classification of finite simple groups" 5049:

One of the more colorful figures in 20th-century mathematics was

4334:

of Euclidean geometry no longer holds. The Russian mathematician

4060:. Pascal and Fermat set the groundwork for the investigations of 3956: 3718: 3533: 3388: 3182: 2986: 2906: 2799:

The next significant mathematical documents from India after the

2765: 2600: 2462: 2328: 2302: 2275: 2114: 2041: 1978: 1898: 1885: 1833:

being the first instance of algebraic symbolism and syncopation.

1628:(paraboloid, ellipsoid, hyperboloid), and an ingenious method of 1509: 1452: 1215: 1095: 1027: 953: 945: 890: 878: 305: 289: 108: 11983:

Shanti Swarup Bhatnagar Prize recipients in Mathematical Science

9187: 8747:

Nicole Oresme and the Medieval Geometry of Qualities and Motions

8405:

Katz, Victor J. (1995). "Ideas of Calculus in Islam and India".

8279:

Gandz and Saloman (1936). "The sources of Khwarizmi's algebra",

8066:(December 1992). "Hellenophilia versus the History of Science". 5932: 5817: 5799: 5779: 4614:, controversial at the time for the use of a computer to do so. 4541:

in 1888. The first international, special-interest society, the

4291:(1777–1855) epitomizes this trend. He did revolutionary work on 4102:(1707–1783). His contributions range from founding the study of 3517:. These and other new sources sparked a renewal of mathematics. 2478: 1535: 371:(Egyptian c. 1890 BC). All of these texts mention the so-called 13084:

The Compendious Book on Calculation by Completion and Balancing

11725: 8706:. Madison: University of Wisconsin Press, pp. 210, 214–15, 236. 3929: 3819: 3799:

Summa de Arithmetica, Geometria, Proportioni et Proportionalità

3494:

The Compendious Book on Calculation by Completion and Balancing

3368: 3178: 3112:

The Compendious Book on Calculation by Completion and Balancing

3024:

The Compendious Book on Calculation by Completion and Balancing

2982: 2538: 2486: 2379: 2375: 2348: 2311: 2005: 1985: 1621: 1525: 1460: 1435: 1391: 1139: 1006: 886: 811: 486: 50:), widely considered the most influential textbook of all time. 34: 29: 10765:

Number Words and Number Symbols: A Cultural History of Numbers

5998:

African fractals : modern computing and indigenous design

5616: 5614: 3991:(1596–1650) allowed those orbits to be plotted on a graph, in 2723:(mature second phase: 2600 to 1900 BC) that flourished in the 1797:, which is also known as "Diophantine analysis". The study of 1243: 12478: 10935: 8993:"2021: 375th birthday of Leibniz, father of computer science" 8732:. Madison: University of Wisconsin Press, pp. 332–45, 382–91. 8392: 7586:(2001). "Panini and Euclid: Reflections on Indian Geometry". 5952: 5177: 4896: 4602:

Notable historical conjectures were finally proven. In 1976,

4495: 4401:

devised an algebra that soon evolved into what is now called

4363: 3811: 3429: 3395:

as well as to predict astronomical phenomena in their native

3387:

system, instead of a base of ten that forms the basis of the

3380: 3205:, and was able to generalize his result for the integrals of 2814: 2630: 2618: 2533:

Even after European mathematics began to flourish during the

2395: 2125:

pieces having an average surface of four millimeters square.

2052: 1817:

had a significant influence on later mathematicians, such as

1778: 1429: 1383: 1127: 1107: 1058: 987: 929: 520: 281: 9383:

Lori Thurgood; Mary J. Golladay; Susan T. Hill (June 2006).

7356:(3 ed.). Jones & Bartlett Learning. p. xxvii. 6409:"One, Two, Three… A Discussion on the Generation of Numbers" 4318: 3659:, proposed to measure instantaneous speed "by the path that 2807:, astronomical treatises from the 4th and 5th centuries AD ( 2719:

The earliest civilization on the Indian subcontinent is the

9782:

The Legacy of Srinivasa Ramanujan, RMS-Lecture Notes Series

7920:

The Crest of the Peacock: Non-European Roots of Mathematics

6095:"Egyptian Algebra – Mathematicians of the African Diaspora" 5611: 5539:

The Crest of the Peacock: Non-European Roots of Mathematics

4994:

plus either addition or multiplication (but not both), was

4052:

began to expand into new areas, with the correspondence of

3400: 3064: 2359: 2213:). The device was used at least until the reign of emperor 1570: 1259:

Greek mathematics refers to the mathematics written in the

1255:

are generally credited with the first proof of the theorem.

968: 925: 839: 810:

The origins of mathematical thought lie in the concepts of

494: 297: 12184:

Infinite series expansions for the trigonometric functions

10537:, Rome: L'Erma di Bretschneider (Accademia di Danimarca), 7350:

Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009).

6177:

The Scientific Enterprise in Antiquity and the Middle Ages

6105: 6033: 3772: 2730:

The oldest extant mathematical records from India are the

2683:, dated between the 2nd century BC and the 2nd century AD. 13146: 10815: 9519:"Fermat's last theorem earns Andrew Wiles the Abel Prize" 9259:"History of the American Mathematical Society, 1888–1938" 5469:

Chap. IV "Egyptian Mathematics and Astronomy", pp. 71–96.

4639: 4450:

nor to construct a square equal in area to a given circle

3830:

it contained, and to aid the education of their sons. In

3588: 2736:

circle with approximately the same area as a given square

2629:, of great influence, for example, in the development of 2587:, whereas in Japan it was more prevalent in the realm of 999:

on clay tablets and dealt with geometrical exercises and

9833:"Ramanujan's Extensions of the Gamma and Beta Functions" 8745:

of Euclid" Q. 14, pp. 560–65, in Marshall Clagett, ed.,

6915:, "Revival and Decline of Greek Mathematics" pp. 190–94) 6884:, "Revival and Decline of Greek Mathematics" pp. 183–90) 3822:

in 1494. It included a 27-page treatise on bookkeeping,

2613:

Sangaku dedicated at Enmanji Temple in Nara city, Japan.

2453:(d. 23 AD) provided a figure of 3.1457 and subsequently 2394:, one of the earliest surviving mathematical texts from 1825:

after trying to generalize a problem he had read in the

1532:, and mechanics, but only half of his writings survive. 920:

mathematics refers to any mathematics of the peoples of

10936:

International Commission for the History of Mathematics

10863:

Earliest Known Uses of Some of the Words of Mathematics

10658:, fourth revised edition. Dover Publications, New York. 10482:

Sleeswyk, Andre (October 1981), "Vitruvius' odometer",

10308:

An introduction of the Early Development of Mathematics

4998:, i.e. could be determined by some algorithm. In 1931, 4746:. Large advances were made in the qualitative study of 4018:

system, which is the foundation of nearly all digital (

3619: 2446: 1544: 13119:

Book on the Measurement of Plane and Spherical Figures

10450:, vol. 3, Cambridge: Cambridge University Press, 10246: 10050:"Mathematicians chase the seven million-dollar proofs" 8967:(3rd. ed.). Courier Dover Publications. pp. 8253:

Abdel Haleem, Muhammad A. S. "The Semitic Languages",

7563: 7561: 7337: 7280: 4429:

reformulated the calculus in a more rigorous fashion.

4377:

The 19th century saw the beginning of a great deal of

2332:, or Chinese abacus. The date of the invention of the 1888:

of Alexandria (AD 350–415). She succeeded her father (

1884:

The first woman mathematician recorded by history was

1198:

Another significant Egyptian mathematical text is the

13836: 12433:

Ramanujan Institute for Advanced Study in Mathematics

12178: 9188:

Grattan-Guinness, Ivor; Grattan-Guinness, I. (2000).

8816:

Sangster, Alan; Greg Stoner & Patricia McCarthy:

8639:(Montréal: Institut d'Études Médiévales), pp. 224–27. 8622:. Madison: University of Wisconsin Press, pp. 421–40. 8492: 8490: 8488: 8486: 6294:"Ancient times table hidden in Chinese bamboo strips" 4326:

This century saw the development of the two forms of

4124: 3845:

In Italy, during the first half of the 16th century,

3446:

ordered all things in measure, and number, and weight

1146:

The most extensive Egyptian mathematical text is the

956:, once again became an important center of study for 386:, who coined the term "mathematics" from the ancient 10556:, Oxford: Oxford University Press, pp. 153–76, 9298:

Molenbroek, P.; Kimura, Shunkichi (3 October 1895).

7918:

Plofker 2009 pp. 197–98; George Gheverghese Joseph,

7676:

Microcontroller programming : the microchip PIC

6941:, "Revival and Decline of Greek Mathematics" p. 194) 6928:, "Revival and Decline of Greek Mathematics" p. 193) 6871:, "Revival and Decline of Greek Mathematics" p. 183) 6858:, "Revival and Decline of Greek Mathematics" p. 181) 6842:, "Revival and Decline of Greek Mathematics" p. 180) 6829:, "Revival and Decline of Greek Mathematics" p. 178) 5718:

Records in Stone: Papers in memory of Alexander Thom

5210: 5076:. He also made major investigations in the areas of 4638:

of (could neither be proved nor disproved from) the

3107:

Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala

2973:

for sine and cosine functions. In the 16th century,

1988:

mathematicians continued under the rule of the late

1321:

to solve problems such as calculating the height of

8843:, chapter 10: Numeration and Arithmetic, page 315, 7558: 5010:. (Peano arithmetic is adequate for a good deal of 3078:and one on methods for solving equations. His book 1793:made significant advances in algebra, particularly 1661:–190 BC) made significant advances to the study of 1413:and a theory of ratios that avoided the problem of 331:The earliest mathematical texts available are from 13266: 12379: 10985:Math Archives (University of Tennessee, Knoxville) 10598: 10339: 8658:, Sterling Publishing Company, Inc., p. 104, 8483: 7820: 7772: 7770: 5903: 5479:Turnbull (1931). "A Manual of Greek Mathematics". 4718:were abstracted using axioms and given names like 4130: 3903:in Europe, which influenced all later work on the 3536:with his merchant father. (Europe was still using 2856:as a "mix of common pebbles and costly crystals". 2788:. Pingala's work also contains the basic ideas of 2768:(roughly 3rd–1st centuries BC) in his treatise of 1439:One of the oldest surviving fragments of Euclid's 10646:Mathematical Thought from Ancient to Modern Times 10554:The Oxford Handbook of the History of Mathematics 9750:Transactions of the American Mathematical Society 9359:Introduction to $ p$ -adic Analytic Number Theory 9224:Proceedings of the Edinburgh Mathematical Society 9141:"Nous connaître | Société Mathématique de France" 8818:"The market for Luca Pacioli’s Summa Arithmetica" 8719:. Madison: University of Wisconsin Press, p. 284. 8633:Mathesis in Philosophiam Scholasticam Introducta: 8461: 8316: 6850: 6848: 6733: 6731: 4118:, and he popularized the use of the Greek letter 4006:, and brought together the concepts now known as 1110:mathematics refers to mathematics written in the 14201: 10619: 9993:"The Mighty Mathematician You've Never Heard Of" 9414:"Encyklopâdie der Mathematischen Wissenschaften" 9297: 8917: 8597:Grant, Edward and John E. Murdoch, eds. (1987). 7809: 7349: 6250: 5676:How Mathematics Happened: The First 50,000 Years 5636:"The Oldest Mathematical Object is in Swaziland" 4852:, by extending the field of real numbers to the 2965:to determine the arctangent, the Madhava-Newton 2698:Indian numerals in stone and copper inscriptions 1298:Greek mathematics is thought to have begun with 504:Many Greek and Arabic texts on mathematics were 10925:(Steven W. Rockey; Cornell University Library). 8749:. Madison: University of Wisconsin Press, 1968. 8322: 7767: 6502:"One of the Oldest Extant Diagrams from Euclid" 4370:, and set the mathematical foundations for the 3998:Building on earlier work by many predecessors, 2077:, which aided Roman surveyors in measuring the 1700:, largely to address the needs of astronomers. 11031:Mathematical Resources: History of Mathematics 10587:Episodes from the Early History of Mathematics 9300:"To Friends and Fellow Workers in Quaternions" 9115:"A Century of the London Mathematical Society" 9068:"Paolo Ruffini's contributions to the quintic" 8577:Renaissance and Renewal in the Twelfth Century 8566:, (Cambridge: Harvard University Press, 1982). 8564:Renaissance and Renewal in the Twelfth Century 7678:. Boca Raton, Florida: CRC Press. p. 37. 6845: 6816:, "Greek Trigonometry and Mensuration" p. 168) 6803:, "Greek Trigonometry and Mensuration" p. 164) 6790:, "Greek Trigonometry and Mensuration" p. 163) 6754:, "Greek Trigonometry and Mensuration" p. 162) 6741:, "Greek Trigonometry and Mensuration" p. 175) 6728: 6725:, "Greek Trigonometry and Mensuration" p. 161) 6235: 6179:. Chicago: University of Chicago Press, p. 75. 5957:Episodes from the Early History of Mathematics 5565:The Nothing That Is: A Natural History of Zero 3918:was the first to use the word, publishing his 3070:In the 9th century, the Persian mathematician 2526:, described in ancient times and perfected by 2278:multiplication table, dated 305 BC during the 1773:Title page of the 1621 edition of Diophantus' 13822: 13343: 12464: 11672: 11058: 10869:Earliest Uses of Various Mathematical Symbols 10699:Geometry and Algebra in Ancient Civilizations 10662: 10425:, Princeton, NJ: Princeton University Press, 9454:Bulletin of the American Mathematical Society 9422:Bulletin of the American Mathematical Society 9263:Bulletin of the American Mathematical Society 9011:An Introduction to the History of Mathematics 8841:Encyclopedia of the History of Arabic Science 7855:. A few years later, perhaps about 775, this 7673: 7443: 6552:An Introduction to the History of Mathematics 6216:An Introduction to the History of Mathematics 6144:An Introduction to the History of Mathematics 5337:List of important publications in mathematics 4871:The development and continual improvement of 4038:, which is the standard design paradigm, or " 3254:. He also wrote influential work on Euclid's 3224:, a book about what he perceived as flaws in 3145:Further developments in algebra were made by 2752:(c. 5th century BC) formulated the rules for 2262:History of science § Chinese mathematics 1856:Among the last great Greek mathematicians is 1122:replaced Egyptian as the written language of 270:mathematical methods and notation of the past 241: 10713: 10329:: CS1 maint: multiple names: authors list ( 10224: 9970:, New York: Marcel Dekker, pp. 99–111, 9968:Emmy Noether: A Tribute to Her Life and Work 9732: 9664:Bourbaki: A Secret Society of Mathematicians 9516: 8579:. Cambridge: Harvard University Press, 1982. 8048:: CS1 maint: multiple names: authors list ( 7962: 7293: 6600: 6598: 5058:who conjectured or proved over 3000 theorems 4698:. Entirely new areas of mathematics such as 4002:discovered the laws of physics that explain 3930:Mathematics during the Scientific Revolution 3082:, written about 825, along with the work of 2784:corresponds to an elementary version of the 2665:History of science § Indian mathematics 1620:bearing his name, obtained formulas for the 1175:; and simplistic understandings of both the 1018:Babylonian mathematics were written using a 11072: 10889:(Scott W. Williams; University at Buffalo). 10614:The History of Mathematics: An Introduction 10463: 10438: 9112: 8730:The Science of Mechanics in the Middle Ages 8717:The Science of Mechanics in the Middle Ages 8704:The Science of Mechanics in the Middle Ages 8620:The Science of Mechanics in the Middle Ages 8535:Boethius: His Life, Thought, and Influence, 8137:(2002). "Was Calculus Invented in India?". 7968: 7567: 7324: 7267: 7241: 7228: 7215: 7133: 7120: 4338:and his rival, the Hungarian mathematician 4154:, did important work on the foundations of 1031:was the best of any civilization until the 13829: 13815: 13767: 13350: 13336: 12471: 12457: 12200:Kerala school of astronomy and mathematics 11679: 11665: 11065: 11051: 9962: 9119:Journal of the London Mathematical Society 8950:. Great Britain: Pelican. pp. 150–51. 8287: 7892:The History of Mathematics: A Brief Course 7865:was translated into Arabic from the Greek. 7582: 7494: 6496: 6020: 5415: 5045:of the Gamma function on the complex plane 4545:, was formed in 1899, in the context of a 3914:grew to be a major branch of mathematics. 3013:History of the Hindu–Arabic numeral system 2712:Ancient Brahmi numerals in a part of India 2671:History of the Hindu–Arabic numeral system 1643:made significant advances in the study of 975:In contrast to the sparsity of sources in 248: 234: 13205:Constantinople observatory of Taqi ad-Din 12480:Mathematics in the medieval Islamic world 10759: 10400:A History of Mathematics: An Introduction 10025:"Mathematics Subject Classification 2000" 9808: 9742:"On highly composite and similar numbers" 9610: 9465: 9274: 9257:Archibald, Raymond Clare (January 1939). 9256: 8781:, ed. G. Nicco Fasola, 2 vols., Florence. 8637:Arts libéraux et philosophie au Moyen Âge 8601:. Cambridge: Cambridge University Press. 8455: 8255:https://doi.org/10.1515/9783110251586.811 8192: 8115:Transactions of the Royal Asiatic Society 7674:Sanchez, Julio; Canton, Maria P. (2007). 7634: 6595: 6487:, "The Age of Plato and Aristotle" p. 98) 6474:, "The Age of Plato and Aristotle" p. 91) 6461:, "The Age of Plato and Aristotle" p. 93) 6448:, "The Age of Plato and Aristotle" p. 92) 6435:, "The Age of Plato and Aristotle" p. 87) 6397:, "The Age of Plato and Aristotle" p. 88) 6381:, "The Age of Plato and Aristotle" p. 86) 6305: 6284: 6282: 6166:, "The Age of Plato and Aristotle" p. 99) 5959:. New York: Random House. pp. 30–31. 5554:. Campus, Frankfurt/New York, pp. 428–37. 4955:. Some of the most important methods and 4618:, building on the work of others, proved 4514:, initiated a long running debate on the 4260:Learn how and when to remove this message 3781:, a painting traditionally attributed to 3352:for numbers 1 through 19, written in the 3222:Discussions of the Difficulties in Euclid 2422:The Nine Chapters on the Mathematical Art 2391:The Nine Chapters on the Mathematical Art 2342:Supplementary Notes on the Art of Figures 2190:and the Romans both invented the wheeled 1361:(60–120 AD) provided one of the earliest 12428:Homi Bhabha Centre for Science Education 10668: 10510: 10481: 10337: 9488: 8648: 8133: 8023: 7531: 7254: 7146: 7107: 7094: 7081: 7068: 6253:The Two-Year College Mathematics Journal 5839: 5653: 5633: 5627: 5593:Geschichte der Mathematik im Mittelalter 5478: 5131:was dozens of pages long. More and more 5036: 4834:became one of the major areas of study. 4675: 4590: 4578:International Congress of Mathematicians 4317: 4276: 4087: 3944: 3883:in which he showed how to deal with the 3824:"Particularis de Computis et Scripturis" 3771: 3708:, the development of mathematics and of 3597:(1323–1382), shown in this contemporary 3343: 3016: 2813: 2674: 2608: 2437:. It created mathematical proof for the 2384: 2310: 2265: 1950: 1835: 1768: 1635: 1534: 1434: 1242: 1094: 1005: 962: 264:deals with the origin of discoveries in 28: 11010:(David Calvis; Baldwin-Wallace College) 10875:Mathematical Words: Origins and Sources 10845:MacTutor History of Mathematics archive 10838: 10781: 10737: 10674:Mathematics in the Time of the Pharaohs 10305: 10047: 9891: 9798: 9611:Wolchover, Natalie (22 February 2013). 9447: 9411: 9040: 8497: 8473:MacTutor History of Mathematics Archive 8359: 8171: 8062: 7620: 7029: 6990: 6951: 6770:. Harwood Publishing, 2007, 131 pages. 5737: 5567:. Allen Lane/The Penguin Press, London. 3464:, a free translation from the Greek of 2445:. The treatise also provides values of 854:of the earliest known demonstration of 539:during the course of the 17th century. 14: 14202: 13357: 13126:Encyclopedia of the Brethren of Purity 11686: 10887:Mathematicians of the African Diaspora 10627:. The Johns Hopkins University Press. 10551: 10342:Mathematics: From the Birth of Numbers 10173:"Big Data for Sustainable Development" 9990: 9700: 9698: 9696: 9694: 9692: 9690: 9688: 9214: 8960: 8936: 8862: 8762:, Foundations of the Formal Sciences, 8360:Sesiano, Jacques (1997). "Abū Kāmil". 8323:Rashed, R.; Armstrong, Angela (1994). 8214:"Ideas of Calculus in Islam and India" 7437: 7424: 7411: 7398: 6895:"Internet History Sourcebooks Project" 6406: 6279: 5995: 5909: 5672: 5640:Mathematicians of the African Diaspora 4655:classification of finite simple groups 3818:") was first printed and published in 3423:Latin translations of the 12th century 3080:On the Calculation with Hindu Numerals 1860:(4th century AD). He is known for his 971:, first half of the 2nd millennium BCE 453:made early contributions, including a 13810: 13331: 12452: 11660: 11046: 10719: 10680: 10581: 10464:Needham, Joseph; Wang, Ling (2000) , 10359: 10346:, New York: W.W. Norton and Company, 10287: 10264: 9940:"grossman - The Erdös Number Project" 9879:"Grossman – the Erdös Number Project" 9830: 9775: 9578:Rocky Mountain Journal of Mathematics 9571: 9491:"Formal Proof—The Four-Color Theorem" 9385:"U.S. Doctorates in the 20th Century" 9355: 9217:"The first hundred years (1883–1983)" 9072:Archive for History of Exact Sciences 9065: 8942: 8856: 8398: 8353: 8325:The Development of Arabic Mathematics 8294: 8267: 7885: 7803: 7790: 7777: 7761: 7534:"The Value of π known to Śulbasūtras" 7482: 7462: 7385: 7311: 7202: 7177: 7159: 7055: 7016: 7003: 6977: 6964: 6938: 6925: 6912: 6881: 6868: 6855: 6839: 6826: 6813: 6800: 6787: 6751: 6738: 6722: 6709: 6696: 6683: 6670: 6657: 6644: 6631: 6618: 6605: 6589: 6576: 6538: 6522: 6484: 6471: 6458: 6445: 6432: 6394: 6378: 6205:, "Ionia and the Pythagoreans" p. 49) 6202: 6192:, "Ionia and the Pythagoreans" p. 43) 6189: 6163: 6112: 6040: 5983: 5970: 5951: 5939: 5827: 5811: 5793: 5773: 5642:. SUNY Buffalo mathematics department 5621: 5390: 4486:established the first foundations of 948:as a place of study. Later under the 397:), meaning "subject of instruction". 11627: 10907:Ancient Rome: The Odometer Of Vitruv 10883:(Larry Riddle; Agnes Scott College). 10593: 10530: 10420: 10396: 8439: 8404: 8375: 8211: 7718: 7698:Anglin, W. S. and J. Lambek (1995). 7541:Indian Journal of History of Science 7338:Berggren, Borwein & Borwein 2004 7281:Berggren, Borwein & Borwein 2004 7189: 7042: 6414:. New Europe College. Archived from 5541:. Penguin Books, London, pp. 140–48. 5533: 5531: 4342:, independently defined and studied 4198:adding citations to reliable sources 4169: 4068:in their discussions over a game of 3524:, serendipitously learned about the 3505:, translated in various versions by 3501:, and the complete text of Euclid's 3413:List of medieval European scientists 3406: 3104:from the title of one of his works, 2499:Precious Mirror of the Four Elements 535:in the development of infinitesimal 11953:Subbayya Sivasankaranarayana Pillai 11639: 10966:Mathematical Association of America 10881:Biographies of Women Mathematicians 10170: 9704: 9685: 9517:Castelvecchi, Davide (2016-03-01). 9489:Gonthier, Georges (December 2008). 8674:in 1647 and by Swiss mathematician 6288: 5537:Joseph, George Gheverghese (1991). 4586:23 unsolved problems in mathematics 4385:in Germany gave a first version of 3867:, together with a solution for the 3417:European science in the Middle Ages 2917:, and describes the formation of a 2140:every other year. In contrast, the 1010:The Babylonian mathematical tablet 838:, found near the headwaters of the 24: 12413:Institute of Mathematical Sciences 10991:The Math Forum (Drexel University) 10570: 10504:10.1038/scientificamerican1081-188 10195: 9778:"The Partition Function Revisited" 8741:Oresme, Nicole. "Questions on the 8550:, Wiesbaden: Franz Steiner Verlag. 6660:, "Archimedes of Syracuse" p. 137) 6647:, "Archimedes of Syracuse" p. 121) 6634:, "Archimedes of Syracuse" p. 125) 6621:, "Archimedes of Syracuse" p. 126) 6608:, "Archimedes of Syracuse" p. 130) 6592:, "Archimedes of Syracuse" p. 120) 5347:List of mathematics history topics 5300:History of ancient numeral systems 5129:Mathematics Subject Classification 4682:relativistic precession of apsides 4409:and has important applications in 3760:Trattato d’Abaco (Abacus Treatise) 3540:.) There, he observed a system of 3285:, the discovery of all the modern 3239:. He was also very influential in 3000: 2881:, he lucidly explained the use of 2617:The mathematics that developed in 2274:, containing the world's earliest 2099:preparation for military campaigns 1341:. Although he was preceded by the 25: 14226: 13388:History and philosophy of science 12423:Harish-Chandra Research Institute 11933:K. R. Parthasarathy (probabilist) 10913: 10804: 10274:(2nd ed.), New York: Wiley, 10096:"Maths genius declines top prize" 9898:The American Mathematical Monthly 9837:The American Mathematical Monthly 9763:10.1090/S0002-9947-1944-0011087-2 9707:"Honoring a Gift from Kumbakonam" 8468:"Abu'l Hasan ibn Ali al Qalasadi" 8442:"Mathematics for All and Forever" 5663:, Colonial Hill, Mount Kisco, NY. 5528: 5409: 5396: 4899:to further number theory and the 4362:, which generalizes the ideas of 3834:, Pacioli introduced symbols for 3765:De quinque corporibus regularibus 3438:and the biblical passage (in the 3086:, were instrumental in spreading 2969:to determine sine and cosine and 2772:uses a device corresponding to a 2441:, and a mathematical formula for 2297:appears reasonable. However, the 1783:Claude Gaspard Bachet de Méziriac 512:. From ancient times through the 320:, trade and also in the field of 14215:History of science by discipline 14184: 14183: 13790: 13789: 13777: 13766: 13396: 13062: 11638: 11626: 11615: 11614: 11602: 11001:History of Mathematics Web Sites 10929: 10851:History of Mathematics Home Page 10809: 10656:A Concise History of Mathematics 10189: 10164: 10140: 10116: 10088: 10041: 10017: 9984: 9956: 9932: 9894:"And What Is Your Erdos Number?" 9885: 9871: 9824: 9799:Bradley, David M. (2005-05-07), 9792: 9769: 9726: 9656: 9632: 9604: 9565: 9510: 9482: 9441: 9405: 9376: 9349: 9291: 9250: 9208: 9181: 9165:"Mathematical Circle of Palermo" 9157: 9133: 9106: 9066:Ayoub, Raymond G. (1980-09-01). 9059: 9034: 9024: 9003: 8985: 8964:A Concise History of Mathematics 8954: 8911: 8830: 8810: 8797: 8784: 8771: 8752: 8735: 8722: 8709: 8696: 8683: 8642: 8625: 8612: 8591: 8582: 8569: 8553: 8540: 8515: 8503: 8433: 8381: 8368: 8273: 8260: 8247: 8205: 8165: 8127: 8056: 8010: 7953: 7929: 7912: 7879: 7870: 7851:, although it may have been the 7796: 7783: 7754: 7712: 7692: 7667: 7614: 7576: 7572:. Univ. of St. Andrew, Scotland. 7525: 7488: 7455: 7430: 7417: 7404: 7391: 7343: 7330: 7317: 7286: 7273: 7260: 7247: 7234: 7221: 7208: 7195: 7183: 7152: 7139: 7126: 7113: 7100: 7087: 6579:, "Euclid of Alexandria" p. 102) 6541:, "Euclid of Alexandria" p. 104) 6525:, "Euclid of Alexandria" p. 100) 6504:. University of British Columbia 6081:www-history.mcs.st-andrews.ac.uk 5393:, "Euclid of Alexandria" p. 119) 5365: 5285:History of mathematical notation 5230:Archives of American Mathematics 5213: 5018:.) A consequence of Gödel's two 4174: 4080:in the 18th and 19th centuries. 3861:published them in his 1545 book 3618: 3587: 2909:'s work contains a study of the 2705: 2691: 2301:, containing the earliest known 2073:(i.e. land surveyor), wrote the 1267:(~600 BC) to the closure of the 1126:scholars. Mathematical study in 551:(descended from the West Arabic) 218: 11523:Computational complexity theory 10362:American Journal of Archaeology 10306:Goodman, Michael, K.J. (2016), 9467:10.1090/S0002-9904-1902-00923-3 9435:10.1090/s0002-9904-1922-03635-x 9276:10.1090/S0002-9904-1939-06908-5 8918:Grattan-Guinness, Ivor (1997). 8803:della Francesca, Piero (1916). 8777:della Francesca, Piero (1942). 7894:. Wiley-Interscience. pp. 7888:"The Mathematics of the Hindus" 7819:(1991). "The Arabic Hegemony". 7353:Calculus: Early Transcendentals 7074: 7061: 7048: 7035: 7022: 7009: 6996: 6983: 6970: 6957: 6944: 6931: 6918: 6905: 6887: 6874: 6861: 6832: 6819: 6806: 6793: 6780: 6757: 6744: 6715: 6712:, "Apollonius of Perga" p. 156) 6702: 6699:, "Apollonius of Perga" p. 152) 6689: 6686:, "Apollonius of Perga" p. 146) 6676: 6673:, "Apollonius of Perga" p. 145) 6663: 6650: 6637: 6624: 6611: 6582: 6569: 6566:, has been more widely used..." 6544: 6515: 6490: 6477: 6464: 6451: 6438: 6425: 6400: 6371: 6350: 6329: 6244: 6229: 6208: 6195: 6182: 6169: 6156: 6136: 6118: 6087: 6069: 6058: 6046: 6014: 5989: 5976: 5963: 5945: 5921:, vol. 3, pp. 417–439 5875: 5848:, Routledge, pp. 307–308, 5833: 5766: 5731: 5710: 5697: 5666: 5598: 5582: 5422:The Exact Sciences in Antiquity 5260:History of the function concept 5142: 4563: 4471:, and the associated fields of 4272: 4185:needs additional citations for 4083: 4064:and the corresponding rules of 3940: 3520:Leonardo of Pisa, now known as 3485:seeking scientific Arabic texts 3138:extended algebra to the set of 3074:wrote an important book on the 3063:, they were not all written by 2358:, compiled by the followers of 2256:Book on Numbers and Computation 2219: 2178: 1844:was designed by mathematicians 1579:summation of an infinite series 497:was given a standard symbol in 12408:Chennai Mathematical Institute 11777:Melpathur Narayana Bhattathiri 10997:(Courtright Memorial Library). 10687:A History of Greek Mathematics 10525:10.1080/0025570X.1998.11996627 9991:Angier, Natalie (2012-03-26). 9194:. W. W. Norton & Company. 9041:Wendorf, Marcia (2020-09-23). 8948:Mathematics in Western Culture 8794:, ed. G. Arrighi, Pisa (1970). 7740:10.1080/10724117.2008.11974752 7568:Connor, J.J.; Robertson, E.F. 5720:. Cambridge University Press. 5570: 5557: 5552:Universalgeschichte der Zahlen 5544: 5515: 5472: 4939:concepts and the expansion of 4535:Edinburgh Mathematical Society 4527:Société Mathématique de France 4309:fundamental theorem of algebra 3743:(c. 1415–1492) wrote books on 3693: 3250:(Nasireddin) made advances in 3072:Muḥammad ibn Mūsā al-Khwārizmī 3029:Muhammad ibn Mūsā al-Khwārizmī 2585:mathematicians and astronomers 2000:mathematicians in comparison. 805: 479:Muḥammad ibn Mūsā al-Khwārizmī 13: 1: 13098:Principles of Hindu Reckoning 10232:, Leiden: Koninklijke Brill, 10218: 10048:Dickson, David (2000-05-01). 9668:American Mathematical Society 9362:. American Mathematical Soc. 8212:Katz, Victor J. (June 1995). 7721:"Math for poets and drummers" 6023:Symmetry: Culture and Science 5523:A Manual of Greek Mathematics 4959:of the 20th century are: the 4640:standard axioms of set theory 4539:American Mathematical Society 4531:Circolo Matematico di Palermo 4336:Nikolai Ivanovich Lobachevsky 3756:(On Perspective for Painting) 3188:." Also in the 10th century, 3007:Mathematics in medieval Islam 2875:, and for the first time, in 2352: 2222: 177 – 192 AD 2203: 2136:and included 356 days plus a 1756: 1731: 1716: 1705: 1682: 1655: 1555: 1464: 1422: 1099:Image of Problem 14 from the 928:) from the days of the early 900: 349: 324:to record time and formulate 44: 12398:Indian Statistical Institute 9356:Murty, M. Ram (2009-02-09). 8521:Caldwell, John (1981). "The 8018:Journal of Indian Philosophy 7623:Journal of Indian Philosophy 7588:Journal of Indian Philosophy 5894:Third Millennium Mathematics 5881:Melville, Duncan J. (2003). 5679:. Prometheus Books. p. 5673:Rudman, Peter Strom (2007). 5659:Marshack, Alexander (1991). 5425:. Vol. 9 (2 ed.). 5051:Srinivasa Aiyangar Ramanujan 4397:. The British mathematician 4372:theory of general relativity 4303:, and on the convergence of 3871:, discovered by his student 3767:(On the Five Regular Solids) 2951:Kerala School of Mathematics 2085:, including the erection of 2016:were far more interested in 1921:with mathematicians such as 1821:, who arrived at his famous 1543:to approximate the value of 469:and were transmitted to the 7: 13739:Neurology and neurosurgery 13288:Hindu–Arabic numeral system 13220:University of al-Qarawiyyin 12418:Indian Institute of Science 12403:Bhaskaracharya Pratishthana 12281:A. A. Krishnaswamy Ayyangar 12246:Shankar Balakrishna Dikshit 12173:Hindu–Arabic numeral system 11026:Using History in Math Class 11016:(Universidad de La La guna) 11014:Historia de las Matemáticas 10941: 10724:, Oxford University Press, 10676:. Cambridge, MA: MIT Press. 9215:Rankin, R. A. (June 1986). 9113:Collingwood, E. F. (1966). 8523:De Institutione Arithmetica 8139:College Mathematics Journal 8032:Journal of Natural Geometry 7806:, "China and India" p. 211) 7793:, "China and India" p. 210) 7780:, "China and India" p. 209) 7764:, "China and India" p. 208) 7485:, "China and India" p. 207) 7465:, "China and India" p. 206) 7388:, "China and India" p. 205) 7314:, "China and India" p. 202) 7205:, "China and India" p. 198) 7180:, "China and India" p. 196) 7162:, "China and India" p. 201) 5883:Third Millennium Chronology 5634:Williams, Scott W. (2005). 5206: 4901:Lucas–Lehmer primality test 4523:London Mathematical Society 4482:In the later 19th century, 4108:Seven Bridges of Königsberg 3497:, translated into Latin by 3462:De institutione arithmetica 2891:Hindu–Arabic numeral system 2514:also contains a diagram of 2433:, and includes material on 2406:commanded all books in the 2160:(100–44 BC) and devised by 1996:, there were no noteworthy 1520:on other subjects, such as 1101:Moscow Mathematical Papyrus 1084: 463:Hindu–Arabic numeral system 368:Moscow Mathematical Papyrus 296:and the Levantine state of 10: 14231: 13190:Al-Mustansiriya University 13169:Islamic geometric patterns 12917:Shams al-Din al-Samarqandi 11913:Subrahmanyan Chandrasekhar 11573:Films about mathematicians 10857:The History of Mathematics 10722:A Brief History of Numbers 10663:Books on a specific period 10575: 10148:"Electronic Math Journals" 9574:"The Discovery of Forcing" 9572:Cohen, Paul (2002-12-01). 9047:interestingengineering.com 8715:Clagett, Marshall (1961). 8702:Clagett, Marshall (1961). 8631:Murdoch, John E. (1969). " 8618:Clagett, Marshall (1961). 8537:(Oxford: Basil Blackwell). 7978:Philosophy East & West 7547:(1): 32–41. Archived from 6407:Calian, George F. (2014). 5854:10.4324/9780203096604.ch15 5327:History of writing numbers 5201:Bureau of Labor Statistics 5187: 5155:Clay Mathematics Institute 5146: 5139:led to online publishing. 5060:, including properties of 5014:, including the notion of 4786:. Other new areas include 4782:led to the development of 4516:foundations of mathematics 4446:trisect an arbitrary angle 3933: 3697: 3470:Introduction to Arithmetic 3420: 3410: 3317:and the development of an 3216:In the late 11th century, 3169:, and the sum of integral 3010: 3004: 2963:the Madhava-Gregory series 2945:Also in the 14th century, 2885:as both a placeholder and 2668: 2662: 2656: 2598: 2565:East Asian cultural sphere 2469:in the 3rd century AD and 2259: 2253: 2247: 2243: 2186:At roughly the same time, 1940: 1803:Diophantine approximations 1415:incommensurable magnitudes 1236: 1130:later continued under the 1088: 1039:gives an approximation of 952:, Mesopotamia, especially 910: 904: 358:Rhind Mathematical Papyrus 158:Relationship with sciences 14179: 14141: 14110: 14069: 14043: 13849: 13762: 13709: 13676: 13628: 13575: 13537: 13461: 13405: 13394: 13365: 13280: 13254: 13228: 13177: 13156: 13071: 13060: 13027: 12971: 12935: 12854: 12808: 12727: 12591: 12495: 12486: 12388: 12352: 12326: 12230: 12192: 12158: 11995: 11923:Veeravalli S. Varadarajan 11890: 11749: 11703: 11694: 11596: 11546: 11503: 11413: 11375: 11342: 11294: 11266: 11213: 11160: 11142:Philosophy of mathematics 11117: 11082: 11022:(Universidade de Coimbra) 10714:Books on a specific topic 10690:. Oxford, Claredon Press. 10589:. New York: Random House. 10128:scholarship.claremont.edu 9543:10.1038/nature.2016.19552 9236:10.1017/S0013091500016849 8728:Clagett, Marshall (1961) 8364:. Springer. pp. 4–5. 7645:10.1007/s10781-007-9025-5 6562:p. 141: "No work, except 6307:10.1038/nature.2014.14482 6238:The Annals of Mathematics 5661:The Roots of Civilization 5521:Heath, Thomas L. (1963). 5280:History of mathematicians 5183: 5159:Millennium Prize Problems 5092:and prime number theory. 4909:recursive function theory 4650:, also using a computer. 4313:quadratic reciprocity law 4165: 4012:Gottfried Wilhelm Leibniz 3950:Gottfried Wilhelm Leibniz 3853:discovered solutions for 3851:Niccolò Fontana Tartaglia 3528:on a trip to what is now 2721:Indus Valley civilization 2679:The numerals used in the 2652: 2575:or the native Vietnamese 1722:–70 AD) is credited with 533:Gottfried Wilhelm Leibniz 12943:Nizam al-Din al-Nisapuri 12902:Muhyi al-Din al-Maghribi 12339:Henry Thomas Colebrooke 11928:S. R. Srinivasa Varadhan 11578:Recreational mathematics 10421:Katz, Victor J. (2007), 10397:Katz, Victor J. (1998), 10288:Cuomo, Serafina (2001), 10271:A History of Mathematics 9892:Goffman, Casper (1969). 9613:"In Computers We Trust?" 9127:10.1112/jlms/s1-41.1.577 8790:della Francesca, Piero. 8546:Folkerts, Menso (1970). 8478:University of St Andrews 7959:Plofker 2009 pp. 217–53. 7719:Hall, Rachel W. (2008). 7570:"The Indian Sulbasutras" 6356:Smith, David E. (1958). 5842:"Calendars and Counting" 5840:Sharlach, Tonia (2006), 5707:. New York: McGraw-Hill. 5358: 5312:History of number theory 5255:History of combinatorics 5176:, first made popular by 5062:highly composite numbers 4754:had begun in the 1890s. 4576:In a 1900 speech to the 4209:"History of mathematics" 4036:Von Neumann architecture 3778:Portrait of Luca Pacioli 3643:One of the 14th-century 3192:translated the works of 2971:the Taylor approximation 2776:. His discussion of the 2594: 2485:to find the volume of a 2040:centered in what is now 1969:), found at the site of 1936: 1929:, the architects of the 1470:) taught, and wrote the 1409:, a precursor of modern 1232: 375:, so, by inference, the 18:Historian of mathematics 13453:20th century in science 13448:19th century in science 13312:History of trigonometry 13307:Trigonometric functions 13301:Western Arabic numerals 13297:Eastern Arabic numerals 12862:Ibn al‐Ha'im al‐Ishbili 11812:Mādhava of Saṅgamagrāma 11463:Mathematical statistics 11453:Mathematical psychology 11423:Engineering mathematics 11357:Algebraic number theory 10923:archive dated 2007/3/17 10828:Renaissance Mathematics 9831:Askey, Richard (1980). 9662:Maurice Mashaal, 2006. 9590:10.1216/rmjm/1181070010 9450:"Mathematical problems" 9448:Hilbert, David (1902). 9412:Pitcher, A. D. (1922). 8863:Sarton, George (1935). 8807:, ed. G. Mancini, Rome. 8779:De Prospectiva Pingendi 8560:Marie-Thérèse d'Alverny 8548:"Boethius" Geometrie II 7600:10.1023/A:1017506118885 7532:Kulkarni, R.P. (1978). 7325:Needham & Wang 1995 7268:Needham & Wang 1995 7242:Needham & Wang 1995 7229:Needham & Wang 1995 7216:Needham & Wang 1995 7134:Needham & Wang 2000 7121:Needham & Wang 2000 6967:, pp. 194, 204–06) 6899:sourcebooks.fordham.edu 6335:David E. Smith (1958), 6065:Egyptian Unit Fractions 6053:Egyptian Unit Fractions 5898:St. Lawrence University 5738:Damerow, Peter (1996). 5563:Kaplan, Robert (1999). 5550:Ifrah, Georges (1986). 5352:Timeline of mathematics 5342:Lists of mathematicians 5322:History of trigonometry 5270:History of group theory 5053:(1887–1920), an Indian 5020:incompleteness theorems 4985:public-key cryptography 4690:came into its own when 4665:, publishing under the 4595:A map illustrating the 3754:De Prospectiva Pingendi 3399:. While the concept of 3339: 3328:During the time of the 3287:trigonometric functions 3258:. In the 15th century, 3039:established across the 2957:and obtained from it a 2947:Madhava of Sangamagrama 2878:Brahma-sphuta-siddhanta 2402:In 212 BC, the Emperor 2162:Sosigenes of Alexandria 2109:, inspired by previous 2022:theoretical mathematics 1811:indeterminate equations 1081:or logical principles. 493:, where the concept of 411:theoretical mathematics 14210:History of mathematics 14102:Medieval Islamic world 13838:History of mathematics 13373:Theories and sociology 13236:Babylonian mathematics 12927:Kamāl al-Dīn al-Fārisī 12912:Qutb al-Din al-Shirazi 12907:al-Hasan al-Marrakushi 12831:Al-Samawal al-Maghribi 12760:Abu Mansur al-Baghdadi 12503:'Abd al-Hamīd ibn Turk 11609:Mathematics portal 11458:Mathematical sociology 11438:Mathematical economics 11433:Mathematical chemistry 11362:Analytic number theory 11243:Differential equations 11037:History of Mathematics 11020:História da Matemática 10995:History of Mathematics 10976:History of Mathematics 10695:van der Waerden, B. L. 10621:Grattan-Guinness, Ivor 10338:Gullberg, Jan (1997), 10251:, New York: Springer, 9776:Murty, M. Ram (2013). 9121:. s1-41 (1): 577–594. 8766:, November 2009, p. 7 8527:De Institutione Musica 8194:10.1006/hmat.2001.2331 7937:"Narayana - Biography" 7849:Brahmasphuta Siddhanta 7823:History of Mathematics 7700:The Heritage of Thales 5986:, "Mesopotamia" p. 39) 5973:, "Mesopotamia" p. 33) 5942:, "Mesopotamia" p. 27) 5830:, "Mesopotamia" p. 41) 5814:, "Mesopotamia" p. 25) 5796:, "Mesopotamia" p. 26) 5776:, "Mesopotamia" p. 24) 5606:History of Mathematics 5290:History of measurement 5174:open access publishing 5046: 4969:error-correcting codes 4965:fast Fourier transform 4684: 4644:Thomas Callister Hales 4599: 4411:electrical engineering 4395:noncommutative algebra 4391:William Rowan Hamilton 4328:non-Euclidean geometry 4323: 4284: 4132: 4095: 3952: 3916:Bartholomaeus Pitiscus 3790: 3599:illuminated manuscript 3474:De institutione musica 3361:Pre-Columbian Americas 3356: 3252:spherical trigonometry 3159:mathematical induction 3094:to the West. The word 3032: 2955:Madhava–Leibniz series 2930:the mean value theorem 2869:Brahmagupta's identity 2828: 2684: 2614: 2557:Vietnamese mathematics 2399: 2318: 2283: 2026:their numerical system 1981: 1853: 1795:indeterminate analysis 1786: 1739:spherical trigonometry 1728:Menelaus of Alexandria 1679:Eratosthenes of Cyrene 1677:Around the same time, 1648: 1626:surfaces of revolution 1616:. He also studied the 1548: 1448: 1405:Eudoxus developed the 1312:Babylonian mathematics 1302:(c. 624–c.546 BC) and 1256: 1104: 1015: 972: 936:almost to the dawn of 907:Babylonian mathematics 431:mechanical engineering 427:structural engineering 292:, followed closely by 262:history of mathematics 51: 14171:Future of mathematics 14148:Women in mathematics 13433:Scientific Revolution 13262:Byzantine mathematics 13050:Ibn Hamza al-Maghribi 12877:Alam al-Din al-Hanafi 12841:Sharaf al-Din al-Tusi 12023:Brāhmasphuṭasiddhānta 11588:Mathematics education 11518:Theory of computation 11238:Hypercomplex analysis 10605:. Simon and Schuster. 10531:Tang, Birgit (2005), 10292:, London: Routledge, 10152:www.stat.berkeley.edu 9009:Eves, Howard (1990). 8961:Struik, Dirk (1987). 8852:10.4324/9780203403600 8650:Pickover, Clifford A. 7990:10.1353/pew.2001.0045 7886:Cooke, Roger (1997). 7340:, pp. 20, 24–26) 7045:, pp. 14–15, 45) 6550:Eves, Howard (1990). 6214:Eves, Howard (1990). 6142:Eves, Howard (1990). 5703:Marshack, A. (1972). 5604:Eves, Howard (1990). 5317:History of statistics 5245:History of arithmetic 5190:Future of mathematics 5133:mathematical journals 5102:, which leads to the 5090:hypergeometric series 5040: 4838:Non-standard analysis 4766:'s axiomatisation of 4688:Differential geometry 4679: 4620:Fermat's Last Theorem 4594: 4419:Augustin-Louis Cauchy 4393:in Ireland developed 4321: 4280: 4150:, who, in the age of 4144:Joseph Louis Lagrange 4133: 4091: 4040:computer architecture 3993:Cartesian coordinates 3948: 3936:Scientific Revolution 3802:(Italian: "Review of 3775: 3741:Piero della Francesca 3698:Further information: 3653:differential calculus 3526:Hindu–Arabic numerals 3411:Further information: 3347: 3301:, the development of 3246:In the 13th century, 3076:Hindu–Arabic numerals 3020: 2949:, the founder of the 2924:In the 12th century, 2873:Brahmagupta's formula 2817: 2774:binary numeral system 2678: 2663:Further information: 2612: 2599:Further information: 2541:missionaries such as 2483:Cavalieri's principle 2429:towers, engineering, 2388: 2316:Counting rod numerals 2314: 2299:Tsinghua Bamboo Slips 2295:Warring States Period 2272:Tsinghua Bamboo Slips 2269: 2254:Further information: 2230:Antikythera mechanism 2194:device for measuring 2038:Etruscan civilization 1955:Equipment used by an 1954: 1941:Further information: 1839: 1799:Diophantine equations 1772: 1690:Sieve of Eratosthenes 1688:–194 BC) devised the 1639: 1538: 1438: 1366:multiplication tables 1246: 1218:(truncated pyramid). 1181:perfect number theory 1177:Sieve of Eratosthenes 1098: 1009: 997:multiplication tables 966: 871:Predynastic Egyptians 622:Eastern Arabic-Indic 506:translated into Latin 457:and the first use of 32: 14123:Over Cantor's theory 13686:Agricultural science 13438:Age of Enlightenment 13267:European mathematics 13215:Maragheh observatory 13040:Muhammad Baqir Yazdi 13019:Ibn Ghazi al-Miknasi 12892:Nasir al-Din al-Tusi 12800:Muhammad al-Baghdadi 12299:T. A. Saraswati Amma 12010:Bakhshali manuscript 11978:Kannan Soundararajan 11568:Informal mathematics 11448:Mathematical physics 11443:Mathematical finance 11428:Mathematical biology 11367:Diophantine geometry 10949:Historia Mathematica 10839:Educational material 10682:Heath, Thomas Little 10670:Gillings, Richard J. 10513:Mathematics Magazine 9964:Alexandrov, Pavel S. 9740:(14 February 1944). 8464:Robertson, Edmund F. 8407:Mathematics Magazine 8387:Woepcke, F. (1853). 8221:Mathematics Magazine 8181:Historia Mathematica 7969:Raju, C. K. (2001). 7876:Plofker 2009 182–207 7584:Bronkhorst, Johannes 7501:D'Ambrosio, Ubiratan 6130:www.math.buffalo.edu 6099:www.math.buffalo.edu 5996:Eglash, Ron (1999). 5919:Historia Mathematica 5589:Juschkewitsch, A. P. 5404:Historia Mathematica 5332:Kenneth O. May Prize 5305:Prehistoric counting 5157:announced the seven 5074:mock theta functions 4953:symbolic computation 4893:Derrick Henry Lehmer 4885:computability theory 4844:, rehabilitated the 4632:continuum hypothesis 4571:Klein's encyclopedia 4462:hypercomplex numbers 4442:Abel–Ruffini theorem 4289:Carl Friedrich Gauss 4282:Carl Friedrich Gauss 4194:improve this article 4148:Pierre-Simon Laplace 4131:{\displaystyle \pi } 4122: 3885:imaginary quantities 3828:mathematical puzzles 3787:Museo di Capodimonte 2889:, and explained the 2859:In the 7th century, 2847:Muslim mathematician 2681:Bakhshali manuscript 2649:theorem comes from. 2549:Japanese mathematics 2443:Gaussian elimination 2306:multiplication table 2128:The creation of the 2075:Categories of Fields 1923:Anthemius of Tralles 1870:Pappus configuration 1858:Pappus of Alexandria 1846:Anthemius of Tralles 1702:Hipparchus of Nicaea 1567:method of exhaustion 1541:method of exhaustion 1539:Archimedes used the 1459:. It was there that 1407:method of exhaustion 1276:is sometimes called 1143:cosmological signs. 1091:Egyptian mathematics 977:Egyptian mathematics 846:), may be more than 842:river (northeastern 477:through the work of 365:c. 1800 BC) and the 123:Discrete mathematics 14159:Approximations of π 14070:By ancient cultures 13724:Veterinary medicine 13418:Classical Antiquity 13185:Al-Azhar University 13112:The Book of Healing 12518:Al-Ḥajjāj ibn Yūsuf 12375:Islamic mathematics 12334:Walter Eugene Clark 12128:Vasishtha Siddhanta 12100:Siddhānta Shiromani 12079:Paitamaha Siddhanta 11958:Tilak Raj Prabhakar 11903:Satyendra Nath Bose 11898:Srinivasa Ramanujan 11852:Nilakantha Somayaji 11583:Mathematics and art 11493:Operations research 11248:Functional analysis 10897:V. Frederick Rickey 10783:Stigler, Stephen M. 10720:Corry, Leo (2015), 10496:1981SciAm.245d.188S 10484:Scientific American 10290:Ancient Mathematics 9819:2005math......5125B 9535:2016Natur.531..287C 9319:1895Natur..52..545M 8758:Heeffer, Albrecht: 8462:O'Connor, John J.; 8080:1992Isis...83..554P 7511:. pp. 411–12. 7149:, pp. 188–200) 5910:Powell, M. (1976), 5595:. Teubner, Leipzig. 5493:1931Natur.128..739T 5265:History of geometry 5250:History of calculus 5163:Poincaré conjecture 4933:operations research 4931:and other areas of 4866:combinatorial games 4864:in connection with 4860:were discovered by 4792:distribution theory 4784:functional analysis 4436:, a Norwegian, and 4356:Riemannian geometry 4344:hyperbolic geometry 4156:celestial mechanics 4072:. Pascal, with his 4050:applied mathematics 3700:Mathematics and art 3679:University of Paris 3655:and the concept of 3578:Arnald of Villanova 3550:positional notation 3548:) which due to the 3511:Herman of Carinthia 3367:that flourished in 3309:, the beginning of 3293:'s introduction of 2865:Brahmagupta theorem 2818:Explanation of the 2744:Pythagorean theorem 2439:Pythagorean theorem 2250:Chinese mathematics 2067:, one of the Roman 2030:the Greek precedent 2018:applied mathematics 1894:Christian community 1890:Theon of Alexandria 1713:Heron of Alexandria 1652:Apollonius of Perga 1641:Apollonius of Perga 1573:under the arc of a 1335:Pythagorean theorem 1304:Pythagoras of Samos 1289:deductive reasoning 1285:inductive reasoning 1274:Alexander the Great 1249:Pythagorean theorem 1223:Berlin Papyrus 6619 1136:Islamic mathematics 1075:Pythagorean theorem 1067:quadratic equations 1014:, dated to 1800 BC. 958:Islamic mathematics 895:Pythagorean triples 545: 475:Islamic mathematics 451:Chinese mathematics 419:applied mathematics 377:Pythagorean theorem 373:Pythagorean triples 57:Part of a series on 13962:Information theory 13359:History of science 13317:History of algebra 13272:Indian mathematics 13246:Indian mathematics 13195:House of Knowledge 12649:Brethren of Purity 12543:Banū Mūsā brothers 11867:Gangesha Upadhyaya 11688:Indian mathematics 11528:Numerical analysis 11137:Mathematical logic 11132:Information theory 11006:2009-05-25 at the 10981:2006-10-04 at the 10960:2020-09-08 at the 10821:The Story of Maths 10761:Menninger, Karl W. 10601:Men of Mathematics 10310:, Hoboken: Wiley, 10226:de Crespigny, Rafe 9997:The New York Times 9715:Notices of the AMS 9499:Notices of the AMS 9084:10.1007/BF00357046 8823:2018-01-26 at the 8331:. pp. 11–12. 7427:, pp. 156–57) 7414:, pp. 154–55) 7401:, pp. 153–56) 7327:, pp. 100–01) 7270:, pp. 99–100) 7123:, pp. 281–85) 7032:, pp. 119–20) 7019:, pp. 207–08) 6993:, pp. 120–21) 6980:, pp. 192–95) 6292:(7 January 2014). 5888:2018-07-07 at the 5846:The Sumerian World 5429:. pp. 1–191. 5427:Dover Publications 5295:History of numbers 5240:History of algebra 5221:Mathematics portal 5066:partition function 5047: 4949:numerical analysis 4917:information theory 4862:John Horton Conway 4808:catastrophe theory 4800:singularity theory 4796:fixed point theory 4778:greatly expanded. 4768:probability theory 4740:algebraic geometry 4724:topological spaces 4700:mathematical logic 4696:general relativity 4685: 4612:four color theorem 4600: 4597:Four Color Theorem 4584:set out a list of 4547:vector controversy 4543:Quaternion Society 4492:mathematical logic 4407:mathematical logic 4332:parallel postulate 4324: 4285: 4128: 4096: 4062:probability theory 3953: 3905:real number system 3847:Scipione del Ferro 3791: 3783:Jacopo de' Barbari 3749:linear perspective 3683:Giovanni di Casali 3649:William Heytesbury 3645:Oxford Calculators 3569:Thomas Bradwardine 3560:Fibonacci sequence 3357: 3319:algebraic notation 3311:algebraic geometry 3299:frequency analysis 3289:besides the sine, 3256:parallel postulate 3233:parallel postulate 3140:irrational numbers 3088:Indian mathematics 3055:, and in parts of 3033: 2959:transformed series 2911:Fibonacci sequence 2829: 2685: 2659:Indian mathematics 2615: 2553:Korean mathematics 2400: 2362:(470–390 BC). The 2319: 2284: 2170:Gregorian calendar 1982: 1927:Isidore of Miletus 1854: 1850:Isidore of Miletus 1787: 1777:, translated into 1649: 1549: 1530:spherical geometry 1498:Euclidean geometry 1482:mathematical rigor 1449: 1339:irrational numbers 1331:Pythagorean School 1293:mathematical rigor 1257: 1227:algebraic equation 1116:Hellenistic period 1105: 1016: 973: 934:Hellenistic period 865:Alexander Marshack 816:patterns in nature 624:(Persian and Urdu) 544:Table of numerals 543: 455:place value system 403:mathematical rigor 224:Mathematics Portal 52: 14197: 14196: 14033:Separation axioms 13804: 13803: 13696:Materials science 13658:Political science 13423:Medieval European 13325: 13324: 13241:Greek mathematics 13164:Alhazen's problem 13058: 13057: 12679:Ibrahim ibn Sinan 12629:Sinān ibn al-Fatḥ 12446: 12445: 12252:Sudhakara Dvivedi 12072:Paulisa Siddhanta 11991: 11990: 11847:Jagannatha Samrat 11842:Achyuta Pisharati 11654: 11653: 11253:Harmonic analysis 10989:History/Biography 10796:978-0-674-40341-3 10789:. Belknap Press. 10774:978-0-262-13040-0 10634:978-0-8018-7397-3 10563:978-0-19-921312-2 10544:978-88-8265-305-7 10475:978-0-521-05803-2 10457:978-0-521-05801-8 10432:978-0-691-11485-9 10414:978-0-321-01618-8 10353:978-0-393-04002-9 10317:978-1-119-10497-1 10299:978-0-415-16495-5 10281:978-0-471-54397-8 10258:978-0-387-20571-7 10249:Pi: A Source Book 10239:978-90-04-15605-0 10196:Rieley, Michael. 10171:Nations, United. 9977:978-0-8247-1550-2 9705:Ono, Ken (2006). 9680:978-0-8218-3967-6 9369:978-0-8218-4774-9 9313:(1353): 545–546. 9201:978-0-393-32030-5 8978:978-0-486-60255-4 8929:978-0-393-32030-5 8665:978-1-4027-5796-9 8529:", pp. 135–54 in 8338:978-0-7923-2565-9 8175:(November 2001). 7827:. Wiley. p. 7685:978-0-8493-7189-9 7518:978-1-4020-0260-1 7363:978-0-7637-5995-7 7294:de Crespigny 2007 7218:, pp. 91–92) 7192:, pp. 194–99 7110:, pp. 18–19) 7084:, pp. 17–18) 6077:"Egyptian Papyri" 5863:978-0-203-09660-4 5690:978-1-59102-477-4 5624:, "Origins" p. 3) 5436:978-0-486-22332-2 5406:, 8, pp. 277–318. 4961:simplex algorithm 4921:signal processing 4889:complexity theory 4854:Hyperreal numbers 4780:Quantum mechanics 4760:Lebesgue integral 4748:dynamical systems 4648:Kepler conjecture 4537:in 1883, and the 4434:Niels Henrik Abel 4383:Hermann Grassmann 4348:Elliptic geometry 4297:complex variables 4270: 4269: 4262: 4244: 4010:. Independently, 3985:analytic geometry 3869:quartic equations 3840:Summa Arithmetica 3832:Summa Arithmetica 3735:compound interest 3663:be described by 3515:Gerard of Cremona 3499:Robert of Chester 3407:Medieval European 3365:Maya civilization 3303:analytic geometry 3248:Nasir al-Din Tusi 3231:, especially the 3167:Pascal's triangle 2915:Pascal's triangle 2905:'s commentary on 2850:Abu Rayhan Biruni 2790:Fibonacci numbers 2639:Gottfried Leibniz 2635:integral calculus 2516:Pascal's triangle 2471:gave a value of π 2465:commented on the 2398:(2nd century AD). 2174:Pope Gregory XIII 2123:opus vermiculatum 2034:Etruscan numerals 1911:Academy of Athens 1868:, as well as the 1764:Ptolemy's theorem 1743:Menelaus' theorem 1569:to calculate the 1518:wrote extensively 1396:Eudoxus of Cnidus 1378:mensa Pythagorica 1300:Thales of Miletus 1269:Academy of Athens 1265:Thales of Miletus 1263:from the time of 1239:Greek mathematics 1112:Egyptian language 802: 801: 663: 625: 552: 483:Maya civilization 399:Greek mathematics 258: 257: 213: 212: 16:(Redirected from 14222: 14187: 14186: 13907:Category theory 13831: 13824: 13817: 13808: 13807: 13797: 13793: 13792: 13785: 13781: 13770: 13769: 13691:Computer science 13539:Natural sciences 13504:Medieval Islamic 13400: 13352: 13345: 13338: 13329: 13328: 13140:Tabula Rogeriana 13066: 13014:Sibt al-Maridini 12674:Sinan ibn Thabit 12583:Abu Said Gorgani 12573:Thābit ibn Qurra 12563:Ishaq ibn Hunayn 12548:Hunayn ibn Ishaq 12493: 12492: 12473: 12466: 12459: 12450: 12449: 12086:Romaka Siddhanta 11968:Akshay Venkatesh 11938:M. S. Narasimhan 11908:P.C. Mahalanobis 11701: 11700: 11681: 11674: 11667: 11658: 11657: 11642: 11641: 11630: 11629: 11618: 11617: 11607: 11606: 11538:Computer algebra 11513:Computer science 11233:Complex analysis 11067: 11060: 11053: 11044: 11043: 10800: 10778: 10756: 10734: 10691: 10677: 10638: 10610:Burton, David M. 10606: 10604: 10590: 10566: 10548: 10527: 10507: 10478: 10460: 10435: 10417: 10403:(2nd ed.), 10393: 10356: 10345: 10334: 10328: 10320: 10302: 10284: 10261: 10243: 10212: 10211: 10209: 10208: 10193: 10187: 10186: 10184: 10183: 10168: 10162: 10161: 10159: 10158: 10144: 10138: 10137: 10135: 10134: 10120: 10114: 10113: 10111: 10109: 10104:. 22 August 2006 10092: 10086: 10085: 10066:10.1038/35013216 10045: 10039: 10038: 10036: 10034: 10029: 10021: 10015: 10014: 10012: 10011: 9988: 9982: 9980: 9960: 9954: 9953: 9951: 9950: 9944:sites.google.com 9936: 9930: 9929: 9889: 9883: 9882: 9875: 9869: 9868: 9828: 9822: 9821: 9812: 9796: 9790: 9789: 9773: 9767: 9766: 9746: 9730: 9724: 9723: 9711: 9702: 9683: 9660: 9654: 9653: 9651: 9650: 9636: 9630: 9629: 9627: 9625: 9608: 9602: 9601: 9569: 9563: 9562: 9514: 9508: 9507: 9495: 9486: 9480: 9479: 9469: 9445: 9439: 9438: 9418: 9409: 9403: 9402: 9400: 9398: 9389: 9380: 9374: 9373: 9353: 9347: 9346: 9327:10.1038/052545a0 9304: 9295: 9289: 9288: 9278: 9254: 9248: 9247: 9221: 9212: 9206: 9205: 9185: 9179: 9178: 9176: 9175: 9161: 9155: 9154: 9152: 9151: 9137: 9131: 9130: 9110: 9104: 9103: 9063: 9057: 9056: 9054: 9053: 9038: 9032: 9028: 9022: 9007: 9001: 9000: 8989: 8983: 8982: 8958: 8952: 8951: 8940: 8934: 8933: 8915: 8909: 8908: 8860: 8854: 8834: 8828: 8814: 8808: 8801: 8795: 8792:Trattato d'Abaco 8788: 8782: 8775: 8769: 8764:Ghent University 8756: 8750: 8739: 8733: 8726: 8720: 8713: 8707: 8700: 8694: 8687: 8681: 8680: 8676:Johann Bernoulli 8646: 8640: 8629: 8623: 8616: 8610: 8595: 8589: 8586: 8580: 8573: 8567: 8557: 8551: 8544: 8538: 8519: 8513: 8507: 8501: 8494: 8481: 8480: 8459: 8453: 8452: 8446: 8440:Alam, S (2015). 8437: 8431: 8430: 8402: 8396: 8385: 8379: 8372: 8366: 8365: 8357: 8351: 8350: 8320: 8314: 8291: 8285: 8277: 8271: 8264: 8258: 8251: 8245: 8244: 8218: 8209: 8203: 8202: 8196: 8169: 8163: 8162: 8131: 8125: 8124: 8060: 8054: 8053: 8047: 8039: 8027: 8021: 8014: 8008: 8007: 8005: 8004: 7975: 7966: 7960: 7957: 7951: 7950: 7948: 7947: 7933: 7927: 7916: 7910: 7909: 7883: 7877: 7874: 7868: 7867: 7853:Surya Siddhanata 7826: 7813: 7807: 7800: 7794: 7787: 7781: 7774: 7765: 7758: 7752: 7751: 7725: 7716: 7710: 7696: 7690: 7689: 7671: 7665: 7664: 7638: 7629:(5–6): 487–520. 7618: 7612: 7611: 7580: 7574: 7573: 7565: 7556: 7555: 7553: 7538: 7529: 7523: 7522: 7492: 7486: 7479: 7466: 7459: 7453: 7447: 7441: 7434: 7428: 7421: 7415: 7408: 7402: 7395: 7389: 7382: 7371: 7369:Extract of p. 27 7367: 7347: 7341: 7334: 7328: 7321: 7315: 7308: 7297: 7290: 7284: 7277: 7271: 7264: 7258: 7251: 7245: 7238: 7232: 7225: 7219: 7212: 7206: 7199: 7193: 7187: 7181: 7174: 7163: 7156: 7150: 7143: 7137: 7130: 7124: 7117: 7111: 7104: 7098: 7091: 7085: 7078: 7072: 7065: 7059: 7052: 7046: 7039: 7033: 7026: 7020: 7013: 7007: 7000: 6994: 6987: 6981: 6974: 6968: 6961: 6955: 6948: 6942: 6935: 6929: 6922: 6916: 6909: 6903: 6902: 6891: 6885: 6878: 6872: 6865: 6859: 6852: 6843: 6836: 6830: 6823: 6817: 6810: 6804: 6797: 6791: 6784: 6778: 6761: 6755: 6748: 6742: 6735: 6726: 6719: 6713: 6706: 6700: 6693: 6687: 6680: 6674: 6667: 6661: 6654: 6648: 6641: 6635: 6628: 6622: 6615: 6609: 6602: 6593: 6586: 6580: 6573: 6567: 6548: 6542: 6535: 6526: 6519: 6513: 6512: 6510: 6509: 6494: 6488: 6481: 6475: 6468: 6462: 6455: 6449: 6442: 6436: 6429: 6423: 6422: 6420: 6413: 6404: 6398: 6391: 6382: 6375: 6369: 6354: 6348: 6333: 6327: 6326: 6324: 6322: 6309: 6286: 6277: 6276: 6248: 6242: 6241: 6233: 6227: 6212: 6206: 6199: 6193: 6186: 6180: 6173: 6167: 6160: 6154: 6140: 6134: 6133: 6122: 6116: 6115:, "Egypt" p. 19) 6109: 6103: 6102: 6091: 6085: 6084: 6073: 6067: 6062: 6056: 6050: 6044: 6043:, "Egypt" p. 11) 6037: 6031: 6030: 6018: 6012: 6011: 5993: 5987: 5980: 5974: 5967: 5961: 5960: 5949: 5943: 5936: 5930: 5929: 5928: 5926: 5916: 5907: 5901: 5879: 5873: 5872: 5871: 5870: 5837: 5831: 5824: 5815: 5808: 5797: 5790: 5777: 5770: 5764: 5763: 5761: 5760: 5735: 5729: 5714: 5708: 5701: 5695: 5694: 5670: 5664: 5657: 5651: 5650: 5648: 5647: 5631: 5625: 5618: 5609: 5602: 5596: 5586: 5580: 5574: 5568: 5561: 5555: 5548: 5542: 5535: 5526: 5519: 5513: 5512: 5501:10.1038/128739a0 5476: 5470: 5468: 5462: 5458: 5456: 5448: 5417:Neugebauer, Otto 5413: 5407: 5400: 5394: 5387: 5372: 5369: 5275:History of logic 5235:Ethnomathematics 5223: 5218: 5217: 5167:Grigori Perelman 5100:Kevin Bacon Game 5086:divergent series 5059: 5028:cannot be proved 5004:Peano arithmetic 4842:Abraham Robinson 4840:, introduced by 4788:Laurent Schwartz 4708:John von Neumann 4671:Nicolas Bourbaki 4630:proved that the 4508:Bertrand Russell 4494:in the hands of 4473:abstract algebra 4427:Karl Weierstrass 4423:Bernhard Riemann 4415:computer science 4379:abstract algebra 4352:Bernhard Riemann 4265: 4258: 4254: 4251: 4245: 4243: 4202: 4178: 4170: 4137: 4135: 4134: 4129: 4116: 4054:Pierre de Fermat 4034:, including the 3901:decimal notation 3873:Lodovico Ferrari 3859:Gerolamo Cardano 3681:and the Italian 3622: 3603:armillary sphere 3591: 3281:notation to the 3260:Ghiyath al-Kashi 3163:binomial theorem 3149:in his treatise 3031:(c. AD 820) 2934:Narayana Pandita 2786:binomial theorem 2754:Sanskrit grammar 2709: 2695: 2530:(AD 1238–1298). 2357: 2354: 2223: 2221: 2212: 2208: 2205: 2182: 2181: 1572–1585 2180: 2119:opus tessellatum 1919:Byzantine empire 1866:centroid theorem 1819:Pierre de Fermat 1761: 1758: 1736: 1733: 1721: 1718: 1710: 1707: 1687: 1684: 1660: 1657: 1615: 1614: 1612: 1611: 1608: 1605: 1598: 1596: 1595: 1592: 1589: 1560: 1557: 1486:axiomatic method 1469: 1466: 1427: 1424: 1388:Platonic Academy 1202:, also from the 1193:geometric series 1185:linear equations 1045: 1044: 981:Cuneiform script 661: 623: 550: 546: 542: 459:negative numbers 355:– 1900 BC), the 354: 351: 312:for purposes of 250: 243: 236: 222: 86: 85: 54: 53: 49: 46: 21: 14230: 14229: 14225: 14224: 14223: 14221: 14220: 14219: 14200: 14199: 14198: 14193: 14175: 14137: 14118:Brouwer–Hilbert 14106: 14065: 14044:Numeral systems 14039: 13901:Grandi's series 13845: 13835: 13805: 13800: 13788: 13776: 13758: 13705: 13672: 13630:Social sciences 13624: 13571: 13533: 13457: 13401: 13392: 13361: 13356: 13326: 13321: 13293:Arabic numerals 13276: 13250: 13224: 13200:House of Wisdom 13173: 13152: 13074: 13067: 13054: 13023: 12967: 12953:Ibn al-Durayhim 12931: 12850: 12816:Jabir ibn Aflah 12804: 12735:Abu Nasr Mansur 12723: 12619:Ahmad ibn Yusuf 12587: 12482: 12477: 12447: 12442: 12390: 12384: 12348: 12322: 12293:C. T. Rajagopal 12240:Bapudeva Sastri 12232: 12226: 12188: 12168:Brahmi numerals 12160: 12154: 12114:Surya Siddhanta 11987: 11963:Manjul Bhargava 11886: 11745: 11690: 11685: 11655: 11650: 11601: 11592: 11542: 11499: 11478:Systems science 11409: 11405:Homotopy theory 11371: 11338: 11290: 11262: 11209: 11156: 11127:Category theory 11113: 11078: 11071: 11039:(Roberta Tucci) 11008:Wayback Machine 10983:Wayback Machine 10962:Wayback Machine 10944: 10932: 10916: 10841: 10812: 10807: 10797: 10775: 10753: 10732: 10716: 10665: 10635: 10578: 10573: 10571:Further reading 10564: 10545: 10476: 10458: 10440:Needham, Joseph 10433: 10415: 10354: 10322: 10321: 10318: 10300: 10282: 10259: 10240: 10221: 10216: 10215: 10206: 10204: 10194: 10190: 10181: 10179: 10169: 10165: 10156: 10154: 10146: 10145: 10141: 10132: 10130: 10122: 10121: 10117: 10107: 10105: 10094: 10093: 10089: 10046: 10042: 10032: 10030: 10027: 10023: 10022: 10018: 10009: 10007: 9989: 9985: 9978: 9961: 9957: 9948: 9946: 9938: 9937: 9933: 9910:10.2307/2317868 9890: 9886: 9877: 9876: 9872: 9849:10.2307/2321202 9829: 9825: 9797: 9793: 9774: 9770: 9744: 9731: 9727: 9709: 9703: 9686: 9661: 9657: 9648: 9646: 9638: 9637: 9633: 9623: 9621: 9618:Quanta Magazine 9609: 9605: 9570: 9566: 9515: 9511: 9493: 9487: 9483: 9460:(10): 437–479. 9446: 9442: 9416: 9410: 9406: 9396: 9394: 9387: 9381: 9377: 9370: 9354: 9350: 9302: 9296: 9292: 9255: 9251: 9219: 9213: 9209: 9202: 9186: 9182: 9173: 9171: 9163: 9162: 9158: 9149: 9147: 9139: 9138: 9134: 9111: 9107: 9064: 9060: 9051: 9049: 9039: 9035: 9029: 9025: 9008: 9004: 8997:people.idsia.ch 8991: 8990: 8986: 8979: 8959: 8955: 8941: 8937: 8930: 8922:. W.W. Norton. 8916: 8912: 8861: 8857: 8835: 8831: 8825:Wayback Machine 8815: 8811: 8802: 8798: 8789: 8785: 8776: 8772: 8757: 8753: 8740: 8736: 8727: 8723: 8714: 8710: 8701: 8697: 8688: 8684: 8666: 8647: 8643: 8630: 8626: 8617: 8613: 8596: 8592: 8587: 8583: 8574: 8570: 8558: 8554: 8545: 8541: 8531:Margaret Gibson 8520: 8516: 8508: 8504: 8495: 8484: 8460: 8456: 8444: 8438: 8434: 8419:10.2307/2691411 8403: 8399: 8386: 8382: 8373: 8369: 8358: 8354: 8339: 8321: 8317: 8292: 8288: 8278: 8274: 8265: 8261: 8252: 8248: 8233:10.2307/2691411 8216: 8210: 8206: 8170: 8166: 8151:10.2307/1558972 8135:Bressoud, David 8132: 8128: 8061: 8057: 8041: 8040: 8028: 8024: 8020:35, pp. 417–33. 8015: 8011: 8002: 8000: 7973: 7967: 7963: 7958: 7954: 7945: 7943: 7935: 7934: 7930: 7917: 7913: 7906: 7884: 7880: 7875: 7871: 7839: 7815: 7814: 7810: 7801: 7797: 7788: 7784: 7775: 7768: 7759: 7755: 7723: 7717: 7713: 7697: 7693: 7686: 7672: 7668: 7636:10.1.1.565.2083 7619: 7615: 7581: 7577: 7566: 7559: 7551: 7536: 7530: 7526: 7519: 7493: 7489: 7480: 7469: 7460: 7456: 7448: 7444: 7435: 7431: 7422: 7418: 7409: 7405: 7396: 7392: 7383: 7374: 7364: 7348: 7344: 7335: 7331: 7322: 7318: 7309: 7300: 7296:, p. 1050) 7291: 7287: 7278: 7274: 7265: 7261: 7252: 7248: 7239: 7235: 7226: 7222: 7213: 7209: 7200: 7196: 7188: 7184: 7175: 7166: 7157: 7153: 7144: 7140: 7131: 7127: 7118: 7114: 7105: 7101: 7092: 7088: 7079: 7075: 7066: 7062: 7053: 7049: 7040: 7036: 7027: 7023: 7014: 7010: 7001: 6997: 6988: 6984: 6975: 6971: 6962: 6958: 6949: 6945: 6936: 6932: 6923: 6919: 6910: 6906: 6893: 6892: 6888: 6879: 6875: 6866: 6862: 6853: 6846: 6837: 6833: 6824: 6820: 6811: 6807: 6798: 6794: 6785: 6781: 6762: 6758: 6749: 6745: 6736: 6729: 6720: 6716: 6707: 6703: 6694: 6690: 6681: 6677: 6668: 6664: 6655: 6651: 6642: 6638: 6629: 6625: 6616: 6612: 6603: 6596: 6587: 6583: 6574: 6570: 6549: 6545: 6536: 6529: 6520: 6516: 6507: 6505: 6495: 6491: 6482: 6478: 6469: 6465: 6456: 6452: 6443: 6439: 6430: 6426: 6418: 6411: 6405: 6401: 6392: 6385: 6376: 6372: 6355: 6351: 6334: 6330: 6320: 6318: 6287: 6280: 6265:10.2307/3026893 6249: 6245: 6234: 6230: 6213: 6209: 6200: 6196: 6187: 6183: 6174: 6170: 6161: 6157: 6141: 6137: 6124: 6123: 6119: 6110: 6106: 6093: 6092: 6088: 6075: 6074: 6070: 6063: 6059: 6051: 6047: 6038: 6034: 6019: 6015: 6008: 5994: 5990: 5981: 5977: 5968: 5964: 5950: 5946: 5937: 5933: 5924: 5922: 5914: 5908: 5904: 5890:Wayback Machine 5880: 5876: 5868: 5866: 5864: 5838: 5834: 5825: 5818: 5809: 5800: 5791: 5780: 5771: 5767: 5758: 5756: 5754: 5736: 5732: 5715: 5711: 5702: 5698: 5691: 5671: 5667: 5658: 5654: 5645: 5643: 5632: 5628: 5619: 5612: 5603: 5599: 5587: 5583: 5575: 5571: 5562: 5558: 5549: 5545: 5536: 5529: 5520: 5516: 5477: 5473: 5460: 5459: 5450: 5449: 5437: 5414: 5410: 5401: 5397: 5388: 5381: 5376: 5375: 5370: 5366: 5361: 5356: 5219: 5212: 5209: 5192: 5186: 5151: 5145: 5078:gamma functions 5057: 4992:natural numbers 4858:surreal numbers 4728:category theory 4692:Albert Einstein 4566: 4458:parameter space 4438:Évariste Galois 4403:Boolean algebra 4275: 4266: 4255: 4249: 4246: 4203: 4201: 4191: 4179: 4168: 4123: 4120: 4119: 4112: 4086: 3969:Johannes Kepler 3943: 3938: 3932: 3877:Rafael Bombelli 3855:cubic equations 3702: 3696: 3641: 3640: 3639: 3638: 3637: 3634:Arabic numerals 3623: 3615: 3614: 3611:harmonic series 3592: 3507:Adelard of Bath 3444:) that God had 3425: 3419: 3409: 3383:of twenty, the 3373:Central America 3342: 3283:Arabic numerals 3241:calendar reform 3237:cubic equations 3116:elementary form 3092:Indian numerals 3015: 3009: 3003: 3001:Islamic empires 2991:differentiation 2899:Brahmi numerals 2895:Arabic numerals 2863:identified the 2831:Around 500 AD, 2758:transformations 2717: 2716: 2715: 2714: 2713: 2710: 2701: 2700: 2699: 2696: 2673: 2667: 2661: 2655: 2607: 2597: 2589:private schools 2512:Precious Mirror 2508:Horner's method 2435:right triangles 2415:of 212 BC, the 2355: 2290:Zhoubi Suanjing 2264: 2258: 2252: 2246: 2218: 2210: 2206: 2188:the Han Chinese 2177: 2150:Julian calendar 2103:Arts and crafts 2065:Siculus Flaccus 1992:and subsequent 1949: 1939: 1913:by the emperor 1862:hexagon theorem 1759: 1734: 1724:Heron's formula 1719: 1708: 1685: 1658: 1609: 1606: 1603: 1602: 1600: 1593: 1590: 1587: 1586: 1584: 1582: 1558: 1467: 1425: 1400:analytic method 1327:Thales' Theorem 1295:to prove them. 1241: 1235: 1093: 1087: 1071:cubic equations 1052:regular numbers 1042: 1040: 915: 909: 903: 828:hunter-gatherer 808: 803: 525:increasing pace 510:Medieval Europe 491:Central America 447:arts and crafts 443:solar calendars 352: 254: 209: 208: 159: 151: 150: 146:Decision theory 94: 47: 23: 22: 15: 12: 11: 5: 14228: 14218: 14217: 14212: 14195: 14194: 14192: 14191: 14180: 14177: 14176: 14174: 14173: 14168: 14167: 14166: 14156: 14155: 14154: 14145: 14143: 14139: 14138: 14136: 14135: 14130: 14128:Leibniz–Newton 14125: 14120: 14114: 14112: 14108: 14107: 14105: 14104: 14099: 14094: 14089: 14087:Ancient Greece 14084: 14079: 14073: 14071: 14067: 14066: 14064: 14063: 14058: 14053: 14047: 14045: 14041: 14040: 14038: 14037: 14036: 14035: 14030: 14029: 14028: 14015: 14014: 14013: 14008: 13998: 13997: 13996: 13990:Number theory 13988: 13983: 13982: 13981: 13971: 13970: 13969: 13959: 13954: 13953: 13952: 13947: 13937: 13936: 13935: 13925: 13920: 13919: 13918: 13913: 13905: 13904: 13903: 13898: 13888: 13887: 13886: 13876: 13875: 13874: 13866: 13865: 13864: 13853: 13851: 13847: 13846: 13834: 13833: 13826: 13819: 13811: 13802: 13801: 13799: 13798: 13786: 13774: 13763: 13760: 13759: 13757: 13756: 13751: 13746: 13741: 13736: 13731: 13726: 13721: 13719:Human medicine 13715: 13713: 13707: 13706: 13704: 13703: 13698: 13693: 13688: 13682: 13680: 13674: 13673: 13671: 13670: 13665: 13660: 13655: 13650: 13645: 13640: 13634: 13632: 13626: 13625: 13623: 13622: 13617: 13612: 13607: 13602: 13597: 13592: 13587: 13581: 13579: 13573: 13572: 13570: 13569: 13564: 13559: 13554: 13549: 13543: 13541: 13535: 13534: 13532: 13531: 13526: 13521: 13516: 13511: 13506: 13501: 13496: 13491: 13486: 13481: 13476: 13471: 13465: 13463: 13459: 13458: 13456: 13455: 13450: 13445: 13440: 13435: 13430: 13425: 13420: 13415: 13409: 13407: 13403: 13402: 13395: 13393: 13391: 13390: 13385: 13380: 13378:Historiography 13375: 13369: 13367: 13363: 13362: 13355: 13354: 13347: 13340: 13332: 13323: 13322: 13320: 13319: 13314: 13309: 13304: 13290: 13284: 13282: 13278: 13277: 13275: 13274: 13269: 13264: 13258: 13256: 13252: 13251: 13249: 13248: 13243: 13238: 13232: 13230: 13226: 13225: 13223: 13222: 13217: 13212: 13207: 13202: 13197: 13192: 13187: 13181: 13179: 13175: 13174: 13172: 13171: 13166: 13160: 13158: 13154: 13153: 13151: 13150: 13143: 13136: 13133:Toledan Tables 13129: 13122: 13115: 13108: 13105:Book of Optics 13101: 13094: 13087: 13079: 13077: 13069: 13068: 13061: 13059: 13056: 13055: 13053: 13052: 13047: 13042: 13037: 13031: 13029: 13025: 13024: 13022: 13021: 13016: 13011: 13006: 13001: 12996: 12991: 12986: 12981: 12975: 12973: 12969: 12968: 12966: 12965: 12960: 12955: 12950: 12945: 12939: 12937: 12933: 12932: 12930: 12929: 12924: 12919: 12914: 12909: 12904: 12899: 12894: 12889: 12884: 12879: 12874: 12869: 12864: 12858: 12856: 12852: 12851: 12849: 12848: 12846:Ibn al-Yasamin 12843: 12838: 12833: 12828: 12823: 12818: 12812: 12810: 12806: 12805: 12803: 12802: 12797: 12792: 12787: 12782: 12777: 12772: 12767: 12762: 12757: 12752: 12747: 12745:Kushyar Gilani 12742: 12737: 12731: 12729: 12725: 12724: 12722: 12721: 12716: 12711: 12706: 12701: 12696: 12691: 12689:Nazif ibn Yumn 12686: 12681: 12676: 12671: 12666: 12661: 12656: 12651: 12646: 12641: 12636: 12631: 12626: 12621: 12616: 12611: 12606: 12601: 12595: 12593: 12589: 12588: 12586: 12585: 12580: 12575: 12570: 12568:Na'im ibn Musa 12565: 12560: 12558:Yusuf al-Khuri 12555: 12550: 12545: 12540: 12535: 12530: 12528:Qusta ibn Luqa 12525: 12520: 12515: 12510: 12505: 12499: 12497: 12490: 12488:Mathematicians 12484: 12483: 12476: 12475: 12468: 12461: 12453: 12444: 12443: 12441: 12440: 12435: 12430: 12425: 12420: 12415: 12410: 12405: 12400: 12394: 12392: 12386: 12385: 12383: 12382: 12377: 12372: 12367: 12362: 12356: 12354: 12350: 12349: 12347: 12346: 12341: 12336: 12330: 12328: 12324: 12323: 12321: 12320: 12314: 12308: 12302: 12296: 12290: 12284: 12278: 12273: 12267: 12264:P. C. Sengupta 12261: 12255: 12249: 12243: 12236: 12234: 12228: 12227: 12225: 12224: 12202: 12196: 12194: 12190: 12189: 12187: 12186: 12181: 12175: 12170: 12164: 12162: 12156: 12155: 12153: 12152: 12145: 12138: 12131: 12124: 12121:Tantrasamgraha 12117: 12110: 12103: 12096: 12089: 12082: 12075: 12068: 12061: 12054: 12047: 12044:Karanapaddhati 12040: 12033: 12030:Ganita Kaumudi 12026: 12019: 12012: 12007: 11999: 11997: 11993: 11992: 11989: 11988: 11986: 11985: 11980: 11975: 11970: 11965: 11960: 11955: 11950: 11948:Harish-Chandra 11945: 11943:C. S. Seshadri 11940: 11935: 11930: 11925: 11920: 11915: 11910: 11905: 11900: 11894: 11892: 11888: 11887: 11885: 11884: 11879: 11877:Sankara Variar 11874: 11869: 11864: 11859: 11854: 11849: 11844: 11839: 11834: 11829: 11824: 11819: 11814: 11809: 11804: 11799: 11794: 11789: 11784: 11779: 11774: 11769: 11764: 11759: 11753: 11751: 11747: 11746: 11744: 11743: 11738: 11733: 11728: 11723: 11718: 11713: 11707: 11705: 11698: 11696:Mathematicians 11692: 11691: 11684: 11683: 11676: 11669: 11661: 11652: 11651: 11649: 11648: 11636: 11624: 11612: 11597: 11594: 11593: 11591: 11590: 11585: 11580: 11575: 11570: 11565: 11564: 11563: 11556:Mathematicians 11552: 11550: 11548:Related topics 11544: 11543: 11541: 11540: 11535: 11530: 11525: 11520: 11515: 11509: 11507: 11501: 11500: 11498: 11497: 11496: 11495: 11490: 11485: 11483:Control theory 11475: 11470: 11465: 11460: 11455: 11450: 11445: 11440: 11435: 11430: 11425: 11419: 11417: 11411: 11410: 11408: 11407: 11402: 11397: 11392: 11387: 11381: 11379: 11373: 11372: 11370: 11369: 11364: 11359: 11354: 11348: 11346: 11340: 11339: 11337: 11336: 11331: 11326: 11321: 11316: 11311: 11306: 11300: 11298: 11292: 11291: 11289: 11288: 11283: 11278: 11272: 11270: 11264: 11263: 11261: 11260: 11258:Measure theory 11255: 11250: 11245: 11240: 11235: 11230: 11225: 11219: 11217: 11211: 11210: 11208: 11207: 11202: 11197: 11192: 11187: 11182: 11177: 11172: 11166: 11164: 11158: 11157: 11155: 11154: 11149: 11144: 11139: 11134: 11129: 11123: 11121: 11115: 11114: 11112: 11111: 11106: 11101: 11100: 11099: 11094: 11083: 11080: 11079: 11070: 11069: 11062: 11055: 11047: 11041: 11040: 11034: 11033:(Bruno Kevius) 11028: 11023: 11017: 11011: 10998: 10992: 10986: 10973: 10952: 10943: 10940: 10939: 10938: 10931: 10928: 10927: 10926: 10915: 10914:Bibliographies 10912: 10911: 10910: 10904: 10901:Victor J. Katz 10890: 10884: 10878: 10872: 10866: 10860: 10854: 10848: 10840: 10837: 10836: 10835: 10834:, Jun 2, 2005) 10825: 10811: 10808: 10806: 10805:External links 10803: 10802: 10801: 10795: 10779: 10773: 10757: 10751: 10735: 10731:978-0198702597 10730: 10715: 10712: 10711: 10710: 10692: 10678: 10664: 10661: 10660: 10659: 10649: 10639: 10633: 10617: 10616:. McGraw Hill. 10607: 10591: 10577: 10574: 10572: 10569: 10568: 10567: 10562: 10549: 10543: 10528: 10508: 10490:(4): 188–200, 10479: 10474: 10461: 10456: 10436: 10431: 10418: 10413: 10405:Addison-Wesley 10394: 10374:10.2307/505056 10357: 10352: 10335: 10316: 10303: 10298: 10285: 10280: 10262: 10257: 10244: 10238: 10220: 10217: 10214: 10213: 10188: 10177:United Nations 10163: 10139: 10115: 10087: 10040: 10016: 9983: 9976: 9955: 9931: 9884: 9870: 9843:(5): 346–359. 9823: 9791: 9768: 9725: 9684: 9655: 9631: 9603: 9564: 9509: 9481: 9440: 9404: 9375: 9368: 9348: 9290: 9249: 9230:(2): 135–150. 9207: 9200: 9180: 9156: 9132: 9105: 9078:(3): 253–277. 9058: 9033: 9023: 9002: 8984: 8977: 8953: 8935: 8928: 8910: 8881:10.1086/346940 8875:(1): 153–244. 8855: 8829: 8809: 8796: 8783: 8770: 8751: 8734: 8721: 8708: 8695: 8682: 8672:Pietro Mengoli 8664: 8641: 8624: 8611: 8590: 8581: 8568: 8552: 8539: 8514: 8502: 8500:, p. 121) 8482: 8454: 8432: 8397: 8380: 8367: 8352: 8337: 8315: 8286: 8272: 8259: 8246: 8204: 8164: 8126: 8088:10.1086/356288 8074:(4): 554–563. 8064:Pingree, David 8055: 8022: 8009: 7984:(3): 325–362. 7961: 7952: 7928: 7911: 7904: 7878: 7869: 7837: 7808: 7795: 7782: 7766: 7753: 7711: 7691: 7684: 7666: 7613: 7594:(1–2): 43–80. 7575: 7557: 7554:on 2012-02-06. 7524: 7517: 7497:Selin, Helaine 7487: 7467: 7454: 7442: 7440:, p. 155) 7429: 7416: 7403: 7390: 7372: 7362: 7342: 7329: 7316: 7298: 7285: 7272: 7259: 7257:, p. 164) 7246: 7233: 7220: 7207: 7194: 7182: 7164: 7151: 7138: 7136:, p. 285) 7125: 7112: 7099: 7086: 7073: 7060: 7058:, p. 256) 7047: 7034: 7021: 7008: 7006:, p. 196) 6995: 6982: 6969: 6956: 6954:, p. 119) 6943: 6930: 6917: 6904: 6886: 6873: 6860: 6844: 6831: 6818: 6805: 6792: 6779: 6756: 6743: 6727: 6714: 6701: 6688: 6675: 6662: 6649: 6636: 6623: 6610: 6594: 6581: 6568: 6543: 6527: 6514: 6498:Bill Casselman 6489: 6476: 6463: 6450: 6437: 6424: 6421:on 2015-10-15. 6399: 6383: 6370: 6349: 6347:, pp. 58, 129. 6328: 6278: 6259:(5): 312–316. 6243: 6228: 6207: 6194: 6181: 6168: 6155: 6135: 6117: 6104: 6086: 6068: 6057: 6045: 6032: 6013: 6006: 5988: 5975: 5962: 5944: 5931: 5902: 5874: 5862: 5832: 5816: 5798: 5778: 5765: 5752: 5730: 5709: 5696: 5689: 5665: 5652: 5626: 5610: 5597: 5581: 5569: 5556: 5543: 5527: 5514: 5471: 5461:|journal= 5435: 5408: 5395: 5378: 5377: 5374: 5373: 5363: 5362: 5360: 5357: 5355: 5354: 5349: 5344: 5339: 5334: 5329: 5324: 5319: 5314: 5309: 5308: 5307: 5302: 5292: 5287: 5282: 5277: 5272: 5267: 5262: 5257: 5252: 5247: 5242: 5237: 5232: 5226: 5225: 5224: 5208: 5205: 5188:Main article: 5185: 5182: 5165:was solved by 5161:. In 2003 the 5144: 5141: 5137:World Wide Web 5043:absolute value 5006:, was in fact 4977:control theory 4913:Claude Shannon 4772:ergodic theory 4756:Measure theory 4659:Jean Dieudonné 4604:Wolfgang Haken 4565: 4562: 4558:p-adic numbers 4512:A.N. Whitehead 4500:L.E.J. Brouwer 4274: 4271: 4268: 4267: 4182: 4180: 4173: 4167: 4164: 4127: 4100:Leonhard Euler 4093:Leonhard Euler 4085: 4082: 4078:utility theory 4028:discrete logic 3989:René Descartes 3961:Hans Lipperhey 3942: 3939: 3931: 3928: 3879:published his 3836:plus and minus 3745:solid geometry 3723:abacus schools 3695: 3692: 3630:Roman numerals 3624: 3617: 3616: 3593: 3586: 3585: 3584: 3583: 3582: 3544:(specifically 3538:Roman numerals 3441:Book of Wisdom 3408: 3405: 3397:Maya astronomy 3341: 3338: 3334:Safavid Empire 3330:Ottoman Empire 3307:Ibn al-Haytham 3198:Ibn al-Haytham 3037:Islamic Empire 3005:Main article: 3002: 2999: 2939:Ganita Kaumudi 2936:completed his 2852:described the 2711: 2704: 2703: 2702: 2697: 2690: 2689: 2688: 2687: 2686: 2657:Main article: 2654: 2651: 2647:Soddy's hexlet 2596: 2593: 2479:the value of π 2427:Chinese pagoda 2280:Warring States 2248:Main article: 2245: 2242: 2154:solar calendar 2142:lunar calendar 2130:Roman calendar 2057:managing taxes 2028:directly from 2002:Ancient Romans 1990:Roman Republic 1947:Roman numerals 1938: 1935: 1663:conic sections 1645:conic sections 1630:exponentiation 1599:< π < 3+ 1522:conic sections 1514:solid geometry 1370:British Museum 1357:mathematician 1355:Neopythagorean 1261:Greek language 1237:Main article: 1234: 1231: 1212:story problems 1204:Middle Kingdom 1200:Moscow papyrus 1173:harmonic means 1152:Middle Kingdom 1089:Main article: 1086: 1083: 1024:numeral system 905:Main article: 902: 899: 807: 804: 800: 799: 796: 793: 790: 787: 784: 781: 778: 775: 772: 769: 765: 764: 761: 758: 755: 752: 749: 746: 743: 740: 737: 734: 730: 729: 726: 723: 720: 717: 714: 711: 708: 705: 702: 699: 695: 694: 691: 688: 685: 682: 679: 676: 673: 670: 667: 664: 657: 656: 653: 650: 647: 644: 641: 638: 635: 632: 629: 626: 619: 618: 615: 612: 609: 606: 603: 600: 597: 594: 591: 588: 584: 583: 580: 577: 574: 571: 568: 565: 562: 559: 556: 553: 541: 437:, creation of 415:ancient Romans 256: 255: 253: 252: 245: 238: 230: 227: 226: 215: 214: 211: 210: 207: 206: 201: 196: 191: 186: 181: 176: 171: 166: 160: 157: 156: 153: 152: 149: 148: 139: 134: 125: 120: 111: 106: 101: 95: 90: 89: 82: 81: 80: 79: 74: 66: 65: 59: 58: 9: 6: 4: 3: 2: 14227: 14216: 14213: 14211: 14208: 14207: 14205: 14190: 14182: 14181: 14178: 14172: 14169: 14165: 14162: 14161: 14160: 14157: 14153: 14150: 14149: 14147: 14146: 14144: 14140: 14134: 14133:Hobbes–Wallis 14131: 14129: 14126: 14124: 14121: 14119: 14116: 14115: 14113: 14111:Controversies 14109: 14103: 14100: 14098: 14095: 14093: 14090: 14088: 14085: 14083: 14082:Ancient Egypt 14080: 14078: 14075: 14074: 14072: 14068: 14062: 14059: 14057: 14054: 14052: 14049: 14048: 14046: 14042: 14034: 14031: 14027: 14024: 14023: 14022: 14019: 14018: 14016: 14012: 14009: 14007: 14004: 14003: 14002: 13999: 13995: 13992: 13991: 13989: 13987: 13986:Math notation 13984: 13980: 13977: 13976: 13975: 13972: 13968: 13965: 13964: 13963: 13960: 13958: 13955: 13951: 13948: 13946: 13943: 13942: 13941: 13938: 13934: 13931: 13930: 13929: 13926: 13924: 13923:Combinatorics 13921: 13917: 13914: 13912: 13909: 13908: 13906: 13902: 13899: 13897: 13894: 13893: 13892: 13889: 13885: 13882: 13881: 13880: 13877: 13873: 13870: 13869: 13867: 13863: 13860: 13859: 13858: 13855: 13854: 13852: 13848: 13843: 13839: 13832: 13827: 13825: 13820: 13818: 13813: 13812: 13809: 13796: 13787: 13784: 13780: 13775: 13773: 13765: 13764: 13761: 13755: 13752: 13750: 13747: 13745: 13742: 13740: 13737: 13735: 13732: 13730: 13727: 13725: 13722: 13720: 13717: 13716: 13714: 13712: 13708: 13702: 13699: 13697: 13694: 13692: 13689: 13687: 13684: 13683: 13681: 13679: 13675: 13669: 13666: 13664: 13661: 13659: 13656: 13654: 13651: 13649: 13646: 13644: 13641: 13639: 13636: 13635: 13633: 13631: 13627: 13621: 13618: 13616: 13613: 13611: 13608: 13606: 13603: 13601: 13598: 13596: 13595:Combinatorics 13593: 13591: 13588: 13586: 13583: 13582: 13580: 13578: 13574: 13568: 13565: 13563: 13562:Earth science 13560: 13558: 13555: 13553: 13550: 13548: 13545: 13544: 13542: 13540: 13536: 13530: 13527: 13525: 13522: 13520: 13517: 13515: 13512: 13510: 13507: 13505: 13502: 13500: 13497: 13495: 13492: 13490: 13487: 13485: 13482: 13480: 13477: 13475: 13472: 13470: 13467: 13466: 13464: 13460: 13454: 13451: 13449: 13446: 13444: 13441: 13439: 13436: 13434: 13431: 13429: 13426: 13424: 13421: 13419: 13416: 13414: 13413:Ancient world 13411: 13410: 13408: 13404: 13399: 13389: 13386: 13384: 13383:Pseudoscience 13381: 13379: 13376: 13374: 13371: 13370: 13368: 13364: 13360: 13353: 13348: 13346: 13341: 13339: 13334: 13333: 13330: 13318: 13315: 13313: 13310: 13308: 13305: 13302: 13298: 13294: 13291: 13289: 13286: 13285: 13283: 13279: 13273: 13270: 13268: 13265: 13263: 13260: 13259: 13257: 13253: 13247: 13244: 13242: 13239: 13237: 13234: 13233: 13231: 13227: 13221: 13218: 13216: 13213: 13211: 13208: 13206: 13203: 13201: 13198: 13196: 13193: 13191: 13188: 13186: 13183: 13182: 13180: 13176: 13170: 13167: 13165: 13162: 13161: 13159: 13155: 13149: 13148: 13144: 13142: 13141: 13137: 13135: 13134: 13130: 13128: 13127: 13123: 13121: 13120: 13116: 13114: 13113: 13109: 13107: 13106: 13102: 13100: 13099: 13095: 13093: 13092: 13088: 13086: 13085: 13081: 13080: 13078: 13076: 13070: 13065: 13051: 13048: 13046: 13043: 13041: 13038: 13036: 13033: 13032: 13030: 13026: 13020: 13017: 13015: 13012: 13010: 13007: 13005: 13002: 13000: 12997: 12995: 12992: 12990: 12987: 12985: 12982: 12980: 12977: 12976: 12974: 12970: 12964: 12961: 12959: 12956: 12954: 12951: 12949: 12948:Ibn al-Shatir 12946: 12944: 12941: 12940: 12938: 12934: 12928: 12925: 12923: 12922:Ibn al-Banna' 12920: 12918: 12915: 12913: 12910: 12908: 12905: 12903: 12900: 12898: 12895: 12893: 12890: 12888: 12885: 12883: 12880: 12878: 12875: 12873: 12870: 12868: 12867:Ahmad al-Buni 12865: 12863: 12860: 12859: 12857: 12853: 12847: 12844: 12842: 12839: 12837: 12834: 12832: 12829: 12827: 12824: 12822: 12819: 12817: 12814: 12813: 12811: 12807: 12801: 12798: 12796: 12793: 12791: 12788: 12786: 12783: 12781: 12778: 12776: 12773: 12771: 12768: 12766: 12763: 12761: 12758: 12756: 12753: 12751: 12748: 12746: 12743: 12741: 12738: 12736: 12733: 12732: 12730: 12726: 12720: 12717: 12715: 12712: 12710: 12707: 12705: 12702: 12700: 12697: 12695: 12692: 12690: 12687: 12685: 12682: 12680: 12677: 12675: 12672: 12670: 12667: 12665: 12662: 12660: 12657: 12655: 12652: 12650: 12647: 12645: 12642: 12640: 12637: 12635: 12632: 12630: 12627: 12625: 12622: 12620: 12617: 12615: 12612: 12610: 12607: 12605: 12602: 12600: 12597: 12596: 12594: 12590: 12584: 12581: 12579: 12576: 12574: 12571: 12569: 12566: 12564: 12561: 12559: 12556: 12554: 12551: 12549: 12546: 12544: 12541: 12539: 12536: 12534: 12531: 12529: 12526: 12524: 12521: 12519: 12516: 12514: 12511: 12509: 12508:Sanad ibn Ali 12506: 12504: 12501: 12500: 12498: 12494: 12491: 12489: 12485: 12481: 12474: 12469: 12467: 12462: 12460: 12455: 12454: 12451: 12439: 12436: 12434: 12431: 12429: 12426: 12424: 12421: 12419: 12416: 12414: 12411: 12409: 12406: 12404: 12401: 12399: 12396: 12395: 12393: 12387: 12381: 12378: 12376: 12373: 12371: 12368: 12366: 12363: 12361: 12358: 12357: 12355: 12353:Other regions 12351: 12345: 12344:David Pingree 12342: 12340: 12337: 12335: 12332: 12331: 12329: 12325: 12318: 12315: 12312: 12309: 12306: 12303: 12300: 12297: 12294: 12291: 12288: 12285: 12282: 12279: 12277: 12274: 12271: 12268: 12265: 12262: 12259: 12258:M. Rangacarya 12256: 12253: 12250: 12247: 12244: 12241: 12238: 12237: 12235: 12231:Historians of 12229: 12222: 12218: 12214: 12210: 12206: 12205:Jantar Mantar 12203: 12201: 12198: 12197: 12195: 12191: 12185: 12182: 12180: 12176: 12174: 12171: 12169: 12166: 12165: 12163: 12157: 12151: 12150: 12146: 12144: 12143: 12139: 12137: 12136: 12132: 12130: 12129: 12125: 12123: 12122: 12118: 12116: 12115: 12111: 12109: 12108: 12104: 12102: 12101: 12097: 12095: 12094: 12090: 12088: 12087: 12083: 12081: 12080: 12076: 12074: 12073: 12069: 12067: 12066: 12062: 12060: 12059: 12055: 12053: 12052: 12048: 12046: 12045: 12041: 12039: 12038: 12034: 12032: 12031: 12027: 12025: 12024: 12020: 12018: 12017: 12013: 12011: 12008: 12006: 12005: 12001: 12000: 11998: 11994: 11984: 11981: 11979: 11976: 11974: 11971: 11969: 11966: 11964: 11961: 11959: 11956: 11954: 11951: 11949: 11946: 11944: 11941: 11939: 11936: 11934: 11931: 11929: 11926: 11924: 11921: 11919: 11916: 11914: 11911: 11909: 11906: 11904: 11901: 11899: 11896: 11895: 11893: 11889: 11883: 11880: 11878: 11875: 11873: 11870: 11868: 11865: 11863: 11860: 11858: 11855: 11853: 11850: 11848: 11845: 11843: 11840: 11838: 11835: 11833: 11830: 11828: 11825: 11823: 11822:Mahendra Sūri 11820: 11818: 11815: 11813: 11810: 11808: 11805: 11803: 11800: 11798: 11795: 11793: 11790: 11788: 11785: 11783: 11780: 11778: 11775: 11773: 11770: 11768: 11765: 11763: 11760: 11758: 11755: 11754: 11752: 11748: 11742: 11739: 11737: 11734: 11732: 11729: 11727: 11724: 11722: 11719: 11717: 11714: 11712: 11709: 11708: 11706: 11702: 11699: 11697: 11693: 11689: 11682: 11677: 11675: 11670: 11668: 11663: 11662: 11659: 11647: 11646: 11637: 11635: 11634: 11625: 11623: 11622: 11613: 11611: 11610: 11605: 11599: 11598: 11595: 11589: 11586: 11584: 11581: 11579: 11576: 11574: 11571: 11569: 11566: 11562: 11559: 11558: 11557: 11554: 11553: 11551: 11549: 11545: 11539: 11536: 11534: 11531: 11529: 11526: 11524: 11521: 11519: 11516: 11514: 11511: 11510: 11508: 11506: 11505:Computational 11502: 11494: 11491: 11489: 11486: 11484: 11481: 11480: 11479: 11476: 11474: 11471: 11469: 11466: 11464: 11461: 11459: 11456: 11454: 11451: 11449: 11446: 11444: 11441: 11439: 11436: 11434: 11431: 11429: 11426: 11424: 11421: 11420: 11418: 11416: 11412: 11406: 11403: 11401: 11398: 11396: 11393: 11391: 11388: 11386: 11383: 11382: 11380: 11378: 11374: 11368: 11365: 11363: 11360: 11358: 11355: 11353: 11350: 11349: 11347: 11345: 11344:Number theory 11341: 11335: 11332: 11330: 11327: 11325: 11322: 11320: 11317: 11315: 11312: 11310: 11307: 11305: 11302: 11301: 11299: 11297: 11293: 11287: 11284: 11282: 11279: 11277: 11276:Combinatorics 11274: 11273: 11271: 11269: 11265: 11259: 11256: 11254: 11251: 11249: 11246: 11244: 11241: 11239: 11236: 11234: 11231: 11229: 11228:Real analysis 11226: 11224: 11221: 11220: 11218: 11216: 11212: 11206: 11203: 11201: 11198: 11196: 11193: 11191: 11188: 11186: 11183: 11181: 11178: 11176: 11173: 11171: 11168: 11167: 11165: 11163: 11159: 11153: 11150: 11148: 11145: 11143: 11140: 11138: 11135: 11133: 11130: 11128: 11125: 11124: 11122: 11120: 11116: 11110: 11107: 11105: 11102: 11098: 11095: 11093: 11090: 11089: 11088: 11085: 11084: 11081: 11076: 11068: 11063: 11061: 11056: 11054: 11049: 11048: 11045: 11038: 11035: 11032: 11029: 11027: 11024: 11021: 11018: 11015: 11012: 11009: 11005: 11002: 10999: 10996: 10993: 10990: 10987: 10984: 10980: 10977: 10974: 10971: 10967: 10963: 10959: 10956: 10953: 10951: 10950: 10946: 10945: 10937: 10934: 10933: 10930:Organizations 10924: 10921: 10918: 10917: 10908: 10905: 10902: 10898: 10894: 10891: 10888: 10885: 10882: 10879: 10876: 10873: 10870: 10867: 10864: 10861: 10858: 10855: 10852: 10849: 10846: 10843: 10842: 10833: 10829: 10826: 10823: 10822: 10817: 10814: 10813: 10810:Documentaries 10798: 10792: 10788: 10784: 10780: 10776: 10770: 10767:. MIT Press. 10766: 10762: 10758: 10754: 10752:0-7868-6362-5 10748: 10744: 10740: 10739:Hoffman, Paul 10736: 10733: 10727: 10723: 10718: 10717: 10708: 10707:0-387-12159-5 10704: 10700: 10696: 10693: 10689: 10688: 10683: 10679: 10675: 10671: 10667: 10666: 10657: 10653: 10652:Struik, D. J. 10650: 10647: 10643: 10642:Kline, Morris 10640: 10636: 10630: 10626: 10622: 10618: 10615: 10611: 10608: 10603: 10602: 10596: 10592: 10588: 10584: 10580: 10579: 10565: 10559: 10555: 10550: 10546: 10540: 10536: 10535: 10529: 10526: 10522: 10519:(3): 163–81, 10518: 10514: 10509: 10505: 10501: 10497: 10493: 10489: 10485: 10480: 10477: 10471: 10467: 10462: 10459: 10453: 10449: 10445: 10441: 10437: 10434: 10428: 10424: 10419: 10416: 10410: 10406: 10402: 10401: 10395: 10391: 10387: 10383: 10379: 10375: 10371: 10368:(3): 253–63, 10367: 10363: 10358: 10355: 10349: 10344: 10343: 10336: 10332: 10326: 10319: 10313: 10309: 10304: 10301: 10295: 10291: 10286: 10283: 10277: 10273: 10272: 10267: 10263: 10260: 10254: 10250: 10245: 10241: 10235: 10231: 10227: 10223: 10222: 10203: 10199: 10192: 10178: 10174: 10167: 10153: 10149: 10143: 10129: 10125: 10119: 10103: 10102: 10097: 10091: 10083: 10079: 10075: 10071: 10067: 10063: 10060:(6785): 383. 10059: 10055: 10051: 10044: 10026: 10020: 10006: 10002: 9998: 9994: 9987: 9979: 9973: 9969: 9965: 9959: 9945: 9941: 9935: 9927: 9923: 9919: 9915: 9911: 9907: 9903: 9899: 9895: 9888: 9880: 9874: 9866: 9862: 9858: 9854: 9850: 9846: 9842: 9838: 9834: 9827: 9820: 9816: 9811: 9806: 9802: 9795: 9787: 9783: 9779: 9772: 9764: 9760: 9756: 9752: 9751: 9743: 9739: 9735: 9729: 9722:(6): 640–651. 9721: 9717: 9716: 9708: 9701: 9699: 9697: 9695: 9693: 9691: 9689: 9681: 9677: 9676:0-8218-3967-5 9673: 9669: 9665: 9659: 9645: 9641: 9635: 9620: 9619: 9614: 9607: 9599: 9595: 9591: 9587: 9583: 9579: 9575: 9568: 9560: 9556: 9552: 9548: 9544: 9540: 9536: 9532: 9529:(7594): 287. 9528: 9524: 9520: 9513: 9505: 9501: 9500: 9492: 9485: 9477: 9473: 9468: 9463: 9459: 9455: 9451: 9444: 9436: 9432: 9428: 9424: 9423: 9415: 9408: 9393: 9386: 9379: 9371: 9365: 9361: 9360: 9352: 9344: 9340: 9336: 9332: 9328: 9324: 9320: 9316: 9312: 9308: 9301: 9294: 9286: 9282: 9277: 9272: 9268: 9264: 9260: 9253: 9245: 9241: 9237: 9233: 9229: 9225: 9218: 9211: 9203: 9197: 9193: 9192: 9184: 9170: 9169:Maths History 9166: 9160: 9146: 9142: 9136: 9128: 9124: 9120: 9116: 9109: 9101: 9097: 9093: 9089: 9085: 9081: 9077: 9073: 9069: 9062: 9048: 9044: 9037: 9027: 9020: 9019:0-03-029558-0 9016: 9012: 9006: 8998: 8994: 8988: 8980: 8974: 8970: 8966: 8965: 8957: 8949: 8945: 8944:Kline, Morris 8939: 8931: 8925: 8921: 8914: 8906: 8902: 8898: 8894: 8890: 8886: 8882: 8878: 8874: 8870: 8866: 8859: 8853: 8849: 8846: 8842: 8838: 8837:Roshdi Rashed 8833: 8826: 8822: 8819: 8813: 8806: 8800: 8793: 8787: 8780: 8774: 8768: 8765: 8761: 8755: 8748: 8744: 8738: 8731: 8725: 8718: 8712: 8705: 8699: 8692: 8686: 8679: 8677: 8673: 8667: 8661: 8657: 8656: 8651: 8645: 8638: 8634: 8628: 8621: 8615: 8608: 8607:0-521-32260-X 8604: 8600: 8594: 8585: 8578: 8572: 8565: 8561: 8556: 8549: 8543: 8536: 8532: 8528: 8524: 8518: 8511: 8506: 8499: 8493: 8491: 8489: 8487: 8479: 8475: 8474: 8469: 8465: 8458: 8450: 8443: 8436: 8428: 8424: 8420: 8416: 8413:(3): 163–74. 8412: 8408: 8401: 8394: 8390: 8384: 8378:, pp. 255–59) 8377: 8371: 8363: 8356: 8348: 8344: 8340: 8334: 8330: 8326: 8319: 8312: 8308: 8304: 8300: 8296: 8290: 8282: 8276: 8269: 8263: 8256: 8250: 8242: 8238: 8234: 8230: 8227:(3): 163–74. 8226: 8222: 8215: 8208: 8201: 8195: 8190: 8186: 8182: 8178: 8174: 8168: 8160: 8156: 8152: 8148: 8144: 8140: 8136: 8130: 8123: 8120: 8116: 8112: 8111:Charles Whish 8105: 8101: 8097: 8093: 8089: 8085: 8081: 8077: 8073: 8069: 8065: 8059: 8051: 8045: 8037: 8033: 8026: 8019: 8013: 7999: 7995: 7991: 7987: 7983: 7979: 7972: 7965: 7956: 7942: 7941:Maths History 7938: 7932: 7925: 7921: 7915: 7907: 7905:0-471-18082-3 7901: 7897: 7893: 7889: 7882: 7873: 7866: 7864: 7863: 7858: 7854: 7850: 7846: 7840: 7838:9780471543978 7834: 7830: 7825: 7824: 7818: 7812: 7805: 7799: 7792: 7786: 7779: 7773: 7771: 7763: 7757: 7749: 7745: 7741: 7737: 7733: 7729: 7728:Math Horizons 7722: 7715: 7709: 7708:0-387-94544-X 7705: 7701: 7695: 7687: 7681: 7677: 7670: 7662: 7658: 7654: 7650: 7646: 7642: 7637: 7632: 7628: 7624: 7617: 7609: 7605: 7601: 7597: 7593: 7589: 7585: 7579: 7571: 7564: 7562: 7550: 7546: 7542: 7535: 7528: 7520: 7514: 7510: 7506: 7502: 7498: 7491: 7484: 7478: 7476: 7474: 7472: 7464: 7458: 7451: 7446: 7439: 7433: 7426: 7420: 7413: 7407: 7400: 7394: 7387: 7381: 7379: 7377: 7370: 7365: 7359: 7355: 7354: 7346: 7339: 7333: 7326: 7320: 7313: 7307: 7305: 7303: 7295: 7289: 7283:, p. 27) 7282: 7276: 7269: 7263: 7256: 7255:Straffin 1998 7250: 7244:, p. 22) 7243: 7237: 7231:, p. 94) 7230: 7224: 7217: 7211: 7204: 7198: 7191: 7186: 7179: 7173: 7171: 7169: 7161: 7155: 7148: 7147:Sleeswyk 1981 7142: 7135: 7129: 7122: 7116: 7109: 7108:Gullberg 1997 7103: 7097:, p. 18) 7096: 7095:Gullberg 1997 7090: 7083: 7082:Gullberg 1997 7077: 7071:, p. 17) 7070: 7069:Gullberg 1997 7064: 7057: 7051: 7044: 7038: 7031: 7025: 7018: 7012: 7005: 6999: 6992: 6986: 6979: 6973: 6966: 6960: 6953: 6947: 6940: 6934: 6927: 6921: 6914: 6908: 6900: 6896: 6890: 6883: 6877: 6870: 6864: 6857: 6851: 6849: 6841: 6835: 6828: 6822: 6815: 6809: 6802: 6796: 6789: 6783: 6777: 6776:1-904275-25-7 6773: 6769: 6766: 6760: 6753: 6747: 6740: 6734: 6732: 6724: 6718: 6711: 6705: 6698: 6692: 6685: 6679: 6672: 6666: 6659: 6653: 6646: 6640: 6633: 6627: 6620: 6614: 6607: 6601: 6599: 6591: 6585: 6578: 6572: 6565: 6561: 6560:0-03-029558-0 6557: 6553: 6547: 6540: 6534: 6532: 6524: 6518: 6503: 6499: 6493: 6486: 6480: 6473: 6467: 6460: 6454: 6447: 6441: 6434: 6428: 6417: 6410: 6403: 6396: 6390: 6388: 6380: 6374: 6367: 6366:0-486-20429-4 6363: 6359: 6353: 6346: 6345:0-486-20429-4 6342: 6338: 6332: 6317: 6313: 6308: 6303: 6299: 6295: 6291: 6285: 6283: 6274: 6270: 6266: 6262: 6258: 6254: 6247: 6239: 6232: 6225: 6224:0-03-029558-0 6221: 6217: 6211: 6204: 6198: 6191: 6185: 6178: 6172: 6165: 6159: 6153: 6152:0-03-029558-0 6149: 6145: 6139: 6131: 6127: 6121: 6114: 6108: 6100: 6096: 6090: 6082: 6078: 6072: 6066: 6061: 6054: 6049: 6042: 6036: 6028: 6024: 6017: 6009: 6003: 5999: 5992: 5985: 5979: 5972: 5966: 5958: 5954: 5948: 5941: 5935: 5920: 5913: 5906: 5899: 5895: 5891: 5887: 5884: 5878: 5865: 5859: 5855: 5851: 5847: 5843: 5836: 5829: 5823: 5821: 5813: 5807: 5805: 5803: 5795: 5789: 5787: 5785: 5783: 5775: 5769: 5755: 5749: 5745: 5741: 5734: 5727: 5726:0-521-33381-4 5723: 5719: 5713: 5706: 5700: 5692: 5686: 5682: 5678: 5677: 5669: 5662: 5656: 5641: 5637: 5630: 5623: 5617: 5615: 5607: 5601: 5594: 5590: 5585: 5579: 5573: 5566: 5560: 5553: 5547: 5540: 5534: 5532: 5524: 5518: 5510: 5506: 5502: 5498: 5494: 5490: 5486: 5482: 5475: 5466: 5454: 5446: 5442: 5438: 5432: 5428: 5424: 5423: 5418: 5412: 5405: 5399: 5392: 5386: 5384: 5379: 5368: 5364: 5353: 5350: 5348: 5345: 5343: 5340: 5338: 5335: 5333: 5330: 5328: 5325: 5323: 5320: 5318: 5315: 5313: 5310: 5306: 5303: 5301: 5298: 5297: 5296: 5293: 5291: 5288: 5286: 5283: 5281: 5278: 5276: 5273: 5271: 5268: 5266: 5263: 5261: 5258: 5256: 5253: 5251: 5248: 5246: 5243: 5241: 5238: 5236: 5233: 5231: 5228: 5227: 5222: 5216: 5211: 5204: 5202: 5198: 5191: 5181: 5179: 5175: 5170: 5168: 5164: 5160: 5156: 5153:In 2000, the 5150: 5140: 5138: 5134: 5130: 5125: 5123: 5119: 5115: 5111: 5107: 5105: 5101: 5097: 5093: 5091: 5087: 5083: 5082:modular forms 5079: 5075: 5071: 5067: 5063: 5056: 5052: 5044: 5039: 5035: 5033: 5032:David Hilbert 5029: 5025: 5021: 5017: 5013: 5012:number theory 5009: 5005: 5001: 4997: 4993: 4988: 4986: 4982: 4981:RSA algorithm 4978: 4974: 4973:Kalman filter 4970: 4966: 4962: 4958: 4954: 4950: 4946: 4942: 4941:combinatorics 4938: 4934: 4930: 4926: 4925:data analysis 4922: 4918: 4914: 4910: 4906: 4902: 4898: 4894: 4890: 4886: 4882: 4878: 4874: 4869: 4867: 4863: 4859: 4855: 4851: 4847: 4846:infinitesimal 4843: 4839: 4835: 4833: 4829: 4825: 4821: 4817: 4813: 4809: 4805: 4801: 4797: 4793: 4789: 4785: 4781: 4777: 4773: 4769: 4765: 4761: 4757: 4753: 4749: 4745: 4741: 4737: 4733: 4729: 4725: 4721: 4720:metric spaces 4717: 4713: 4709: 4705: 4701: 4697: 4693: 4689: 4683: 4678: 4674: 4672: 4668: 4664: 4660: 4656: 4651: 4649: 4645: 4641: 4637: 4633: 4629: 4625: 4621: 4617: 4613: 4609: 4608:Kenneth Appel 4605: 4598: 4593: 4589: 4587: 4583: 4582:David Hilbert 4579: 4574: 4572: 4561: 4559: 4555: 4550: 4548: 4544: 4540: 4536: 4533:in 1884, the 4532: 4529:in 1872, the 4528: 4525:in 1865, the 4524: 4519: 4517: 4513: 4509: 4505: 4504:David Hilbert 4501: 4497: 4493: 4489: 4485: 4480: 4478: 4474: 4470: 4465: 4463: 4459: 4455: 4451: 4447: 4443: 4439: 4435: 4430: 4428: 4424: 4420: 4416: 4412: 4408: 4404: 4400: 4396: 4392: 4388: 4387:vector spaces 4384: 4380: 4375: 4373: 4369: 4365: 4361: 4357: 4353: 4349: 4345: 4341: 4337: 4333: 4329: 4320: 4316: 4314: 4310: 4306: 4302: 4298: 4294: 4290: 4283: 4279: 4264: 4261: 4253: 4242: 4239: 4235: 4232: 4228: 4225: 4221: 4218: 4214: 4211: – 4210: 4206: 4205:Find sources: 4199: 4195: 4189: 4188: 4183:This section 4181: 4177: 4172: 4171: 4163: 4161: 4157: 4153: 4149: 4145: 4140: 4125: 4117: 4115: 4109: 4105: 4101: 4094: 4090: 4081: 4079: 4075: 4071: 4067: 4066:combinatorics 4063: 4059: 4058:Blaise Pascal 4055: 4051: 4046: 4043: 4041: 4037: 4033: 4029: 4025: 4021: 4017: 4016:binary number 4013: 4009: 4005: 4004:Kepler's Laws 4001: 3996: 3994: 3990: 3987:developed by 3986: 3982: 3978: 3974: 3970: 3966: 3962: 3958: 3951: 3947: 3937: 3927: 3923: 3921: 3920:Trigonometria 3917: 3913: 3908: 3906: 3902: 3898: 3897: 3892: 3888: 3886: 3882: 3878: 3874: 3870: 3866: 3865: 3860: 3856: 3852: 3848: 3843: 3841: 3837: 3833: 3829: 3825: 3821: 3817: 3813: 3809: 3805: 3801: 3800: 3795: 3788: 3784: 3780: 3779: 3774: 3770: 3768: 3766: 3761: 3757: 3755: 3750: 3746: 3742: 3738: 3736: 3732: 3728: 3724: 3720: 3716: 3711: 3707: 3701: 3691: 3689: 3684: 3680: 3676: 3675:Nicole Oresme 3672: 3668: 3666: 3662: 3658: 3654: 3650: 3646: 3635: 3631: 3627: 3621: 3612: 3608: 3604: 3600: 3596: 3595:Nicole Oresme 3590: 3581: 3579: 3575: 3570: 3566: 3563: 3561: 3557: 3556: 3551: 3547: 3543: 3539: 3535: 3531: 3527: 3523: 3518: 3516: 3512: 3508: 3504: 3500: 3496: 3495: 3490: 3486: 3481: 3479: 3475: 3471: 3467: 3463: 3459: 3458: 3453: 3449: 3447: 3443: 3442: 3437: 3436: 3431: 3424: 3418: 3414: 3404: 3402: 3398: 3394: 3393:Maya calendar 3390: 3386: 3382: 3378: 3377:Maya numerals 3374: 3370: 3366: 3362: 3355: 3351: 3350:Maya numerals 3346: 3337: 3335: 3331: 3326: 3324: 3320: 3316: 3312: 3308: 3304: 3300: 3296: 3295:cryptanalysis 3292: 3288: 3284: 3280: 3279:decimal point 3275: 3273: 3269: 3265: 3261: 3257: 3253: 3249: 3244: 3242: 3238: 3234: 3230: 3229: 3223: 3219: 3214: 3212: 3211:fourth degree 3208: 3204: 3199: 3196:into Arabic. 3195: 3191: 3187: 3184: 3180: 3176: 3172: 3168: 3164: 3160: 3156: 3152: 3148: 3143: 3141: 3137: 3132: 3129: 3125: 3121: 3117: 3113: 3109: 3108: 3103: 3099: 3098: 3093: 3089: 3085: 3081: 3077: 3073: 3068: 3066: 3062: 3058: 3054: 3050: 3046: 3042: 3038: 3030: 3026: 3025: 3019: 3014: 3008: 2998: 2996: 2992: 2988: 2984: 2980: 2976: 2972: 2968: 2964: 2960: 2956: 2952: 2948: 2943: 2941: 2940: 2935: 2931: 2927: 2922: 2920: 2916: 2912: 2908: 2904: 2900: 2896: 2892: 2888: 2887:decimal digit 2884: 2880: 2879: 2874: 2870: 2866: 2862: 2857: 2855: 2851: 2848: 2844: 2840: 2839: 2834: 2827: 2826: 2821: 2816: 2812: 2810: 2806: 2802: 2797: 2795: 2791: 2787: 2783: 2779: 2778:combinatorics 2775: 2771: 2767: 2763: 2759: 2755: 2751: 2747: 2745: 2741: 2737: 2733: 2728: 2726: 2722: 2708: 2694: 2682: 2677: 2672: 2666: 2660: 2650: 2648: 2642: 2640: 2636: 2632: 2628: 2627:Seki Takakazu 2624: 2620: 2611: 2606: 2605:Seki Takakazu 2602: 2592: 2590: 2586: 2582: 2578: 2574: 2570: 2566: 2562: 2558: 2554: 2550: 2546: 2544: 2540: 2536: 2531: 2529: 2525: 2524:magic circles 2521: 2517: 2513: 2509: 2505: 2501: 2500: 2495: 2490: 2488: 2484: 2480: 2476: 2472: 2468: 2467:Nine Chapters 2464: 2460: 2456: 2452: 2448: 2444: 2440: 2436: 2432: 2428: 2424: 2423: 2418: 2414: 2409: 2405: 2404:Qin Shi Huang 2397: 2393: 2392: 2387: 2383: 2381: 2377: 2373: 2369: 2368:circumference 2365: 2361: 2356: 330 BC 2350: 2345: 2343: 2339: 2335: 2331: 2330: 2325: 2317: 2313: 2309: 2307: 2304: 2300: 2296: 2292: 2291: 2281: 2277: 2273: 2268: 2263: 2257: 2251: 2241: 2239: 2235: 2231: 2228:found in the 2227: 2216: 2201: 2197: 2193: 2189: 2184: 2175: 2172:organized by 2171: 2167: 2164:to include a 2163: 2159: 2158:Julius Caesar 2156:organized by 2155: 2151: 2147: 2143: 2139: 2135: 2134:Roman Kingdom 2131: 2126: 2124: 2120: 2116: 2112: 2111:Greek designs 2108: 2107:Roman mosaics 2104: 2100: 2096: 2095:road-building 2092: 2088: 2084: 2080: 2079:surface areas 2076: 2072: 2071: 2066: 2062: 2058: 2055:, as well as 2054: 2049: 2047: 2046:central Italy 2043: 2039: 2035: 2031: 2027: 2023: 2019: 2015: 2011: 2007: 2003: 1999: 1995: 1991: 1987: 1980: 1976: 1972: 1968: 1967: 1962: 1958: 1957:ancient Roman 1953: 1948: 1944: 1934: 1932: 1928: 1924: 1920: 1916: 1912: 1908: 1904: 1900: 1895: 1891: 1887: 1882: 1879: 1875: 1871: 1867: 1863: 1859: 1851: 1847: 1843: 1838: 1834: 1832: 1828: 1824: 1820: 1816: 1812: 1808: 1804: 1800: 1796: 1792: 1784: 1780: 1776: 1771: 1767: 1765: 1754: 1750: 1749: 1744: 1740: 1735: 100 AD 1729: 1725: 1714: 1703: 1699: 1695: 1694:prime numbers 1691: 1680: 1675: 1672: 1668: 1664: 1653: 1646: 1642: 1638: 1634: 1631: 1627: 1623: 1619: 1580: 1576: 1572: 1568: 1564: 1553: 1546: 1542: 1537: 1533: 1531: 1527: 1523: 1519: 1515: 1511: 1507: 1506:number theory 1503: 1499: 1495: 1491: 1487: 1483: 1479: 1475: 1474: 1468: 300 BC 1462: 1458: 1454: 1446: 1442: 1437: 1433: 1431: 1426: 322 BC 1420: 1416: 1412: 1408: 1403: 1401: 1397: 1393: 1389: 1385: 1381: 1379: 1375: 1371: 1367: 1364: 1360: 1356: 1352: 1348: 1344: 1340: 1336: 1332: 1328: 1324: 1320: 1315: 1313: 1309: 1305: 1301: 1296: 1294: 1290: 1286: 1281: 1280:mathematics. 1279: 1275: 1270: 1266: 1262: 1254: 1250: 1245: 1240: 1230: 1228: 1224: 1221:Finally, the 1219: 1217: 1213: 1209: 1208:word problems 1205: 1201: 1196: 1194: 1190: 1186: 1182: 1178: 1174: 1170: 1166: 1162: 1161:prime numbers 1158: 1153: 1149: 1148:Rhind papyrus 1144: 1141: 1137: 1133: 1129: 1125: 1121: 1117: 1113: 1109: 1102: 1097: 1092: 1082: 1080: 1076: 1072: 1068: 1064: 1060: 1057: 1053: 1048: 1038: 1034: 1029: 1025: 1021: 1013: 1008: 1004: 1002: 998: 993: 989: 984: 982: 978: 970: 965: 961: 959: 955: 951: 947: 943: 939: 935: 931: 927: 923: 919: 914: 908: 898: 896: 892: 888: 884: 880: 877:monuments in 876: 872: 868: 866: 861: 860:prime numbers 857: 853: 849: 845: 841: 837: 832: 829: 825: 821: 817: 813: 797: 794: 791: 788: 785: 782: 779: 776: 773: 770: 767: 766: 762: 759: 756: 753: 750: 747: 744: 741: 738: 735: 732: 731: 727: 724: 721: 718: 715: 712: 709: 706: 703: 700: 697: 696: 692: 689: 686: 683: 680: 677: 674: 671: 668: 665: 659: 658: 654: 651: 648: 645: 642: 639: 636: 633: 630: 627: 621: 620: 616: 613: 610: 607: 604: 601: 598: 595: 592: 589: 587:Arabic-Indic 586: 585: 581: 578: 575: 572: 569: 566: 563: 560: 557: 554: 548: 547: 540: 538: 534: 530: 526: 522: 519: 515: 511: 507: 502: 500: 499:Maya numerals 496: 492: 488: 484: 480: 476: 472: 471:Western world 468: 464: 460: 456: 452: 448: 444: 440: 436: 432: 428: 424: 420: 416: 412: 408: 404: 400: 396: 392: 389: 385: 380: 378: 374: 370: 369: 364: 360: 359: 348: 344: 343: 338: 334: 329: 327: 323: 319: 315: 311: 307: 303: 299: 295: 294:Ancient Egypt 291: 287: 283: 279: 275: 272:. Before the 271: 267: 263: 251: 246: 244: 239: 237: 232: 231: 229: 228: 225: 221: 217: 216: 205: 202: 200: 197: 195: 192: 190: 187: 185: 182: 180: 177: 175: 172: 170: 167: 165: 162: 161: 155: 154: 147: 143: 140: 138: 135: 133: 129: 126: 124: 121: 119: 115: 112: 110: 107: 105: 102: 100: 99:Number theory 97: 96: 93: 88: 87: 84: 83: 78: 75: 73: 70: 69: 68: 67: 64: 61: 60: 56: 55: 48: 300 BC 42: 41: 36: 33:A proof from 31: 27: 19: 14061:Hindu-Arabic 13957:Group theory 13945:Trigonometry 13916:Topos theory 13837: 13734:Neuroscience 13638:Anthropology 13620:Trigonometry 13576: 13145: 13138: 13131: 13124: 13117: 13110: 13103: 13096: 13089: 13082: 13073:Mathematical 13028:16th century 12979:Ibn al-Majdi 12972:15th century 12936:14th century 12855:13th century 12809:12th century 12795:Omar Khayyam 12728:11th century 12624:Aṣ-Ṣaidanānī 12592:10th century 12553:Al-Khwarizmi 12391:institutions 12311:K. S. Shukla 12283:(1892– 1953) 12149:Yavanajataka 12147: 12140: 12133: 12126: 12119: 12112: 12107:Śulba Sūtras 12105: 12098: 12093:Sadratnamala 12091: 12084: 12077: 12070: 12063: 12056: 12049: 12042: 12037:Kanakkusaram 12035: 12028: 12021: 12014: 12002: 11872:Varāhamihira 11837:Parameshvara 11792:Govindasvāmi 11762:Āryabhaṭa II 11643: 11631: 11619: 11600: 11533:Optimization 11395:Differential 11319:Differential 11286:Order theory 11281:Graph theory 11185:Group theory 11086: 10970:Math History 10969: 10947: 10831: 10819: 10786: 10764: 10745:. Hyperion. 10742: 10721: 10701:, Springer, 10698: 10685: 10673: 10655: 10645: 10624: 10613: 10600: 10586: 10583:Aaboe, Asger 10553: 10533: 10516: 10512: 10487: 10483: 10465: 10447: 10422: 10399: 10365: 10361: 10341: 10307: 10289: 10270: 10248: 10229: 10205:. Retrieved 10201: 10191: 10180:. Retrieved 10176: 10166: 10155:. Retrieved 10151: 10142: 10131:. Retrieved 10127: 10118: 10106:. Retrieved 10099: 10090: 10057: 10053: 10043: 10031:. Retrieved 10019: 10008:. Retrieved 9996: 9986: 9967: 9958: 9947:. Retrieved 9943: 9934: 9901: 9897: 9887: 9873: 9840: 9836: 9826: 9810:math/0505125 9800: 9794: 9785: 9781: 9771: 9754: 9748: 9728: 9719: 9713: 9663: 9658: 9647:. Retrieved 9643: 9634: 9622:. Retrieved 9616: 9606: 9581: 9577: 9567: 9526: 9522: 9512: 9503: 9497: 9484: 9457: 9453: 9443: 9426: 9420: 9407: 9395:. Retrieved 9391: 9378: 9358: 9351: 9310: 9306: 9293: 9269:(1): 31–46. 9266: 9262: 9252: 9227: 9223: 9210: 9190: 9183: 9172:. Retrieved 9168: 9159: 9148:. Retrieved 9145:smf.emath.fr 9144: 9135: 9118: 9108: 9075: 9071: 9061: 9050:. Retrieved 9046: 9036: 9026: 9013:, Saunders. 9010: 9005: 8996: 8987: 8963: 8956: 8947: 8938: 8919: 8913: 8872: 8868: 8858: 8840: 8832: 8812: 8804: 8799: 8791: 8786: 8778: 8773: 8759: 8754: 8746: 8742: 8737: 8729: 8724: 8716: 8711: 8703: 8698: 8685: 8669: 8654: 8644: 8636: 8632: 8627: 8619: 8614: 8598: 8593: 8584: 8576: 8571: 8563: 8555: 8547: 8542: 8534: 8526: 8522: 8517: 8509: 8505: 8498:Goodman 2016 8471: 8457: 8448: 8435: 8410: 8406: 8400: 8388: 8383: 8370: 8361: 8355: 8324: 8318: 8310: 8306: 8302: 8298: 8289: 8280: 8275: 8262: 8249: 8224: 8220: 8207: 8198: 8184: 8180: 8173:Plofker, Kim 8167: 8142: 8138: 8129: 8118: 8114: 8107: 8071: 8067: 8058: 8044:cite journal 8038:(1): 77–104. 8035: 8031: 8025: 8017: 8012: 8001:. Retrieved 7981: 7977: 7964: 7955: 7944:. Retrieved 7940: 7931: 7923: 7919: 7914: 7891: 7881: 7872: 7860: 7856: 7852: 7848: 7844: 7842: 7822: 7811: 7798: 7785: 7756: 7734:(3): 10–11. 7731: 7727: 7714: 7702:, Springer, 7699: 7694: 7675: 7669: 7626: 7622: 7616: 7591: 7587: 7578: 7549:the original 7544: 7540: 7527: 7504: 7490: 7457: 7445: 7432: 7419: 7406: 7393: 7352: 7345: 7332: 7319: 7288: 7275: 7262: 7249: 7236: 7223: 7210: 7197: 7185: 7154: 7141: 7128: 7115: 7102: 7089: 7076: 7063: 7050: 7037: 7030:Goodman 2016 7024: 7011: 6998: 6991:Goodman 2016 6985: 6972: 6959: 6952:Goodman 2016 6946: 6933: 6920: 6907: 6898: 6889: 6876: 6863: 6834: 6821: 6808: 6795: 6782: 6764: 6759: 6746: 6717: 6704: 6691: 6678: 6665: 6652: 6639: 6626: 6613: 6584: 6571: 6554:, Saunders. 6551: 6546: 6517: 6506:. Retrieved 6492: 6479: 6466: 6453: 6440: 6427: 6416:the original 6402: 6373: 6357: 6352: 6336: 6331: 6321:15 September 6319:. Retrieved 6297: 6256: 6252: 6246: 6237: 6231: 6218:, Saunders, 6215: 6210: 6197: 6184: 6176: 6171: 6158: 6146:, Saunders, 6143: 6138: 6129: 6120: 6107: 6098: 6089: 6080: 6071: 6060: 6055:at MathPages 6048: 6035: 6026: 6022: 6016: 5997: 5991: 5978: 5965: 5956: 5953:Aaboe, Asger 5947: 5934: 5923:, retrieved 5918: 5905: 5893: 5877: 5867:, retrieved 5845: 5835: 5768: 5757:. Retrieved 5746:. Springer. 5743: 5733: 5717: 5712: 5704: 5699: 5675: 5668: 5660: 5655: 5644:. Retrieved 5639: 5629: 5605: 5600: 5592: 5584: 5572: 5564: 5559: 5551: 5546: 5538: 5522: 5517: 5484: 5480: 5474: 5421: 5411: 5403: 5398: 5367: 5193: 5171: 5152: 5143:21st century 5126: 5110:Emmy Noether 5108: 5104:Erdős number 5094: 5048: 5016:prime number 4989: 4945:graph theory 4929:optimization 4870: 4836: 4832:Lie algebras 4812:model theory 4744:sheaf theory 4732:Grothendieck 4686: 4652: 4616:Andrew Wiles 4601: 4575: 4567: 4564:20th century 4551: 4520: 4484:Georg Cantor 4481: 4469:group theory 4466: 4431: 4399:George Boole 4376: 4340:János Bolyai 4330:, where the 4325: 4286: 4273:19th century 4256: 4247: 4237: 4230: 4223: 4216: 4204: 4192:Please help 4187:verification 4184: 4141: 4113: 4104:graph theory 4097: 4084:18th century 4047: 4044: 4000:Isaac Newton 3997: 3954: 3941:17th century 3924: 3919: 3912:trigonometry 3909: 3894: 3891:Simon Stevin 3889: 3880: 3862: 3844: 3839: 3831: 3823: 3797: 3794:Luca Pacioli 3792: 3776: 3763: 3759: 3752: 3751:, including 3739: 3726: 3703: 3687: 3673: 3669: 3664: 3660: 3642: 3567: 3564: 3553: 3519: 3502: 3492: 3489:al-Khwārizmī 3487:, including 3482: 3477: 3473: 3469: 3461: 3455: 3450: 3445: 3439: 3433: 3426: 3358: 3327: 3315:Omar Khayyam 3276: 3263: 3245: 3227: 3221: 3218:Omar Khayyam 3215: 3150: 3144: 3133: 3123: 3111: 3105: 3101: 3095: 3079: 3069: 3049:North Africa 3045:Central Asia 3034: 3022: 2978: 2967:power series 2953:, found the 2944: 2937: 2923: 2876: 2858: 2853: 2842: 2836: 2830: 2823: 2809:Gupta period 2804: 2801:Sulba Sutras 2800: 2798: 2793: 2748: 2732:Sulba Sutras 2729: 2718: 2643: 2616: 2569:Ming dynasty 2547: 2543:Matteo Ricci 2532: 2520:magic square 2511: 2497: 2494:Song dynasty 2491: 2466: 2420: 2413:book burning 2401: 2389: 2363: 2346: 2341: 2333: 2327: 2324:Rod numerals 2320: 2288: 2285: 2211: 15 BC 2207: 80 BC 2185: 2127: 2087:architecture 2074: 2068: 2050: 2036:used by the 1998:native Latin 1994:Roman Empire 1986:ethnic Greek 1983: 1964: 1943:Roman abacus 1931:Hagia Sophia 1883: 1877: 1874:Pappus graph 1855: 1842:Hagia Sophia 1830: 1826: 1823:Last Theorem 1814: 1806: 1788: 1774: 1760: AD 90 1746: 1737:) pioneered 1698:trigonometry 1692:for finding 1676: 1670: 1650: 1561:–212 BC) of 1550: 1501: 1493: 1489: 1484:through the 1477: 1471: 1450: 1440: 1404: 1382: 1377: 1317:Thales used 1316: 1297: 1282: 1258: 1253:Pythagoreans 1220: 1211: 1207: 1197: 1145: 1106: 1054:, and their 1049: 1017: 1012:Plimpton 322 985: 974: 938:Christianity 932:through the 916: 913:Plimpton 322 869: 851: 836:Ishango bone 833: 809: 529:Isaac Newton 503: 394: 390: 384:Pythagoreans 381: 366: 356: 342:Plimpton 322 340: 330: 300:began using 278:Mesopotamian 261: 259: 71: 38: 26: 14077:Mesopotamia 14051:Prehistoric 14011:Probability 13868:Algorithms 13701:Engineering 13643:Archaeology 13610:Probability 13577:Mathematics 13443:Romanticism 13428:Renaissance 13091:De Gradibus 13045:Taqi ad-Din 13035:Al-Birjandi 13009:al-Qalaṣādī 12790:Al-Isfizari 12755:Ibn al-Samh 12684:Al-Isfahani 12664:al-Uqlidisi 12634:al-Khojandi 12599:Abu al-Wafa 12538:al-Dinawari 12496:9th century 12327:Translators 12319:(1919–2005) 12317:K. V. Sarma 12313:(1918–2007) 12307:(1918–1992) 12301:(1918–2000) 12295:(1903–1978) 12289:(1901–1954) 12287:A. N. Singh 12272:(1888–1958) 12270:B. B. Datta 12266:(1876–1962) 12260:(1861–1916) 12254:(1855–1910) 12248:(1853–1898) 12242:(1821–1900) 12233:mathematics 12177:Symbol for 12161:innovations 12058:Lokavibhaga 12004:Aryabhatiya 11802:Jyeṣṭhadeva 11787:Brahmagupta 11772:Bhāskara II 11757:Āryabhaṭa I 11741:Yajnavalkya 11645:WikiProject 11488:Game theory 11468:Probability 11205:Homological 11195:Multilinear 11175:Commutative 11152:Type theory 11119:Foundations 11075:mathematics 10955:Convergence 10832:In Our Time 10595:Bell, E. T. 10266:Boyer, C.B. 10202:www.bls.gov 9757:: 448–469. 9738:Erdős, Paul 9734:Alaoglu, L. 9506:(11): 1382. 8145:(1): 2–13. 7862:Tetrabiblos 7438:Volkov 2009 7425:Volkov 2009 7412:Volkov 2009 7399:Volkov 2009 5487:(3235): 5. 5070:asymptotics 4905:Rózsa Péter 4881:Alan Turing 4776:Knot theory 4712:game theory 4694:used it in 4646:proved the 4642:. In 1998, 4636:independent 4610:proved the 4556:introduced 4554:Kurt Hensel 4311:and of the 4024:solid-state 3977:John Napier 3965:Tycho Brahe 3731:bookkeeping 3706:Renaissance 3704:During the 3694:Renaissance 3555:Liber Abaci 3354:Maya script 3323:al-Qalasādī 3207:polynomials 3041:Middle East 2995:integration 2979:Yukti-bhāṣā 2975:Jyesthadeva 2926:Bhāskara II 2861:Brahmagupta 2854:Aryabhatiya 2843:Aryabhatiya 2838:Aryabhatiya 2740:square root 2725:Indus river 2621:during the 2535:Renaissance 2475:Zu Chongzhi 2459:square root 2417:Han dynasty 2083:engineering 2014:calculators 1831:Arithmetica 1827:Arithmetica 1815:Arithmetica 1807:Arithmetica 1775:Arithmetica 1480:introduced 1445:Oxyrhynchus 1443:, found at 1411:integration 1363:Greco-Roman 1343:Babylonians 1278:Hellenistic 1187:as well as 1134:as part of 1132:Arab Empire 1114:. From the 1033:Renaissance 1020:sexagesimal 950:Arab Empire 922:Mesopotamia 806:Prehistoric 660:Devanagari 518:Renaissance 514:Middle Ages 445:, and even 435:bookkeeping 353: 2000 333:Mesopotamia 266:mathematics 189:Linguistics 179:Computation 174:Geosciences 137:Probability 63:Mathematics 14204:Categories 14001:Statistics 13933:Logarithms 13879:Arithmetic 13678:Technology 13663:Psychology 13615:Statistics 13462:By culture 13366:Background 13255:Influenced 13229:Influences 12999:Ali Qushji 12958:Al-Khalili 12826:Al-Khazini 12821:Al-Kharaqī 12780:al-Zarqālī 12770:al-Jayyānī 12714:al-Majriti 12699:Abu al-Jud 12669:Al-Battani 12644:Al-Saghani 12639:Al-Nayrizi 12578:al-Marwazi 12513:al-Jawharī 12276:T. Hayashi 12159:Pioneering 12142:Yuktibhāṣā 12065:Pātīgaṇita 12016:Bijaganita 11973:Ravi Vakil 11827:Munishvara 11807:Kamalakara 11782:Brahmadeva 11767:Bhāskara I 11716:Baudhayana 11473:Statistics 11352:Arithmetic 11314:Arithmetic 11180:Elementary 11147:Set theory 10968:'s online 10444:Wang, Ling 10219:References 10207:2023-11-28 10182:2023-11-28 10157:2024-08-05 10133:2024-08-05 10108:28 January 10010:2024-04-20 9949:2024-01-28 9904:(7): 791. 9788:: 261–279. 9649:2024-01-28 9644:Plus Maths 9624:28 January 9174:2024-01-28 9150:2024-01-28 9052:2023-10-14 8295:Boyer 1991 8268:Boyer 1991 8187:(4): 293. 8003:2020-02-11 7946:2022-10-03 7857:Siddhanata 7804:Boyer 1991 7791:Boyer 1991 7778:Boyer 1991 7762:Boyer 1991 7483:Boyer 1991 7463:Boyer 1991 7386:Boyer 1991 7312:Boyer 1991 7203:Boyer 1991 7178:Boyer 1991 7160:Boyer 1991 7056:Joyce 1979 7017:Cuomo 2001 7004:Cuomo 2001 6978:Cuomo 2001 6965:Cuomo 2001 6939:Boyer 1991 6926:Boyer 1991 6913:Boyer 1991 6882:Boyer 1991 6869:Boyer 1991 6856:Boyer 1991 6840:Boyer 1991 6827:Boyer 1991 6814:Boyer 1991 6801:Boyer 1991 6788:Boyer 1991 6763:S.C. Roy. 6752:Boyer 1991 6739:Boyer 1991 6723:Boyer 1991 6710:Boyer 1991 6697:Boyer 1991 6684:Boyer 1991 6671:Boyer 1991 6658:Boyer 1991 6645:Boyer 1991 6632:Boyer 1991 6619:Boyer 1991 6606:Boyer 1991 6590:Boyer 1991 6577:Boyer 1991 6539:Boyer 1991 6523:Boyer 1991 6508:2008-09-26 6485:Boyer 1991 6472:Boyer 1991 6459:Boyer 1991 6446:Boyer 1991 6433:Boyer 1991 6395:Boyer 1991 6379:Boyer 1991 6203:Boyer 1991 6190:Boyer 1991 6164:Boyer 1991 6113:Boyer 1991 6041:Boyer 1991 6029:: 174–177. 6007:0813526140 5984:Boyer 1991 5971:Boyer 1991 5940:Boyer 1991 5869:2023-07-07 5828:Boyer 1991 5812:Boyer 1991 5794:Boyer 1991 5774:Boyer 1991 5759:2019-08-17 5753:0792338162 5646:2006-05-06 5622:Boyer 1991 5391:Boyer 1991 5147:See also: 5096:Paul Erdős 5055:autodidact 5008:incomplete 5000:Kurt Gödel 4957:algorithms 4943:including 4895:'s use of 4828:Lie groups 4824:Lie theory 4816:Mandelbrot 4764:Kolmogorov 4716:structures 4663:André Weil 4628:Kurt Gödel 4624:Paul Cohen 4488:set theory 4454:dimensions 4250:April 2021 4220:newspapers 4160:statistics 4020:electronic 3981:Jost Bürgi 3973:logarithms 3934:See also: 3896:De Thiende 3875:. In 1572 3816:Proportion 3804:Arithmetic 3725:(known as 3710:accounting 3651:, lacking 3607:divergence 3542:arithmetic 3466:Nicomachus 3457:quadrivium 3421:See also: 3209:up to the 3203:paraboloid 3194:Diophantus 3134:In Egypt, 3128:exposition 3021:Page from 3011:See also: 2835:wrote the 2825:Yuktibhāṣā 2805:Siddhantas 2669:See also: 2623:Edo period 2581:algorithms 2504:Zhu Shijie 2455:Zhang Heng 2408:Qin Empire 2260:See also: 2234:Roman mile 2226:technology 2209: – c. 2146:solar year 2117:tile, the 1903:Simplicius 1878:Collection 1791:Diophantus 1709: 190 1686: 276 1659: 262 1559: 287 1552:Archimedes 1457:Alexandria 1376:name: the 1359:Nicomachus 1189:arithmetic 1165:arithmetic 1056:reciprocal 1022:(base-60) 918:Babylonian 911:See also: 901:Babylonian 875:megalithic 347:Babylonian 302:arithmetic 280:states of 274:modern age 199:Philosophy 142:Statistics 132:Set theory 14021:Manifolds 14017:Topology 13928:Functions 13772:Timelines 13749:Pathology 13744:Nutrition 13668:Sociology 13648:Economics 13557:Chemistry 13547:Astronomy 13484:Byzantine 13479:Brazilian 13474:Argentine 13004:al-Wafa'i 12994:Ulugh Beg 12897:al-Abhari 12882:Ibn Adlan 12872:Ibn Munim 12836:al-Hassar 12775:al-Nasawī 12750:Al-Biruni 12719:al-Jabali 12709:Al-Karaji 12659:Ibn Yunus 12614:Abu Kamil 12609:Al-Qabisi 12604:al-Khazin 12533:Al-Mahani 12305:S. N. Sen 12213:New Delhi 12135:Veṇvāroha 11996:Treatises 11797:Halayudha 11750:Classical 11721:Katyayana 11711:Apastamba 11400:Geometric 11390:Algebraic 11329:Euclidean 11304:Algebraic 11200:Universal 10446:(1995) , 10390:191394716 10268:(1991) , 10074:1476-4687 10005:0362-4331 9918:0002-9890 9857:0002-9890 9598:0035-7596 9551:1476-4687 9476:0002-9904 9335:1476-4687 9285:0002-9904 9244:1464-3839 9100:123447349 9092:1432-0657 8905:143395001 8889:0021-1753 8845:Routledge 8376:Katz 1998 8311:muqabalah 8303:muqabalah 8284:numbers". 7998:170341845 7653:0022-1791 7631:CiteSeerX 7608:115779583 7190:Katz 2007 7043:Tang 2005 6564:The Bible 6368:, p. 129. 6316:130132289 6290:Qiu, Jane 5463:ignored ( 5453:cite book 5419:(1969) . 4996:decidable 4873:computers 4826:with its 4804:René Thom 4667:pseudonym 4622:in 1995. 4552:In 1897, 4293:functions 4126:π 4106:with the 4032:computers 3881:L'Algebra 3864:Ars Magna 3785:, 1495, ( 3626:Adam Ries 3522:Fibonacci 3385:vigesimal 3226:Euclid's 3190:Abul Wafa 3183:algebraic 3175:historian 3151:al-Fakhri 3147:Al-Karaji 3136:Abu Kamil 3120:reduction 3097:algorithm 2903:Halayudha 2833:Aryabhata 2820:sine rule 2794:mātrāmeru 2762:recursion 2561:Confucian 2477:computed 2431:surveying 2200:Vitruvius 2196:distances 2138:leap year 2070:gromatici 2020:than the 2010:surveyors 1984:Although 1973:, modern 1966:gromatici 1915:Justinian 1720: 10 1577:with the 1419:Aristotle 1169:geometric 1157:composite 992:metrology 988:Sumerians 930:Sumerians 856:sequences 820:magnitude 549:European 423:surveying 326:calendars 322:astronomy 204:Education 194:Economics 169:Chemistry 14189:Category 14164:timeline 14152:timeline 14026:timeline 14006:timeline 13994:timeline 13979:timeline 13967:timeline 13950:timeline 13940:Geometry 13911:timeline 13896:timeline 13891:Calculus 13884:timeline 13872:timeline 13862:timeline 13850:By topic 13842:timeline 13795:Category 13754:Pharmacy 13711:Medicine 13600:Geometry 13590:Calculus 13509:Japanese 13157:Concepts 12989:al-Kāshī 12963:al-Umawi 12765:Avicenna 12704:Al-Sijzi 12654:Ibn Sahl 12523:Al-Kindi 12221:Varanasi 12179:zero (0) 12051:Līlāvatī 11918:C.R. Rao 11882:Virasena 11862:Sridhara 11832:Narayana 11817:Mahāvīra 11621:Category 11377:Topology 11324:Discrete 11309:Analytic 11296:Geometry 11268:Discrete 11223:Calculus 11215:Analysis 11170:Abstract 11109:Glossary 11092:Timeline 11004:Archived 10979:Archived 10972:Magazine 10958:Archived 10942:Journals 10818:(2008). 10785:(1990). 10763:(1969). 10741:(1998). 10697:(1983). 10684:(1921). 10672:(1972). 10654:(1987). 10623:(2003). 10612:(1997). 10597:(1937). 10585:(1964). 10325:citation 10228:(2007), 10101:BBC News 10082:10839504 9559:26983518 8946:(1953). 8821:Archived 8743:Geometry 8678:in 1687. 8652:(2009), 8525:and the 8347:29181926 8329:Springer 8104:68570164 7845:Sindhind 7661:52885600 7509:Springer 7503:(eds.). 5955:(1998). 5886:Archived 5591:(1964). 5445:14884919 5207:See also 5197:big data 5122:algebras 5068:and its 5024:analysis 4979:and the 4937:discrete 4877:industry 4820:fractals 4752:Poincaré 4704:topology 4477:symmetry 4368:surfaces 4360:manifold 4301:geometry 4152:Napoleon 4070:gambling 4008:calculus 3808:Geometry 3715:Flanders 3688:Elements 3601:with an 3574:al-Kindi 3546:algorism 3503:Elements 3478:Elements 3452:Boethius 3291:al-Kindi 3228:Elements 3186:calculus 3084:Al-Kindi 2803:are the 2792:(called 2528:Yang Hui 2372:diameter 2334:suan pan 2329:suan pan 2238:cogwheel 2215:Commodus 2192:odometer 2166:leap day 2105:such as 2089:such as 2061:treasury 2059:for the 2032:or from 2004:such as 1975:Budapest 1971:Aquincum 1961:surveyor 1907:Eutocius 1748:Almagest 1741:through 1667:parabola 1575:parabola 1563:Syracuse 1502:Elements 1494:Elements 1490:Elements 1478:Elements 1473:Elements 1441:Elements 1374:Medieval 1349:and the 1323:pyramids 1319:geometry 1308:Egyptian 1124:Egyptian 1108:Egyptian 1085:Egyptian 1037:YBC 7289 1001:division 942:Seleucid 924:(modern 891:ellipses 883:Scotland 733:Chinese 698:Bengali 537:calculus 363:Egyptian 318:commerce 314:taxation 310:geometry 268:and the 118:Analysis 114:Calculus 104:Geometry 40:Elements 14056:Ancient 13857:Algebra 13729:Anatomy 13653:History 13585:Algebra 13567:Physics 13552:Biology 13529:Spanish 13524:Russian 13519:Mexican 13494:Chinese 13469:African 13281:Related 13210:Madrasa 13178:Centers 12984:al-Rūmī 12887:al-Urdi 12785:ibn Hud 12740:Alhazen 12694:al-Qūhī 12360:Babylon 12193:Centres 11857:Śrīpati 11736:Pingala 11704:Ancient 11633:Commons 11415:Applied 11385:General 11162:Algebra 11087:History 10576:General 10492:Bibcode 10033:5 April 9926:2317868 9865:2321202 9815:Bibcode 9531:Bibcode 9429:: 474. 9397:5 April 9392:nih.gov 9343:4008586 9315:Bibcode 8839:(1996) 8689:extent. 8533:, ed., 8512:, 11:20 8427:2691411 8307:al-jabr 8299:al-jabr 8241:2691411 8159:1558972 8119:without 8076:Bibcode 7896:213–215 7748:3637061 6767:, p. 1 6273:3026893 5925:July 6, 5509:3994109 5489:Bibcode 4738:recast 4234:scholar 4158:and on 3957:Galileo 3719:Germany 3677:at the 3609:of the 3534:Algeria 3435:Timaeus 3389:decimal 3379:used a 3359:In the 3268:Ruffini 3124:al-jabr 3102:algebra 2987:Muziris 2907:Pingala 2770:prosody 2766:Pingala 2601:Sangaku 2577:Chữ Nôm 2573:Chinese 2563:-based 2463:Liu Hui 2461:of 10. 2451:Liu Xin 2364:Mo Jing 2303:decimal 2276:decimal 2244:Chinese 2115:tessera 2091:bridges 2042:Tuscany 1979:Hungary 1899:Proclus 1886:Hypatia 1753:Ptolemy 1622:volumes 1613:⁠ 1601:⁠ 1597:⁠ 1585:⁠ 1510:algebra 1453:Musaeum 1351:Chinese 1347:Indians 1216:frustum 1138:, when 1041:√ 1028:decimal 954:Baghdad 946:Babylon 887:circles 879:England 662:(Hindi) 395:mathema 306:algebra 290:Assyria 184:Biology 164:Physics 109:Algebra 72:History 13783:Portal 13514:Korean 13499:Indian 13489:French 13406:By era 12389:Modern 12380:Europe 12370:Greece 12217:Ujjain 12209:Jaipur 11891:Modern 11731:Pāṇini 11726:Manava 11334:Finite 11190:Linear 11097:Future 11073:Major 10964:, the 10899:& 10793: 10771: 10749: 10728: 10705: 10631: 10560: 10541: 10472: 10454: 10429: 10411: 10388: 10382:505056 10380: 10350: 10314: 10296: 10278: 10255: 10236: 10080: 10072: 10054:Nature 10003: 9974: 9924: 9916: 9863: 9855: 9674: 9596: 9557: 9549: 9523:Nature 9474: 9366: 9341: 9333: 9307:Nature 9283: 9242: 9198: 9098: 9090: 9017: 8975: 8926: 8903: 8897:225223 8895: 8887: 8662: 8605: 8510:Wisdom 8425: 8345: 8335: 8281:Osiris 8239: 8157: 8102: 8096:234257 8094: 7996: 7902: 7835: 7746: 7706: 7682: 7659: 7651: 7633: 7606: 7515: 7360: 6774: 6558: 6364: 6343: 6314: 6298:Nature 6271: 6222: 6150: 6004: 5860: 5750: 5724: 5687: 5507: 5481:Nature 5443: 5433: 5184:Future 5120:, and 5118:fields 5072:, and 5064:, the 4971:, the 4963:, the 4850:limits 4814:, and 4770:, and 4742:using 4706:, and 4510:, and 4425:, and 4364:curves 4305:series 4236: 4229: 4222: 4215: 4207: 4166:Modern 3820:Venice 3762:, and 3727:abbaco 3657:limits 3530:Béjaïa 3513:, and 3369:Mexico 3363:, the 3272:Horner 3220:wrote 3179:theory 3173:. The 3061:Arabic 3053:Iberia 2983:Jesuit 2919:matrix 2782:meters 2760:, and 2750:Pāṇini 2653:Indian 2555:, and 2539:Jesuit 2510:. The 2487:sphere 2380:volume 2378:, and 2376:radius 2351:canon 2349:Mohist 2338:Xu Yue 2282:period 2097:, and 2006:Cicero 1876:. His 1813:. The 1671:Conics 1618:spiral 1526:optics 1500:, the 1461:Euclid 1392:Athens 1353:, the 1251:. The 1140:Arabic 1079:proofs 1063:linear 893:, and 848:20,000 822:, and 812:number 768:Tamil 487:Mexico 461:. The 413:, the 407:proofs 391:μάθημα 35:Euclid 14142:Other 14097:India 14092:China 13974:Logic 13605:Logic 13075:works 12365:China 11561:lists 11104:Lists 11077:areas 10386:S2CID 10378:JSTOR 10028:(PDF) 9922:JSTOR 9861:JSTOR 9805:arXiv 9745:(PDF) 9710:(PDF) 9584:(4). 9494:(PDF) 9417:(PDF) 9388:(PDF) 9339:S2CID 9303:(PDF) 9220:(PDF) 9096:S2CID 8901:S2CID 8893:JSTOR 8445:(PDF) 8423:JSTOR 8393:Paris 8237:JSTOR 8217:(PDF) 8155:JSTOR 8100:S2CID 8092:JSTOR 7994:S2CID 7974:(PDF) 7817:Boyer 7744:S2CID 7724:(PDF) 7657:S2CID 7604:S2CID 7552:(PDF) 7537:(PDF) 6419:(PDF) 6412:(PDF) 6312:S2CID 6269:JSTOR 5915:(PDF) 5505:S2CID 5359:Notes 5178:arXiv 5114:rings 4975:from 4897:ENIAC 4750:that 4736:Serre 4496:Peano 4299:, in 4241:JSTOR 4227:books 4074:wager 3812:Ratio 3721:) or 3661:would 3430:Plato 3171:cubes 3155:proof 3065:Arabs 3057:India 2631:wasan 2619:Japan 2595:Japan 2396:China 2053:fraud 1959:land 1937:Roman 1779:Latin 1430:logic 1421:(384– 1390:, in 1384:Plato 1233:Greek 1128:Egypt 1120:Greek 1059:pairs 852:tally 844:Congo 521:Italy 467:India 439:lunar 417:used 388:Greek 337:Egypt 286:Akkad 282:Sumer 128:Logic 92:Areas 77:Index 12438:TIFR 10791:ISBN 10769:ISBN 10747:ISBN 10726:ISBN 10703:ISBN 10629:ISBN 10558:ISBN 10539:ISBN 10470:ISBN 10452:ISBN 10427:ISBN 10409:ISBN 10348:ISBN 10331:link 10312:ISBN 10294:ISBN 10276:ISBN 10253:ISBN 10234:ISBN 10110:2024 10078:PMID 10070:ISSN 10035:2023 10001:ISSN 9972:ISBN 9914:ISSN 9853:ISSN 9672:ISBN 9626:2024 9594:ISSN 9555:PMID 9547:ISSN 9472:ISSN 9399:2023 9364:ISBN 9331:ISSN 9281:ISSN 9240:ISSN 9196:ISBN 9088:ISSN 9015:ISBN 8973:ISBN 8924:ISBN 8885:ISSN 8869:Isis 8660:ISBN 8603:ISBN 8343:OCLC 8333:ISBN 8301:and 8068:Isis 8050:link 7900:ISBN 7833:ISBN 7704:ISBN 7680:ISBN 7649:ISSN 7513:ISBN 7358:ISBN 6772:ISBN 6556:ISBN 6362:ISBN 6341:ISBN 6323:2014 6220:ISBN 6148:ISBN 6002:ISBN 5927:2023 5858:ISBN 5748:ISBN 5722:ISBN 5685:ISBN 5465:help 5441:PMID 5431:ISBN 5041:The 4951:and 4830:and 4802:and 4734:and 4661:and 4626:and 4606:and 4460:and 4413:and 4366:and 4213:news 4056:and 3979:and 3963:'s. 3849:and 3814:and 3747:and 3717:and 3576:and 3415:and 3401:zero 3381:base 3371:and 3348:The 3340:Maya 3332:and 3297:and 3270:and 3090:and 3035:The 2993:and 2913:and 2883:zero 2871:and 2603:and 2522:and 2360:Mozi 2270:The 2152:, a 2012:and 1945:and 1925:and 1905:and 1872:and 1864:and 1848:and 1840:The 1801:and 1571:area 1512:and 1310:and 1247:The 1191:and 1179:and 1171:and 1159:and 1069:and 969:Susa 926:Iraq 881:and 840:Nile 834:The 824:form 531:and 495:zero 489:and 473:via 441:and 335:and 308:and 298:Ebla 288:and 260:The 144:and 130:and 116:and 13147:Zij 10816:BBC 10521:doi 10500:doi 10488:252 10370:doi 10062:doi 10058:405 9906:doi 9845:doi 9759:doi 9586:doi 9539:doi 9527:531 9462:doi 9431:doi 9323:doi 9271:doi 9232:doi 9123:doi 9080:doi 9031:493 8877:doi 8848:doi 8415:doi 8229:doi 8189:doi 8147:doi 8084:doi 7986:doi 7829:226 7736:doi 7641:doi 7596:doi 6302:doi 6261:doi 6027:6–1 5850:doi 5497:doi 5485:128 4983:of 4915:'s 4907:'s 4883:'s 4818:'s 4806:'s 4790:'s 4710:'s 4634:is 4417:. 4295:of 4196:by 3975:by 3893:'s 3796:'s 3491:'s 3468:'s 3432:'s 3321:by 3313:by 3305:by 3181:of 3157:by 3027:by 2822:in 2796:). 2780:of 2502:by 2340:'s 1781:by 1751:of 1624:of 1455:of 1210:or 858:of 485:of 421:in 405:in 37:'s 14206:: 13299:, 12219:, 12215:, 12211:, 10903:). 10644:. 10517:71 10515:, 10498:, 10486:, 10442:; 10407:, 10384:, 10376:, 10366:83 10364:, 10327:}} 10323:{{ 10200:. 10175:. 10150:. 10126:. 10098:. 10076:. 10068:. 10056:. 10052:. 9999:. 9995:. 9942:. 9920:. 9912:. 9902:76 9900:. 9896:. 9859:. 9851:. 9841:87 9839:. 9835:. 9813:, 9803:, 9786:20 9784:. 9780:. 9755:56 9753:. 9747:. 9736:; 9720:53 9718:. 9712:. 9687:^ 9678:, 9670:. 9666:. 9642:. 9615:. 9592:. 9582:32 9580:. 9576:. 9553:. 9545:. 9537:. 9525:. 9521:. 9504:55 9502:. 9496:. 9470:. 9456:. 9452:. 9427:28 9425:. 9419:. 9390:. 9337:. 9329:. 9321:. 9311:52 9309:. 9305:. 9279:. 9267:45 9265:. 9261:. 9238:. 9228:26 9226:. 9222:. 9167:. 9143:. 9117:. 9094:. 9086:. 9076:23 9074:. 9070:. 9045:. 8995:. 8971:. 8969:89 8899:. 8891:. 8883:. 8873:23 8871:. 8867:. 8668:, 8485:^ 8476:, 8470:, 8466:, 8447:. 8421:. 8411:68 8409:. 8391:. 8341:. 8327:. 8235:. 8225:68 8223:. 8219:. 8197:. 8185:28 8183:. 8179:. 8153:. 8143:33 8141:. 8106:. 8098:. 8090:. 8082:. 8072:83 8070:. 8046:}} 8042:{{ 8036:20 8034:. 7992:. 7982:51 7980:. 7976:. 7939:. 7898:. 7890:. 7841:. 7831:. 7769:^ 7742:. 7732:15 7730:. 7726:. 7655:. 7647:. 7639:. 7627:35 7625:. 7602:. 7592:29 7590:. 7560:^ 7545:13 7543:. 7539:. 7507:. 7499:; 7470:^ 7375:^ 7301:^ 7167:^ 6897:. 6847:^ 6730:^ 6597:^ 6530:^ 6500:. 6386:^ 6310:. 6300:. 6296:. 6281:^ 6267:. 6257:11 6255:. 6128:. 6097:. 6079:. 6025:. 5917:, 5896:. 5892:, 5856:, 5844:, 5819:^ 5801:^ 5781:^ 5742:. 5683:. 5681:64 5638:. 5613:^ 5530:^ 5503:. 5495:. 5483:. 5457:: 5455:}} 5451:{{ 5439:. 5382:^ 5180:. 5124:. 5116:, 5088:, 5084:, 5080:, 4987:. 4967:, 4927:; 4923:; 4919:; 4911:; 4903:; 4891:; 4887:; 4868:. 4822:. 4810:, 4798:, 4794:, 4774:. 4762:, 4730:. 4722:, 4702:, 4580:, 4573:. 4560:. 4549:. 4518:. 4506:, 4502:, 4498:, 4479:. 4464:. 4421:, 4389:, 4381:. 4374:. 4315:. 4162:. 4030:) 4026:, 4022:, 3995:. 3907:. 3857:. 3810:, 3806:, 3789:). 3769:. 3758:, 3665:if 3647:, 3532:, 3509:, 3472:; 3448:. 3325:. 3274:. 3243:. 3165:, 3051:, 3047:, 3043:, 2942:. 2921:. 2867:, 2764:. 2641:. 2591:. 2551:, 2489:. 2382:. 2374:, 2370:, 2353:c. 2344:. 2220:r. 2204:c. 2179:r. 2101:. 2093:, 2063:. 2048:. 2044:, 1977:, 1901:, 1757:c. 1732:c. 1717:c. 1706:c. 1683:c. 1656:c. 1610:70 1604:10 1594:71 1588:10 1583:3+ 1556:c. 1545:pi 1528:, 1524:, 1508:, 1465:c. 1432:. 1423:c. 1380:. 1345:, 1229:. 1195:. 1167:, 1163:; 1118:, 1065:, 960:. 889:, 818:, 814:, 798:௯ 763:九 728:৯ 693:९ 655:۹ 617:٩ 582:9 501:. 449:. 433:, 429:, 425:, 350:c. 339:– 328:. 316:, 304:, 284:, 45:c. 13844:) 13840:( 13830:e 13823:t 13816:v 13351:e 13344:t 13337:v 13303:) 13295:( 12472:e 12465:t 12458:v 12223:) 12207:( 11680:e 11673:t 11666:v 11066:e 11059:t 11052:v 10895:( 10824:. 10799:. 10777:. 10755:. 10709:. 10648:. 10637:. 10547:. 10523:: 10506:. 10502:: 10494:: 10392:. 10372:: 10333:) 10242:. 10210:. 10185:. 10160:. 10136:. 10112:. 10084:. 10064:: 10037:. 10013:. 9981:. 9952:. 9928:. 9908:: 9881:. 9867:. 9847:: 9817:: 9807:: 9765:. 9761:: 9682:. 9652:. 9628:. 9600:. 9588:: 9561:. 9541:: 9533:: 9478:. 9464:: 9458:8 9437:. 9433:: 9401:. 9372:. 9345:. 9325:: 9317:: 9287:. 9273:: 9246:. 9234:: 9204:. 9177:. 9153:. 9129:. 9125:: 9102:. 9082:: 9055:. 8999:. 8981:. 8932:. 8907:. 8879:: 8850:: 8693:. 8609:. 8496:( 8451:. 8429:. 8417:: 8395:. 8374:( 8349:. 8293:( 8266:( 8243:. 8231:: 8191:: 8161:. 8149:: 8086:: 8078:: 8052:) 8006:. 7988:: 7949:. 7908:. 7802:( 7789:( 7776:( 7760:( 7750:. 7738:: 7688:. 7663:. 7643:: 7610:. 7598:: 7521:. 7481:( 7461:( 7436:( 7423:( 7410:( 7397:( 7384:( 7366:. 7336:( 7323:( 7310:( 7292:( 7279:( 7266:( 7253:( 7240:( 7227:( 7214:( 7201:( 7176:( 7158:( 7145:( 7132:( 7119:( 7106:( 7093:( 7080:( 7067:( 7054:( 7041:( 7028:( 7015:( 7002:( 6989:( 6976:( 6963:( 6950:( 6937:( 6924:( 6911:( 6901:. 6880:( 6867:( 6854:( 6838:( 6825:( 6812:( 6799:( 6786:( 6750:( 6737:( 6721:( 6708:( 6695:( 6682:( 6669:( 6656:( 6643:( 6630:( 6617:( 6604:( 6588:( 6575:( 6537:( 6521:( 6511:. 6483:( 6470:( 6457:( 6444:( 6431:( 6393:( 6377:( 6325:. 6304:: 6275:. 6263:: 6240:. 6226:. 6201:( 6188:( 6162:( 6132:. 6111:( 6101:. 6083:. 6039:( 6010:. 5982:( 5969:( 5938:( 5900:. 5852:: 5826:( 5810:( 5792:( 5772:( 5762:. 5728:. 5693:. 5649:. 5620:( 5511:. 5499:: 5491:: 5467:) 5447:. 5389:( 4669:" 4263:) 4257:( 4252:) 4248:( 4238:· 4231:· 4224:· 4217:· 4190:. 4114:i 3636:. 3613:. 3264:n 3110:( 2447:π 2217:( 2202:( 2176:( 1963:( 1852:. 1785:. 1755:( 1730:( 1715:( 1704:( 1681:( 1654:( 1647:. 1607:/ 1591:/ 1554:( 1547:. 1463:( 1043:2 795:௮ 792:௭ 789:௬ 786:௫ 783:௪ 780:௩ 777:௨ 774:௧ 771:௦ 760:八 757:七 754:六 751:五 748:四 745:三 742:二 739:一 736:零 725:৮ 722:৭ 719:৬ 716:৫ 713:৪ 710:৩ 707:২ 704:১ 701:০ 690:८ 687:७ 684:६ 681:५ 678:४ 675:३ 672:२ 669:१ 666:० 652:۸ 649:۷ 646:۶ 643:۵ 640:۴ 637:۳ 634:۲ 631:۱ 628:۰ 614:٨ 611:٧ 608:٦ 605:٥ 602:٤ 599:٣ 596:٢ 593:١ 590:٠ 579:8 576:7 573:6 570:5 567:4 564:3 561:2 558:1 555:0 393:( 361:( 345:( 249:e 242:t 235:v 43:( 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.