33:
1383:
528:
540:
552:
491:. In November 1889, Lie suffered a mental breakdown and had to be hospitalized until June 1890. Subsequently he returned to his post, but over the years his anaemia progressed to the point where he returned to his homeland. In 1898 he tendered his resignation in May, and left for home in September the same year. He died the following year in 1899 at the age of 56, due to
426:(On a Class of Geometric Transformations). It would be described by Darboux as "one of the most handsome discoveries of modern Geometry". The next year, the Norwegian Parliament established an extraordinary professorship for him. That same year, Lie visited Klein, who was then at
1468:
448:
At the end of 1872, Sophus Lie proposed to Anna Birch, then eighteen years old, and they were married in 1874. The couple had three children: Marie (b. 1877), Dagny (b. 1880) and Herman (b. 1884).
362:(known then as Christiania). After graduating from high school, his ambition towards a military career was dashed when the army rejected him due to poor eyesight. He then enrolled at the
605:. However, the subject of Lie groups as it is studied today is vastly different from what the research by Sophus Lie was about and "among the 19th century masters, Lie's work is
1483:
415:
where he was arrested, suspected of being a German spy, garnering him fame in Norway. He was released from prison after a month, thanks to the intervention of
Darboux.
1416:
1463:
882:
1453:
484:, published in Leipzig in three volumes from 1888 to 1893. Decades later, Engel would also be one of the two editors of Lie's collected works.
1488:
1478:
190:
958:
1422:
1344:
518:
1253:
527:
1473:
1398:
1392:
1363:
453:
1404:
1410:
1405:"On complexes â in particular, line and sphere complexes â with applications to the theory of partial differential equations"
809:
781:
664:
539:
175:
1423:
U. Amaldi, "On the principal results obtained in the theory of continuous groups since the death of Sophus Lie (1898â1907)"
878:
551:
351:. He was the youngest of six children born to Lutheran pastor Johann Herman Lie and his wife, who came from a well-known
1257:
131:
1317:
1290:
943:
304:
1448:
1282:
427:
733:
656:
580:
465:
931:
757:
659:. English translation available: Edited and translated from the German and with a foreword by Joël Merker, see
1303:
473:
123:
119:
506:
1263:
1066:
1029:
992:
510:
438:
601:
used Lie's work on group theory in his papers from 1922 and 1923, and Lie groups today play a role in
488:
776:
636:
363:
1458:
1368:
1150:
238:
1338:
624:. He gathered support for the establishment of an award for outstanding work in pure mathematics.
514:
358:
He had his primary education in the south-eastern coast of Moss, before attending high school in
171:
252:
336:
167:
159:
115:
966:
575:) could be better understood by "linearizing" them, and studying the corresponding generating
567:
Lie's principal tool, and one of his greatest achievements, was the discovery that continuous
1358:
938:, Lie groups: History, frontiers and applications, vol. 1, Math Sci Press, p. iii,
568:
477:
222:
1193:(with links to 1923 review of Vol. III, 1925 review of Vol. V, & 1928 review of Vol. VI)
632:
260:
1443:
1438:
1227:
907:
1309:
1235:
8:
1354:
404:
400:
379:
328:
234:
151:
147:
111:
1305:
Felix Klein and Sophus Lie: Evolution of the idea of symmetry in the nineteenth century
1275:
995:
988:
862:
690:
Vorlesungen ĂŒber differentialgleichungen mit bekannten infinitesimalen transformationen
668:
588:
408:
316:
272:
256:
218:
101:
1378:
1313:
1286:
1215:
1184:
1132:
939:
805:
751:
660:
602:
492:
458:
442:
185:
1207:
1179:
1154:
1127:
1106:
1087:
1050:
1013:
846:
829:
627:
Lie advised many doctoral students who went on to become successful mathematicians.
1387:
1249:
1231:
1174:
1122:
1082:
1045:
1008:
841:
431:
290:
229:
163:
91:
741:
631:
became widely regarded as one of the greatest mathematicians of the 20th century.
1399:"The foundations of the theory of infinite continuous transformation groups â II"
1223:
1032:
Vorlesungen ĂŒber continuerliche
Gruppen mit geometrischen und anderen Anwendungen
695:
617:
248:
1393:"The foundations of the theory of infinite continuous transformation groups â I"
1374:
1270:
1102:
825:
771:
396:
628:
487:
In 1886, Lie became a professor at
Leipzig, replacing Klein, who had moved to
264:
1432:
1333:
1219:
1188:
1136:
737:
412:
324:
1299:
598:
576:
348:
268:
60:
1337:
621:
592:
496:
469:
388:
208:
139:
135:
32:
339:. He also made substantial contributions to the development of algebra.
613:
155:
418:
Lie obtained his PhD at the
University of Christiania (in present-day
890:
Proceedings of the Sophus Lie
Memorial Conference, Oslo, August, 1992
584:
572:
480:
by then). Engel would help Lie to write his most important treatise,
441:, editing and publishing the mathematical works of their countryman,
391:
and they became close friends. When he left Berlin, Lie travelled to
352:
143:
347:
Marius Sophus Lie was born on 17 December 1842 in the small town of
457:, together with the physician Jacob Worm-MĂŒller, and the biologist
332:
672:
1469:
Corresponding members of the Saint
Petersburg Academy of Sciences
395:, where he was joined by Klein two months later. There, they met
387:, where he stayed from September to February 1870. There, he met
127:
1277:
The mathematician Sophus Lie: It was the audacity of my thinking
1411:"Foundations of an invariant theory of contact transformations"
635:'s work was proved to be of importance to a variety of fields.
384:
321:
612:
Sophus Lie was an eager proponent in the establishment of the
296:
1425:
English translation of a survey paper that followed his death
583:). The generators are subject to a linearized version of the
392:
519:
National
Academy of Sciences of the United States of America
383:. That same year he received a scholarship and travelled to
533:
419:
374:
359:
79:
1417:"The infinitesimal contact transformations of mechanics"
468:
arrived at
Christiania to help him, with the support of
1484:
Foreign associates of the National Academy of Sciences
1401:
An English translation of a key paper by Lie (Part II)
639:
made contributions to various fields of mathematics.
373:, was published in 1869 by the Academy of Sciences in
1395:
An English translation of a key paper by Lie (Part I)
1352:
892:, Oslo: Scandinavian University Press, pp. 3â21.
305:
293:
591:, and have the structure of what is today called a
1274:
1109:Gesammelte Abhandlungen. Geometrische Abhandlungen
545:Title page to "Theorie der Transformationsgruppen"
620:, and the lack of a prize for mathematics in the
411:) had to leave France very quickly. Lie left for
1430:
1248:
824:
557:Preface to "Theorie der Transformationsgruppen"
371:ReprÀsentation der ImaginÀren der Plangeometrie
1143:
1302:(1988), Grant, Hardy; Shenitzer, Abe (eds.),
1167:Bulletin of the American Mathematical Society
1115:Bulletin of the American Mathematical Society
1095:
1064:
1027:
987:
495:, a disease caused by impaired absorption of
437:In 1872, Lie spent eight years together with
320:; 17 December 1842 â 18 February 1899) was a
1419:An English translation of a key paper by Lie
1413:An English translation of a key paper by Lie
1407:An English translation of a key paper by Lie
1348:(11th ed.). Cambridge University Press.
1163:, Norwegian edition published by Aschehoug)"
936:Sophus Lie's 1880 transformation group paper
1208:"Sophus Lie: A Sketch of his Life and Work"
864:Over en classe geometriske Transformationer
804:. Cambridge University Press. p. 201.
728:. Written with the help of Georg Scheffers.
718:. Written with the help of Friedrich Engel.
708:. Written with the help of Georg Scheffers.
684:. Written with the help of Friedrich Engel.
424:Over en Classe geometriske Transformationer
1214:, vol. 9, no. 1, pp. 1â38,
1149:
616:. Inspired by the Nansen fund named after
31:
1464:Members of the French Academy of Sciences
1205:
1178:
1126:
1101:
1086:
1049:
1012:
845:
1332:
1269:
1069:Geometrie der BerĂŒhrungstransformationen
877:
724:Geometrie der BerĂŒhrungstransformationen
704:Vorlesungen ĂŒber continuierliche Gruppen
1364:MacTutor History of Mathematics Archive
930:
454:Archiv for Mathematik og Naturvidenskab
1431:
1298:
1155:"Book Review: vol. IV of Sophus Lie's
746:, Leipzig: Teubner; 7 vols., 1922â1960
714:Theorie der Transformationsgruppen III
369:Sophus Lie's first mathematical work,
1454:19th-century Norwegian mathematicians
901:
899:
854:
799:
782:List of things named after Sophus Lie
680:Theorie der Transformationsgruppen II
517:in 1895 and foreign associate of the
509:in 1878, Corresponding Member of the
315:
1489:Academic staff of Leipzig University
1479:Foreign members of the Royal Society
651:Theorie der Transformationsgruppen I
451:From 1876, he co-edited the journal
860:
726:(in German), Leipzig: B. G. Teubner
721:
716:(in German), Leipzig: B. G. Teubner
711:
706:(in German), Leipzig: B. G. Teubner
701:
692:(in German), Leipzig: B. G. Teubner
687:
682:(in German), Leipzig: B. G. Teubner
677:
653:(in German), Leipzig: B. G. Teubner
648:
505:He was made Honorary Member of the
327:. He largely created the theory of
13:
1259:Dictionary of Scientific Biography
896:
871:
609:certainly the least known today".
482:Theorie der Transformationsgruppen
342:
14:
1500:
1326:
867:(PhD). University of Christiania.
422:) in 1871 with a thesis entitled
1474:University of Christiania alumni
905:
550:
538:
526:
289:
1180:10.1090/S0002-9904-1930-04950-2
1128:10.1090/S0002-9904-1939-07032-8
1088:10.1090/s0002-9904-1897-00430-x
1058:
1051:10.1090/s0002-9904-1895-00283-9
1014:10.1090/s0002-9904-1898-00476-7
959:"The History of the Abel Prize"
883:"Sophus Lie, the Mathematician"
847:10.1090/s0002-9904-1899-00628-1
731:
513:in 1892, Foreign Member of the
331:and applied it to the study of
132:CarathĂ©odoryâJacobiâLie theorem
1021:
981:
951:
924:
818:
793:
1:
1199:
476:(who were both professors at
1384:Works by or about Sophus Lie
124:Infinitesimal transformation
7:
1107:"Book Review: Sophus Lie's
909:Marius Sophus Lie Biography
765:
694:. Written with the help of
655:. Written with the help of
507:London Mathematical Society
10:
1505:
1339:"Lie, Marius Sophus"
756:: CS1 maint: postscript (
511:French Academy of Sciences
439:Peter Ludwig Mejdell Sylow
403:. But on 19 July 1870 the
1206:Fritzsche, Bernd (1999),
802:Remarkable Mathematicians
777:List of simple Lie groups
637:Hans Frederick Blichfeldt
562:
407:began and Klein (who was
364:University of Christiania
278:
244:
228:
219:University of Christiania
214:
204:
197:
181:
107:
102:University of Christiania
97:
87:
68:
42:
30:
23:
1369:University of St Andrews
1300:Yaglom, Isaak Moiseevich
787:
642:
581:infinitesimal generators
571:(now called, after him,
239:Cato Maximilian Guldberg
1449:People from Eid, Norway
1345:EncyclopĂŠdia Britannica
1264:Charles Scribner's Sons
1157:Gesammelte Abhandlungen
743:Gesammelte Abhandlungen
515:Royal Society of London
16:Norwegian mathematician
1065:Lovett, E. O. (1897).
1028:Brooks, J. M. (1895).
912:. World of Mathematics
337:differential equations
120:Contact transformation
116:Differential invariant
1212:Journal of Lie Theory
1111:, Volumes I & II"
1075:Bull. Amer. Math. Soc
1038:Bull. Amer. Math. Soc
1001:Bull. Amer. Math. Soc
834:Bull. Amer. Math. Soc
569:transformation groups
223:University of Leipzig
1355:Robertson, Edmund F.
1254:"Lie, Marius Sophus"
1161:Samlede Avhandlinger
861:Lie, Sophus (1871).
800:James, Ioan (2002).
722:Lie, Sophus (1896),
712:Lie, Sophus (1893),
702:Lie, Sophus (1893),
688:Lie, Sophus (1891),
678:Lie, Sophus (1890),
649:Lie, Sophus (1888),
253:Lucjan Emil Böttcher
1375:Works by Sophus Lie
1353:O'Connor, John J.;
1103:Schilling, O. F. G.
430:and working on the
405:Franco-Prussian War
329:continuous symmetry
235:Carl Anton Bjerknes
172:LieâKolchin theorem
168:Lie's third theorem
152:Lie sphere geometry
148:Lie product formula
112:One-parameter group
879:Helgason, Sigurdur
633:Kazimierz ƻorawski
589:commutator bracket
273:Edgar Odell Lovett
261:Kazimierz ƻorawski
257:Gerhard Kowalewski
1379:Project Gutenberg
1357:(February 2000),
1250:Freudenthal, Hans
1151:Carmichael, R. D.
811:978-0-521-52094-2
665:978-3-662-46210-2
603:quantum mechanics
587:, now called the
493:pernicious anemia
459:Georg Ossian Sars
443:Niels Henrik Abel
285:Marius Sophus Lie
282:
281:
245:Doctoral students
199:Scientific career
186:Lobachevsky Medal
47:Marius Sophus Lie
1496:
1388:Internet Archive
1371:
1349:
1341:
1322:
1295:
1280:
1266:
1245:
1244:
1242:
1194:
1192:
1182:
1147:
1141:
1140:
1130:
1099:
1093:
1092:
1090:
1062:
1056:
1055:
1053:
1025:
1019:
1018:
1016:
985:
979:
978:
976:
974:
969:on 16 March 2018
965:. Archived from
963:www.abelprize.no
955:
949:
948:
928:
922:
921:
919:
917:
903:
894:
893:
887:
875:
869:
868:
858:
852:
851:
849:
822:
816:
815:
797:
761:
755:
747:
734:Engel, Friedrich
727:
717:
707:
693:
683:
654:
554:
542:
530:
432:Erlangen program
380:Crelle's Journal
319:
314:
308:
303:
302:
299:
298:
295:
230:Doctoral advisor
75:
72:18 February 1899
57:17 December 1842
56:
54:
35:
21:
20:
1504:
1503:
1499:
1498:
1497:
1495:
1494:
1493:
1459:Group theorists
1429:
1428:
1329:
1320:
1293:
1283:Springer-Verlag
1271:Stubhaug, Arild
1240:
1238:
1202:
1197:
1148:
1144:
1100:
1096:
1063:
1059:
1044:(10): 241â248.
1026:
1022:
986:
982:
972:
970:
957:
956:
952:
946:
932:Hermann, Robert
929:
925:
915:
913:
906:Gale, Thomson.
904:
897:
885:
876:
872:
859:
855:
826:Darboux, Gaston
823:
819:
812:
798:
794:
790:
768:
749:
748:
696:Georg Scheffers
657:Friedrich Engel
645:
618:Fridtjof Nansen
579:(the so-called
565:
558:
555:
546:
543:
534:
531:
500:
466:Friedrich Engel
345:
343:Life and career
312:
306:
292:
288:
271:
267:
263:
259:
255:
251:
249:Hans Blichfeldt
237:
221:
189:
174:
170:
166:
162:
158:
154:
150:
146:
142:
138:
134:
130:
126:
122:
118:
114:
98:Alma mater
83:
77:
73:
64:
58:
52:
50:
49:
48:
38:
26:
17:
12:
11:
5:
1502:
1492:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1427:
1426:
1420:
1414:
1408:
1402:
1396:
1390:
1381:
1372:
1350:
1336:, ed. (1911).
1334:Chisholm, Hugh
1328:
1327:External links
1325:
1324:
1323:
1318:
1296:
1291:
1267:
1246:
1201:
1198:
1196:
1195:
1173:(5): 337â338.
1142:
1121:(7): 513â514.
1094:
1081:(9): 321â350.
1057:
1020:
1007:(4): 155â167.
980:
950:
944:
934:, ed. (1975),
923:
895:
870:
853:
840:(7): 367â370.
817:
810:
791:
789:
786:
785:
784:
779:
774:
772:Lie derivative
767:
764:
763:
762:
738:Heegaard, Poul
729:
719:
709:
699:
685:
675:
644:
641:
564:
561:
560:
559:
556:
549:
547:
544:
537:
535:
532:
525:
498:
401:Gaston Darboux
397:Camille Jordan
344:
341:
280:
279:
276:
275:
246:
242:
241:
232:
226:
225:
216:
212:
211:
206:
202:
201:
195:
194:
183:
179:
178:
109:
108:Known for
105:
104:
99:
95:
94:
89:
85:
84:
78:
76:(aged 56)
70:
66:
65:
59:
46:
44:
40:
39:
36:
28:
27:
24:
15:
9:
6:
4:
3:
2:
1501:
1490:
1487:
1485:
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1436:
1434:
1424:
1421:
1418:
1415:
1412:
1409:
1406:
1403:
1400:
1397:
1394:
1391:
1389:
1385:
1382:
1380:
1376:
1373:
1370:
1366:
1365:
1360:
1356:
1351:
1347:
1346:
1340:
1335:
1331:
1330:
1321:
1319:3-7643-3316-2
1315:
1311:
1307:
1306:
1301:
1297:
1294:
1292:3-540-42137-8
1288:
1284:
1279:
1278:
1272:
1268:
1265:
1261:
1260:
1255:
1252:(1970â1980),
1251:
1247:
1237:
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1204:
1203:
1190:
1186:
1181:
1176:
1172:
1168:
1164:
1162:
1158:
1152:
1146:
1138:
1134:
1129:
1124:
1120:
1116:
1112:
1110:
1104:
1098:
1089:
1084:
1080:
1076:
1072:
1070:
1061:
1052:
1047:
1043:
1039:
1035:
1033:
1024:
1015:
1010:
1006:
1002:
998:
996:
990:
989:Lovett, E. O.
984:
968:
964:
960:
954:
947:
945:0-915692-10-4
941:
937:
933:
927:
911:
910:
902:
900:
891:
884:
880:
874:
866:
865:
857:
848:
843:
839:
835:
831:
827:
821:
813:
807:
803:
796:
792:
783:
780:
778:
775:
773:
770:
769:
759:
753:
745:
744:
739:
735:
732:Lie, Sophus,
730:
725:
720:
715:
710:
705:
700:
697:
691:
686:
681:
676:
674:
670:
666:
662:
658:
652:
647:
646:
640:
638:
634:
630:
625:
623:
619:
615:
610:
608:
604:
600:
596:
594:
590:
586:
582:
578:
577:vector fields
574:
570:
553:
548:
541:
536:
529:
524:
523:
522:
520:
516:
512:
508:
503:
501:
494:
490:
485:
483:
479:
475:
471:
467:
462:
460:
456:
455:
449:
446:
444:
440:
435:
433:
429:
425:
421:
416:
414:
413:Fontainebleau
410:
406:
402:
398:
394:
390:
386:
382:
381:
376:
372:
367:
365:
361:
356:
354:
350:
340:
338:
334:
330:
326:
325:mathematician
323:
318:
317:[liË]
310:
309:
301:
286:
277:
274:
270:
266:
262:
258:
254:
250:
247:
243:
240:
236:
233:
231:
227:
224:
220:
217:
213:
210:
207:
203:
200:
196:
192:
187:
184:
180:
177:
176:See full list
173:
169:
165:
164:Lie's theorem
161:
160:Lie transform
157:
153:
149:
145:
141:
137:
133:
129:
125:
121:
117:
113:
110:
106:
103:
100:
96:
93:
90:
86:
81:
71:
67:
62:
45:
41:
34:
29:
22:
19:
1362:
1359:"Sophus Lie"
1343:
1304:
1276:
1258:
1239:, retrieved
1211:
1170:
1166:
1160:
1156:
1145:
1118:
1114:
1108:
1097:
1078:
1074:
1068:
1060:
1041:
1037:
1031:
1023:
1004:
1000:
994:
983:
971:. Retrieved
967:the original
962:
953:
935:
926:
914:. Retrieved
908:
889:
873:
863:
856:
837:
833:
830:"Sophus Lie"
820:
801:
795:
742:
723:
713:
703:
689:
679:
650:
626:
611:
606:
599:Hermann Weyl
597:
566:
504:
486:
481:
474:Adolph Mayer
463:
452:
450:
447:
436:
423:
417:
378:
377:and also by
370:
368:
357:
349:Nordfjordeid
346:
284:
283:
269:Elling Holst
215:Institutions
198:
74:(1899-02-18)
61:Nordfjordeid
18:
1444:1899 deaths
1439:1842 births
629:Ălie Cartan
622:Nobel Prize
593:Lie algebra
389:Felix Klein
375:Christiania
265:Ălie Cartan
209:Mathematics
140:Lie bracket
136:Lie algebra
88:Nationality
37:Lie in 1896
1433:Categories
1310:BirkhÀuser
1241:2 December
1236:0927.01029
1200:References
973:4 February
916:23 January
614:Abel Prize
573:Lie groups
313:Norwegian:
156:Lie theory
80:Kristiania
53:1842-12-17
25:Sophus Lie
1220:0949-5932
1189:0002-9904
1137:0002-9904
1067:"Review:
1030:"Review:
993:"Review:
673:1003.3202
607:in detail
585:group law
497:vitamin B
489:Göttingen
464:In 1884,
353:Trondheim
322:Norwegian
144:Lie group
92:Norwegian
1273:(2002),
1153:(1930).
1105:(1939).
991:(1898).
881:(1994),
828:(1899).
766:See also
752:citation
740:(eds.),
521:in 1895.
428:Erlangen
409:Prussian
355:family.
333:geometry
191:ForMemRS
82:, Norway
63:, Norway
1386:at the
1228:1680023
478:Leipzig
128:W-curve
1316:
1289:
1234:
1226:
1218:
1187:
1135:
942:
808:
663:
563:Legacy
385:Berlin
205:Fields
193:(1895)
188:(1897)
182:Awards
886:(PDF)
788:Notes
669:arXiv
643:Books
470:Klein
393:Paris
1314:ISBN
1287:ISBN
1243:2010
1216:ISSN
1185:ISSN
1133:ISSN
975:2021
940:ISBN
918:2009
806:ISBN
758:link
667:and
661:ISBN
472:and
420:Oslo
399:and
360:Oslo
335:and
69:Died
43:Born
1377:at
1232:Zbl
1175:doi
1123:doi
1083:doi
1046:doi
1009:doi
842:doi
307:LEE
1435::
1367:,
1361:,
1342:.
1312:,
1308:,
1285:,
1281:,
1262:,
1256:,
1230:,
1224:MR
1222:,
1210:,
1183:.
1171:36
1169:.
1165:.
1131:.
1119:45
1117:.
1113:.
1077:.
1073:.
1040:.
1036:.
1003:.
999:.
961:.
898:^
888:,
836:.
832:.
754:}}
750:{{
736:;
595:.
502:.
499:12
461:.
445:.
434:.
366:.
311:;
297:iË
1191:.
1177::
1159:(
1139:.
1125::
1091:.
1085::
1079:3
1071:"
1054:.
1048::
1042:1
1034:"
1017:.
1011::
1005:4
997:"
977:.
920:.
850:.
844::
838:5
814:.
760:)
698:.
671::
300:/
294:l
291:/
287:(
55:)
51:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
