522:
and ornamentics," and "Some moments in the development of mathematical ideas." Black
Mountain College faculty contacted him shortly after concerning a full-time position. After negotiating his salary from $ 25 to $ 40 per month, Dehn and his wife moved into housing provided by the school and he began teaching in January 1945.
521:
In March 1944, Dehn was invited to give two talks at Black
Mountain College on the philosophy and history of mathematics. He noted in a letter that a lecture on an advanced mathematical topic didn't seem appropriate given the audience. He instead offered up the lectures "Common roots of mathematics
572:
He enjoyed the forested mountains found in Black
Mountain, and would often hold class in the woods, giving lectures during hikes. His lectures frequently drifted off topic on tangents about philosophy, the arts, and nature and their connection to mathematics. He and his wife took part in community
31:
525:
While at Black
Mountain College, Dehn taught courses in Mathematics, Philosophy, Greek, and Italian. In his class "Geometry for Artists," Dehn introduced students to geometric concepts such as
468:, and Weil considered Dehn's seminar to be his most important contribution to mathematics. As an example of its influence, the seminar has been credited for inspiring Siegel's discovery of the
460:
at
Frankfurt, where he stayed until he was forced to retire in 1935. During this time he taught a seminar on historical works of mathematics. The seminar attracted prolific mathematicians
1134:
234:. Dehn's early life and career took place in Germany. However, he was forced to retire in 1935 and eventually fled Germany in 1939 and emigrated to the United States.
1149:
1154:
1159:
604:
130:
1174:
1114:
1109:
716:
The story of his travel in 1940 from Norway via
Stockholm, Moscow, trans-Siberian train, Vladivostok, Japan to San Francisco is described in
730:
1124:
1119:
491:
475:
Dehn stayed in
Germany until January 1939, when he fled to Copenhagen, and then to Trondheim, Norway, where he took a position at the
1169:
1164:
818:
479:. In October 1940 he left Norway for America by way of Siberia and Japan (the Atlantic crossing was considered too dangerous).
932:
569:. His classes had an emphasis on the way shapes relate to each other, a concept that can be useful in artistic mediums.
1028:
965:
1068:
843:
476:
923:
Schlomiuk, Norbert (2004). "André Weil: The Man and the
Historian of Mathematics". In Grattan-Guinness, Ivor (ed.).
1129:
674:
487:
384:
880:
639:
506:
73:
796:
1084:
752:
679:
450:
317:
441:
in terms of the length of that relation, is also named after him. In 1914 he proved that the left and right
878:
Siegel, Carl Ludwig; Lenzen, Kevin M. (1979-12-01). "On the history of the frankfurt mathematics seminar".
986:
Sher, R. B. (1994). Stewart, Ian (ed.). "Max Dehn and Black
Mountain College". The Mathematical Tourist.
169:
469:
403:
360:
341:
246:
134:
305:
92:
664:
614:
445:
are not equivalent. In the early 1920s Dehn introduced the result that would come to be known as the
864:
1139:
823:
438:
337:
329:
165:
417:
Dehn married
Antonie Landau on August 23, 1912. Also in 1912, Dehn invented what is now known as
407:
1020:
1014:
957:
499:
483:
434:
368:
231:
173:
838:
813:
380:
250:
1080:
949:
774:
1144:
1104:
1099:
584:, which allowed him to remain on campus and act as an advisor. Unfortunately he died of an
446:
309:
138:
8:
856:
810:
694:
684:
495:
426:
418:
254:
195:
106:
573:
meetings and often ate in the dining room. They also regularly had long breakfasts with
905:
860:
718:
581:
574:
566:
461:
270:
1064:
1024:
961:
950:
928:
909:
897:
654:
457:
422:
325:
722:
390:
In 1910 Dehn published a paper on three-dimensional topology in which he introduced
995:
889:
852:
797:"Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture"
689:
534:
526:
349:
290:
180:
1060:
669:
619:
542:
530:
399:
395:
376:
114:
1052:
609:
510:
345:
262:
199:
102:
1093:
1056:
901:
659:
430:
364:
301:
266:
238:
219:
185:
122:
55:
775:"Max Dehn: An Artist among Mathematicians and a Mathematician among Artists"
465:
748:
629:
442:
391:
333:
258:
242:
203:
110:
649:
155:
1051:. Translated from the German and with introductions and an appendix by
999:
893:
634:
624:
538:
482:
In America, Dehn obtained a position at Idaho Southern University (now
321:
274:
126:
118:
558:
585:
562:
554:
356:
297:
227:
223:
600:
A wide variety of concepts have been named for Dehn. Among them:
589:
550:
313:
286:
51:
839:"Max Dehn and the Origins of Topology and Infinite Group Theory"
592:
trees from the campus. He is buried in the woods on the campus.
546:
498:. Finally in 1945, he moved to the experimental arts college,
328:. From 1900 to 1911 he was an employee and researcher at the
324:
as counterexamples to the theorem in geometries without the
723:"Max Dehn, Kurt Gödel, and the Trans-Siberian Escape Route"
30:
394:
and used it to construct homology spheres. He also stated
1135:
Jewish emigrants from Nazi Germany to the United States
379:. In 1908 he believed that he had found a proof of the
375:. Also in 1907, he described the construction of a new
316:. In 1900 he wrote his dissertation on the role of the
1016:
The Honors Class: Hilbert's Problems and Their Solvers
952:
The Honors Class: Hilbert's Problems and Their Solvers
795:Bergmann, Birgit and Moritz Epple, and Ruti Ungar
808:
218:(November 13, 1878 – June 27, 1952) was a German
1091:
588:shortly after witnessing the removal of several
344:, by introducing what was afterwards called the
1019:. Natick, Massachusetts: A K Peters. pp.
437:, which estimates the area of a relation in a
348:. This was the first resolution of one of the
285:Dehn was born to a family of Jewish origin in
1155:Academic staff of Goethe University Frankfurt
956:. Natick, Massachusetts: A K Peters. p.
916:
877:
836:
731:Notices of the American Mathematical Society
1150:Academic staff of the University of MĂĽnster
449:; its proof would be published in 1927 by
402:in 1929. The result was proved in 1957 by
941:
922:
516:
398:, but an error was found in his proof by
249:, making him the first to resolve one of
16:German-American mathematician (1878–1952)
1160:Illinois Institute of Technology faculty
712:
710:
421:and used it in his work on the word and
320:in axiomatic geometry, constructing the
1012:
1006:
981:
979:
977:
947:
819:MacTutor History of Mathematics Archive
768:
766:
764:
762:
760:
502:, where he was the only mathematician.
1092:
779:Black Mountain College Studies Journal
772:
717:
1175:Mathematicians from the German Empire
927:. Hindustan Book Agency. p. 62.
707:
367:the first book on the foundations of
308:in 1899, and obtained a proof of the
1115:20th-century American mathematicians
1110:19th-century American mathematicians
985:
974:
925:History of the Mathematical Sciences
865:10.4169/amer.math.monthly.122.03.217
857:10.4169/amer.math.monthly.122.03.217
757:
580:In the summer of 1952 Dehn was made
1049:Papers on group theory and topology
472:among Riemann's unpublished notes.
253:. Dehn's doctoral students include
13:
1125:20th-century German mathematicians
1120:19th-century German mathematicians
1041:
14:
1186:
1074:
844:The American Mathematical Monthly
477:Norwegian Institute of Technology
355:Dehn's interests later turned to
265:; he also mentored mathematician
675:Mapping class group of a surface
488:Illinois Institute of Technology
486:). In 1942 he took a job at the
251:Hilbert's well-known 23 problems
29:
1063:, New York, 1987. viii+396 pp.
1170:Black Mountain College faculty
1165:Idaho State University faculty
988:The Mathematical Intelligencer
881:The Mathematical Intelligencer
871:
830:
802:
789:
742:
296:He studied the foundations of
74:Black Mountain, North Carolina
1:
1085:University of Texas at Austin
1013:Yandell, Benjamin H. (2002).
948:Yandell, Benjamin H. (2002).
753:Mathematics Genealogy Project
700:
680:Non-Archimedean ordered field
773:Peifer, David (March 2011).
414:, was posed by him in 1911.
280:
222:most famous for his work in
7:
595:
170:Goethe University Frankfurt
10:
1191:
645:Other topics of interest
640:Dehn–Sommerville equations
490:, and in 1943 he moved to
404:Christos Papakyriakopoulos
361:combinatorial group theory
318:Legendre angle sum theorem
135:Dehn-Sommerville equations
665:Group isomorphism problem
209:
191:
179:
161:
151:
144:
98:
88:
80:
62:
37:
28:
21:
824:University of St Andrews
439:finitely presented group
363:. In 1907 he wrote with
1130:Scientists from Hamburg
605:Dehn's rigidity theorem
456:In 1922 Dehn succeeded
408:word problem for groups
342:Hilbert's third problem
247:Hilbert's third problem
131:Dehn's rigidity theorem
93:University of Göttingen
1055:. With an appendix by
517:Black Mountain College
500:Black Mountain College
484:Idaho State University
470:Riemann–Siegel formula
435:geometric group theory
369:combinatorial topology
245:in 1900 Dehn resolved
237:Dehn was a student of
232:geometric group theory
174:Black Mountain College
837:David Peifer (2015).
338:University of MĂĽnster
330:University of MĂĽnster
166:University of MĂĽnster
811:Robertson, Edmund F.
447:Dehn-Nielsen theorem
340:in 1900 he resolved
310:Jordan curve theorem
139:Dehn-Nielsen theorem
809:O'Connor, John J.;
695:Undecidable problem
685:Scissors congruence
567:regular polyhedrons
496:Annapolis, Maryland
381:Poincaré conjecture
255:Ott-Heinrich Keller
196:Ott-Heinrich Keller
1000:10.1007/BF03026616
894:10.1007/BF03028242
582:Professor Emeritus
575:Buckminster Fuller
492:St. John's College
462:Carl Ludwig Siegel
429:. The notion of a
410:, also called the
271:Dorothea Rockburne
934:978-93-86279-16-3
719:Dawson, J. W. Jr.
655:Conjugacy problem
458:Ludwig Bieberbach
326:Archimedean axiom
213:
212:
192:Doctoral students
146:Scientific career
48:November 13, 1878
1182:
1035:
1034:
1010:
1004:
1003:
983:
972:
971:
955:
945:
939:
938:
920:
914:
913:
875:
869:
868:
834:
828:
827:
806:
800:
793:
787:
786:
770:
755:
746:
740:
739:
727:
714:
690:Two ears theorem
615:Dehn's algorithm
419:Dehn's algorithm
387:found an error.
371:, then known as
350:Hilbert Problems
291:Imperial Germany
269:and the artists
216:Max Wilhelm Dehn
181:Doctoral advisor
107:Dehn's algorithm
69:
47:
45:
33:
19:
18:
1190:
1189:
1185:
1184:
1183:
1181:
1180:
1179:
1140:Group theorists
1090:
1089:
1077:
1061:Springer-Verlag
1044:
1042:Further reading
1039:
1038:
1031:
1011:
1007:
984:
975:
968:
946:
942:
935:
921:
917:
876:
872:
835:
831:
807:
803:
794:
790:
771:
758:
747:
743:
725:
715:
708:
703:
670:Lotschnittaxiom
598:
545:sectioned into
519:
400:Hellmuth Kneser
377:homology sphere
283:
202:
198:
172:
168:
137:
133:
129:
125:
121:
117:
113:
109:
105:
89:Alma mater
76:
71:
67:
58:
49:
43:
41:
24:
17:
12:
11:
5:
1188:
1178:
1177:
1172:
1167:
1162:
1157:
1152:
1147:
1142:
1137:
1132:
1127:
1122:
1117:
1112:
1107:
1102:
1088:
1087:
1081:Dehn's archive
1076:
1075:External links
1073:
1072:
1071:
1053:John Stillwell
1043:
1040:
1037:
1036:
1030:978-1568812168
1029:
1005:
973:
967:978-1568812168
966:
940:
933:
915:
888:(4): 223–230.
870:
851:(3): 217–233.
829:
801:
788:
756:
741:
705:
704:
702:
699:
698:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
643:
642:
637:
632:
627:
622:
617:
612:
610:Dehn invariant
607:
597:
594:
577:and his wife.
518:
515:
511:North Carolina
507:Black Mountain
373:analysis situs
346:Dehn invariant
282:
279:
263:Wilhelm Magnus
211:
210:
207:
206:
200:Wilhelm Magnus
193:
189:
188:
183:
177:
176:
163:
159:
158:
153:
149:
148:
142:
141:
103:Dehn invariant
100:
99:Known for
96:
95:
90:
86:
85:
82:
78:
77:
72:
70:(aged 73)
64:
60:
59:
50:
39:
35:
34:
26:
25:
22:
15:
9:
6:
4:
3:
2:
1187:
1176:
1173:
1171:
1168:
1166:
1163:
1161:
1158:
1156:
1153:
1151:
1148:
1146:
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1097:
1095:
1086:
1082:
1079:
1078:
1070:
1069:0-387-96416-9
1066:
1062:
1058:
1057:Otto Schreier
1054:
1050:
1046:
1045:
1032:
1026:
1022:
1018:
1017:
1009:
1001:
997:
993:
989:
982:
980:
978:
969:
963:
959:
954:
953:
944:
936:
930:
926:
919:
911:
907:
903:
899:
895:
891:
887:
883:
882:
874:
866:
862:
858:
854:
850:
846:
845:
840:
833:
825:
821:
820:
815:
812:
805:
798:
792:
784:
780:
776:
769:
767:
765:
763:
761:
754:
750:
745:
737:
733:
732:
724:
720:
713:
711:
706:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
660:Freiheitssatz
658:
656:
653:
651:
648:
647:
646:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
602:
601:
593:
591:
587:
583:
578:
576:
570:
568:
564:
560:
556:
552:
548:
544:
540:
536:
532:
528:
523:
514:
512:
508:
503:
501:
497:
493:
489:
485:
480:
478:
473:
471:
467:
463:
459:
454:
452:
451:Jakob Nielsen
448:
444:
443:trefoil knots
440:
436:
432:
431:Dehn function
428:
425:problems for
424:
420:
415:
413:
409:
405:
401:
397:
393:
388:
386:
382:
378:
374:
370:
366:
365:Poul Heegaard
362:
358:
353:
351:
347:
343:
339:
335:
331:
327:
323:
319:
315:
311:
307:
303:
299:
294:
292:
288:
278:
276:
272:
268:
267:Peter Nemenyi
264:
260:
256:
252:
248:
244:
241:, and in his
240:
239:David Hilbert
235:
233:
229:
225:
221:
220:mathematician
217:
208:
205:
201:
197:
194:
190:
187:
186:David Hilbert
184:
182:
178:
175:
171:
167:
164:
160:
157:
154:
150:
147:
143:
140:
136:
132:
128:
124:
123:Dehn function
120:
116:
112:
108:
104:
101:
97:
94:
91:
87:
83:
79:
75:
66:June 27, 1952
65:
61:
57:
56:German Empire
53:
40:
36:
32:
27:
20:
1048:
1015:
1008:
994:(1): 54–55.
991:
987:
951:
943:
924:
918:
885:
879:
873:
848:
842:
832:
817:
804:
791:
782:
778:
744:
738:: 1068–1075.
735:
729:
644:
630:Dehn surgery
620:Dehn's lemma
599:
579:
571:
524:
520:
504:
481:
474:
455:
416:
412:Dehn problem
411:
396:Dehn's lemma
392:Dehn surgery
389:
372:
354:
334:habilitation
295:
284:
259:Ruth Moufang
243:habilitation
236:
215:
214:
204:Ruth Moufang
162:Institutions
145:
115:Dehn's lemma
111:Dehn surgery
68:(1952-06-27)
1145:Topologists
1105:1952 deaths
1100:1878 births
650:Chiral knot
505:He died in
322:Dehn planes
156:Mathematics
81:Nationality
1094:Categories
1047:Max Dehn,
814:"Max Dehn"
701:References
635:Dehn twist
625:Dehn plane
559:hyperbolas
466:André Weil
275:Ruth Asawa
127:Dehn plane
119:Dehn twist
44:1878-11-13
1083:– at the
910:124018033
902:0343-6993
555:parabolas
513:in 1952.
423:conjugacy
332:. In his
306:Göttingen
281:Biography
749:Max Dehn
721:(2002).
596:See also
586:embolism
551:ellipses
357:topology
314:polygons
298:geometry
228:topology
224:geometry
84:American
23:Max Dehn
1021:134–135
751:at the
590:dogwood
563:spheres
547:circles
336:at the
302:Hilbert
287:Hamburg
52:Hamburg
1067:
1027:
964:
931:
908:
900:
863:
557:, and
539:solids
535:planes
527:points
427:groups
406:. The
385:Tietze
383:, but
261:, and
152:Fields
906:S2CID
861:JSTOR
726:(PDF)
543:cones
531:lines
300:with
1065:ISBN
1025:ISBN
962:ISBN
929:ISBN
898:ISSN
799:2012
565:and
537:and
464:and
359:and
312:for
273:and
230:and
63:Died
38:Born
996:doi
958:208
890:doi
853:doi
849:122
494:in
433:in
304:at
1096::
1059:.
1023:.
992:16
990:.
976:^
960:.
904:.
896:.
884:.
859:.
847:.
841:.
822:.
816:.
781:.
777:.
759:^
736:49
734:.
728:.
709:^
561:;
553:,
549:,
541:;
533:,
529:,
509:,
453:.
352:.
293:.
289:,
277:.
257:,
226:,
54:,
1033:.
1002:.
998::
970:.
937:.
912:.
892::
886:1
867:.
855::
826:.
785:.
783:1
46:)
42:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
