423:
509:, Pontryagin, who was a member of the executive committee of the IMU at the time, vigorously objected. Although the IMU stood by its decision to award Margulis the Fields Medal, Margulis was denied a Soviet exit visa by the Soviet authorities and was unable to attend the 1978 ICM in person.
49:
992:
599:
1137:
1132:
291:
1122:
1107:
594:
478:, who openly supported the Russian Orthodox Church and had recently been arrested. They then proceeded to follow their plan of reorganizing the Society.
1102:
261:
explosion when he was 14. His mother
Tatyana Andreyevna, who did not know mathematical symbols, read mathematical books and papers (notably those of
273:) to him, and later worked as his secretary. His mother used alternative names for math symbols, such as "tails up" for the set-union symbol
1092:
416:, to describe situations where the applied control at each moment is either the maximum positive 'steer', or the maximum negative 'steer'.
1147:
470:
Pontryagin participated in a few notorious political campaigns in the Soviet Union. In 1930, he and several other young members of the
1127:
1187:
506:
1142:
1117:
1162:
1152:
1112:
1097:
806:
744:
636:
614:
574:
409:
132:
128:
498:
490:
313:
309:
386:
229:. Completely blind from the age of 14, he made major discoveries in a number of fields of mathematics, including
124:
1182:
556:
1952 - Foundations of
Combinatorial Topology (translated from 1947 original Russian edition) 2015 Dover reprint
398:
394:
942:
1172:
1050:
1177:
559:
1962 - Ordinary
Differential Equations (translated from Russian by Leonas Kacinskas and Walter B. Counts)
471:
455:
1157:
341:
17:
760:
304:
who would become his doctoral thesis advisor. After graduating in 1929, he obtained a position at
620:
427:
305:
297:
657:
419:
Pontryagin authored several influential monographs as well as popular textbooks in mathematics.
363:
329:
734:
413:
325:
234:
795:
1167:
1087:
1082:
1061:
830:
545:
367:
276:
8:
1067:
586:
443:
379:
175:
834:
1025:
715:
631:
481:
Pontryagin was accused of anti-Semitism on several occasions. For example, he attacked
337:
266:
230:
116:
412:
is fundamental to the modern theory of optimization. He also introduced the idea of a
901:
846:
821:
802:
740:
719:
707:
687:
590:
570:
540:, Princeton Mathematical Series, vol. 2, Princeton: Princeton University Press,
514:
451:
447:
333:
183:
179:
926:
905:
886:
865:
332:
while still a student. He went on to lay foundations for the abstract theory of the
1017:
981:
921:
881:
838:
779:
699:
626:
494:
371:
362:, and co-discoverers of the central idea of this theory, that framed cobordism and
301:
203:
161:
156:
120:
842:
819:
Pontryagin, LS (September 14, 1979). "Soviet Anti-Semitism: Reply by
Pontryagin".
798:
564:
541:
482:
459:
405:
390:
270:
238:
187:
366:
are equivalent. This led to the introduction around 1940 of a theory of certain
796:
Mathematics without borders: a history of the
International Mathematical Union.
76:
986:
965:
1076:
711:
475:
439:
347:
In 1935, he was able to compute the homology groups of the classical compact
226:
171:
1046:
1062:
Kutateladze S. S., Sic
Transit... or Heroes, Villains, and Rights of Memory
850:
566:
Ordinary
Differential Equations: Adiwes International Series in Mathematics
502:
258:
223:
106:
95:
355:
550:
254:
149:
1055:
775:
1029:
703:
512:
Pontryagin rejected charges of antisemitism in an article published in
262:
31:
359:
348:
1021:
422:
375:
623:, also called the Pontryagin–Kuratowski theorem, on planar graphs
519:
518:
in 1979. In his memoirs
Pontryagin claims that he struggled with
486:
48:
523:
474:
publicly denounced as counter-revolutionary the
Society's head
431:
250:
72:
465:
385:
In 1942 he introduced the cohomology operations now called
778:, by Lev Pontryagin, Narod Publications, Moscow, 1998 (in
253:
and lost his eyesight completely due to an unsuccessful
1068:
Kutateladze S. S., The
Tragedy of Mathematics in Russia
736:
What's Happening in the Mathematical Sciences, Volume 8
1008:
by Pontryagin, Boltyanskii, Gamkrelidze, Mishchenko".
1004:
Blum, Edward Kenneth (December 1963). "Reviewed Work:
351:, which he would later call his greatest achievement.
340:. Using these tools, he was able to solve the case of
300:, where he was strongly influenced by the lectures of
655:
279:
30:"Pontryagin" redirects here. Not to be confused with
1003:
1138:
Recipients of the Order of the Red Banner of Labour
485:
for being a "mediocre scientist" representing the "
312:in Moscow. In 1970 he became vice president of the
940:
426:Monument to Lev Pontryagin on wall of building on
285:
1133:Recipients of the Order of the October Revolution
1074:
951:MAA Reviews, Mathematical Association of America
688:"Around the graves of Petrovskii and Pontryagin"
493:. When a prominent Soviet Jewish mathematician,
1123:Recipients of the Order of the Badge of Honour
739:, American Mathematical Society, p. 126,
604:: The Mathematical Theory of Optimal Processes
489:", while both men were vice-presidents of the
358:, he is regarded as one of the co-founders of
914:Bulletin of the American Mathematical Society
874:Bulletin of the American Mathematical Society
753:
1108:Full Members of the USSR Academy of Sciences
1006:The Mathematical Theory of Optimal Processes
963:
763:". MacTutor History of Mathematics archive.
863:
818:
656:Robertson, Edmund; O'Connor, John (1999).
562:
535:
1103:Academic staff of Moscow State University
985:
925:
885:
771:
769:
732:
466:Controversy and antisemitism allegations
421:
244:
222:) (3 September 1908 – 3 May 1988) was a
941:Satzer, William J. (October 21, 2015).
759:O'Connor, John J; Edmund F. Robertson "
14:
1075:
900:
766:
685:
945:Foundations of combinatorial topology
908:Foundations of combinatorial topology
218:, first name sometimes anglicized as
790:
788:
681:
679:
677:
1093:20th-century Russian mathematicians
434:, where he lived from 1939 to 1988.
24:
1148:Recipients of the USSR State Prize
25:
1199:
1040:
1010:The American Mathematical Monthly
785:
674:
563:Pontryagin, L. S. (15 May 2014).
53:Lev Semyonovich Pontryagin (left)
1128:Recipients of the Order of Lenin
522:, which he considered a form of
491:International Mathematical Union
393:there are specific instances of
314:International Mathematical Union
47:
1188:Burials at Novodevichy Cemetery
997:
968:Ordinary Differential Equations
957:
934:
927:10.1090/S0002-9904-1953-09702-6
887:10.1090/S0002-9904-1940-07199-X
529:
404:Starting in 1952, he worked in
125:Pontryagin cohomology operation
1143:Recipients of the Stalin Prize
974:Canadian Mathematical Bulletin
894:
857:
812:
726:
692:The Mathematical Intelligencer
649:
637:Pontryagin's maximum principle
438:Pontryagin's students include
129:Pontryagin's maximum principle
13:
1:
1118:Recipients of the Lenin Prize
1051:Mathematics Genealogy Project
843:10.1126/science.205.4411.1083
686:Maritz, Pieter (2003-06-01).
615:Andronov–Pontryagin criterion
133:Andronov–Pontryagin criterion
1163:Scientists with disabilities
1153:Blind scholars and academics
658:"Lev Pontryagin - Biography"
617:for planar dynamical systems
344:for abelian groups in 1934.
7:
1056:Autobiography of Pontryagin
608:
472:Moscow Mathematical Society
10:
1204:
1113:Heroes of Socialist Labour
1098:Mathematicians from Moscow
964:Brauer, Fred (June 1964).
864:Puckett Jr, W. T. (1940).
374:, designed to vanish on a
200:Lev Semyonovich Pontryagin
29:
987:10.1017/S0008439500027119
207:
193:
167:
155:
145:
138:
112:
102:
83:
58:
46:
39:
733:Mackenzie, Dana (2010),
642:
308:. In 1934 he joined the
536:Pontrjagin, L. (1939),
342:Hilbert's fifth problem
319:
306:Moscow State University
298:Moscow State University
208:Лев Семёнович Понтрягин
497:, was selected by the
450:, Yevgeny Mishchenko,
435:
368:characteristic classes
287:
1183:Soviet mathematicians
505:at the upcoming 1978
425:
324:Pontryagin worked on
288:
286:{\displaystyle \cup }
245:Early life and career
235:differential topology
1173:Russian blind people
970:by L. S. Pontryagin"
621:Kuratowski's theorem
277:
27:Soviet mathematician
1178:Soviet blind people
835:1979Sci...205.1083P
829:(4411): 1083–1084.
587:Vladimir Boltyansky
444:Vladimir Boltyansky
414:bang–bang principle
296:In 1925 he entered
176:Vladimir Boltyansky
868:Topological Groups
704:10.1007/BF02984835
632:Pontryagin duality
595:Evgenii Mishchenko
538:Topological Groups
436:
387:Pontryagin squares
372:Pontryagin classes
338:Pontryagin duality
283:
267:J. H. C. Whitehead
231:algebraic topology
117:Pontryagin duality
1158:Control theorists
1016:(10): 1114–1116.
591:Revaz Gamkrelidze
452:Mikhail Postnikov
448:Revaz Gamkrelidze
410:maximum principle
399:Pontryagin spaces
334:Fourier transform
310:Steklov Institute
197:
196:
184:Mikhail Postnikov
180:Revaz Gamkrelidze
168:Doctoral students
140:Scientific career
16:(Redirected from
1195:
1034:
1033:
1001:
995:
991:
989:
961:
955:
954:
938:
932:
931:
929:
898:
892:
891:
889:
861:
855:
854:
816:
810:
792:
783:
773:
764:
757:
751:
749:
730:
724:
723:
683:
672:
671:
669:
668:
653:
627:Pontryagin class
603:
580:
548:
495:Grigory Margulis
487:Zionism movement
456:Vladimir Rokhlin
360:cobordism theory
302:Pavel Alexandrov
292:
290:
289:
284:
209:
162:Pavel Alexandrov
157:Doctoral advisor
121:Pontryagin class
90:
69:3 September 1908
68:
66:
51:
37:
36:
21:
1203:
1202:
1198:
1197:
1196:
1194:
1193:
1192:
1073:
1072:
1043:
1038:
1037:
1022:10.2307/2312867
1002:
998:
962:
958:
939:
935:
899:
895:
862:
858:
817:
813:
799:Springer-Verlag
793:
786:
774:
767:
761:Nathan Jacobson
758:
754:
747:
731:
727:
684:
675:
666:
664:
654:
650:
645:
611:
597:
577:
549:(translated by
532:
501:to receive the
483:Nathan Jacobson
468:
460:Mikhail Zelikin
428:Leninsky Avenue
406:optimal control
391:operator theory
389:. Moreover, in
364:stable homotopy
322:
278:
275:
274:
271:Hassler Whitney
249:He was born in
247:
239:optimal control
210:, also written
188:Mikhail Zelikin
186:
182:
178:
174:
131:
127:
123:
119:
98:
92:
88:
79:
70:
64:
62:
54:
42:
35:
28:
23:
22:
15:
12:
11:
5:
1201:
1191:
1190:
1185:
1180:
1175:
1170:
1165:
1160:
1155:
1150:
1145:
1140:
1135:
1130:
1125:
1120:
1115:
1110:
1105:
1100:
1095:
1090:
1085:
1071:
1070:
1065:
1059:
1053:
1047:Lev Pontryagin
1042:
1041:External links
1039:
1036:
1035:
996:
980:(2): 315–316.
956:
933:
920:(2): 188–190.
906:"Book Review:
893:
880:(5): 382–385.
866:"Book Review:
856:
811:
784:
765:
752:
745:
725:
673:
647:
646:
644:
641:
640:
639:
634:
629:
624:
618:
610:
607:
606:
605:
583:
582:
581:
575:
557:
554:
531:
528:
467:
464:
321:
318:
282:
246:
243:
195:
194:
191:
190:
169:
165:
164:
159:
153:
152:
147:
143:
142:
136:
135:
114:
113:Known for
110:
109:
104:
100:
99:
93:
91:(aged 79)
85:
81:
80:
77:Russian Empire
71:
60:
56:
55:
52:
44:
43:
41:Lev Pontryagin
40:
26:
9:
6:
4:
3:
2:
1200:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1154:
1151:
1149:
1146:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1114:
1111:
1109:
1106:
1104:
1101:
1099:
1096:
1094:
1091:
1089:
1086:
1084:
1081:
1080:
1078:
1069:
1066:
1063:
1060:
1057:
1054:
1052:
1048:
1045:
1044:
1031:
1027:
1023:
1019:
1015:
1011:
1007:
1000:
994:
988:
983:
979:
975:
971:
969:
960:
952:
948:
946:
937:
928:
923:
919:
915:
911:
909:
903:
902:Massey, W. S.
897:
888:
883:
879:
875:
871:
869:
860:
852:
848:
844:
840:
836:
832:
828:
824:
823:
815:
809:; pp. 205-206
808:
807:0-387-98358-9
804:
800:
797:
794:Olli Lehto.
791:
789:
781:
777:
772:
770:
762:
756:
748:
746:9780821849996
742:
738:
737:
729:
721:
717:
713:
709:
705:
701:
697:
693:
689:
682:
680:
678:
663:
659:
652:
648:
638:
635:
633:
630:
628:
625:
622:
619:
616:
613:
612:
601:
596:
592:
588:
584:
578:
576:9781483156491
572:
568:
567:
561:
560:
558:
555:
552:
547:
543:
539:
534:
533:
527:
525:
521:
517:
516:
510:
508:
504:
500:
496:
492:
488:
484:
479:
477:
476:Dmitri Egorov
473:
463:
461:
457:
453:
449:
445:
441:
440:Dmitri Anosov
433:
429:
424:
420:
417:
415:
411:
407:
402:
400:
396:
392:
388:
383:
381:
377:
373:
370:, now called
369:
365:
361:
357:
352:
350:
345:
343:
339:
336:, now called
335:
331:
327:
317:
315:
311:
307:
303:
299:
294:
280:
272:
268:
264:
260:
256:
252:
242:
240:
236:
232:
228:
227:mathematician
225:
221:
217:
213:
205:
201:
192:
189:
185:
181:
177:
173:
172:Dmitri Anosov
170:
166:
163:
160:
158:
154:
151:
148:
144:
141:
137:
134:
130:
126:
122:
118:
115:
111:
108:
105:
101:
97:
86:
82:
78:
74:
61:
57:
50:
45:
38:
33:
19:
1058:(in Russian)
1013:
1009:
1005:
999:
977:
973:
967:
959:
950:
944:
936:
917:
913:
907:
896:
877:
873:
867:
859:
826:
820:
814:
755:
735:
728:
698:(2): 55–73.
695:
691:
665:. Retrieved
661:
651:
585:1962 - with
569:. Elsevier.
565:
537:
530:Publications
513:
511:
503:Fields Medal
480:
469:
437:
418:
408:theory. His
403:
395:Krein spaces
384:
353:
346:
323:
295:
259:primus stove
248:
219:
215:
211:
199:
198:
139:
107:Soviet Union
96:Soviet Union
89:(1988-05-03)
1168:Topologists
1088:1988 deaths
1083:1908 births
966:"Review of
943:"Review of
598: [
551:Emma Lehmer
328:theory for
255:eye surgery
150:Mathematics
103:Nationality
1077:Categories
667:2023-06-19
378:that is a
349:Lie groups
263:Heinz Hopf
216:Pontrjagin
212:Pontriagin
87:3 May 1988
65:1908-09-03
32:Portnyagin
18:Pontryagin
720:122503334
712:0343-6993
356:René Thom
281:∪
993:page 316
904:(1953).
851:17735029
801:, 1998.
662:MacTutor
609:See also
380:boundary
376:manifold
330:homology
257:after a
94:Moscow,
1049:at the
1030:2312867
831:Bibcode
822:Science
780:Russian
776:Memoirs
546:0000265
520:Zionism
515:Science
397:called
326:duality
204:Russian
1028:
849:
805:
743:
718:
710:
593:, and
573:
544:
524:racism
458:, and
432:Moscow
269:, and
251:Moscow
224:Soviet
146:Fields
73:Moscow
1026:JSTOR
716:S2CID
643:Notes
602:]
354:With
847:PMID
803:ISBN
741:ISBN
708:ISSN
571:ISBN
320:Work
237:and
220:Leon
84:Died
59:Born
1018:doi
982:doi
922:doi
882:doi
839:doi
827:205
700:doi
507:ICM
499:IMU
430:in
382:.
214:or
1079::
1024:.
1014:70
1012:.
976:.
972:.
949:.
918:59
916:.
912:.
878:46
876:.
872:.
845:.
837:.
825:.
787:^
782:).
768:^
714:.
706:.
696:25
694:.
690:.
676:^
660:.
600:ru
589:,
542:MR
526:.
462:.
454:,
446:,
442:,
401:.
316:.
293:.
265:,
241:.
233:,
206::
75:,
1064:.
1032:.
1020::
990:.
984::
978:7
953:.
947:"
930:.
924::
910:"
890:.
884::
870:"
853:.
841::
833::
750:.
722:.
702::
670:.
579:.
553:)
202:(
67:)
63:(
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
