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had its difficulties as well; in one case, paper shortages were such that a lengthy Itô article could not be published in a
Japanese journal and he had to arrange for an American journal to publish it instead. Ito later referred to his time at Nagoya as having been during "the dark age of World War
1228:"Junko Ito, left, daughter of Japanese mathematician Kiyoshi Ito, receives the Gauss Prize from Spanish King Juan Carlos I during the opening ceremony of the International Congress of Mathematicians celebrated in Madrid Tuesday, Aug. 22, 2006. (AP Photo/Bernat Armangue)"
523:, including problems accessing libraries and especially the loss of contact with Western mathematicians and the lack of awareness of results from them. For instance, the only other Japanese mathematician actively interested in Itô's work during the war,
481:
474:
445:
1959:
551:, appeared in 1953. Itô remained affiliated with Kyoto until his retirement in 1979. However, beginning in the 1950s, Itô spent long periods of time away from Japan. He was at the
492:, There he was given rein by management to continue his research. His breakthrough paper, "On Stochastic Processes", appeared in 1942. In 1943, was appointed an assistant professor at
709:
2014:
586:, where he was a professor of mathematics for six years until 1975. This was his longest stint outside Japan. Among the courses he taught at Cornell was one in Higher Calculus.
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2009:
2004:
1155:
609:. However, his ability to converse in foreign languages was a different matter, and by his own admission his accent made him largely incomprehensible to Americans.
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1994:
1979:
1969:
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After this period he continued to develop his ideas on stochastic analysis with many important papers on the topic. In 1952, he became a professor at the
1954:
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616:. After his retirement, he became professor emeritus at Kyoto University. He also had a post-retirement position as a professor at the private
910:
881:
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in 1962. So much were Itô's results useful to financial mathematics that he was sometimes called "the most famous
Japanese in Wall Street".
368:
Itô's methods are also used in other fields, including biology and physics. These include his results being used in applications related to
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1999:
1974:
1939:
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personally presented the medal to Itô at a special ceremony held in Kyoto. In
October 2008, Itô was honored with Japan's
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noted that "People all over realized that what Ito had done explained things that were unexplainable before." Economist
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298:. But he also spent multi-year stints at several foreign institutions, the longest of which took place at
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275:. He also pioneered the world connections between stochastic calculus and differential geometry, known as
1684:
449:
Kiyosi Itô (right) with Seizō Itō in 1937. Seizō is Kiyosi's brother. Seizō later became a mathematician.
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504:. From investigations done during this period he published a series of articles in which he defined the
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Kunita, Hiroshi (May 2010), "Itô's stochastic calculus: its surprising power for applications",
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When Itô left
Cornell and returned to the University of Kyoto, he served as director of their
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stated that Itô's work had provided him "a very useful tool" in his own prize-winning work.
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527:, read a mimeographed copy a paper while in a military camp. Scholarly activity during the
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Kiyosi Itô(1915-2008) / Eightieth
Birthday Lecture RIMS, Kyoto University, September 1995
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361:. In particular, the Itô's lemma's best known application is in the derivation of the
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In his later years, Itô struggled with poor health. Itô was awarded the inaugural
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Itô (right) with Issei
Shiraishi in 1935. Shiraishi later became a mathematician.
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Itô, Kiyosi (2014) . "Foreword". In
Stroock, D. W.; Varadhan, S. R. S. (eds.).
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Foundations of
Stochastic Differential Equations in Infinite Dimensional Spaces
662:
for his lifetime achievements. As he due to his health was unable to travel to
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for several years, a common practice among higher-ranking
Japanese academics.
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469:, he studied mathematics and became interested in the underdeveloped field of
338:(also known as the Itô formula). Itô also made contributions to the study of
1214:
Cornell
University Announcements: College of Arts and Sciences, 1974–75
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and is applied in various fields, and is perhaps best known for its use in
17:
1152:"Celebrating Cornell University luminaries in mathematics and statistics"
430:). The alternative spellings Itoh and Ito are also sometimes seen in the
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at the Research Institute for Mathematical Sciences, Kyoto University
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at the Research Institute for Mathematical Sciences, Kyoto University
663:
1082:"Professor Kiyosi Itô: mathematician and probability theory expert"
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Itô was born on 7 September 1915 in a farming area located west of
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for most of his career and eventually became the director of their
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1048:"Kiyosi Ito, 93, Mathematician Who Described Random Motion, Dies"
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808:"Stochastic differential equations in a differentiable manifold"
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These works were published despite the difficulties of life in
496:, where he benefited from discussions with the mathematicians
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From 1939 to 1943 he worked as a Statistical Officer with the
384:, in additional to use in various mathematic subjects such as
1202:. Vol. 1. Singapore: World Scientific. pp. 531–535.
935:"Cornellians at the International Congress of Mathematicians"
1246:"Gauss prize lecture - On Kiyosi Itô's work and its impact"
734:
Zenkoku Sizyo Sugaku Danwakai-si (J. Pan-Japan Math. Coll.)
353:
Itô calculus is a method used in the mathematical study of
465:. He excelled in his studies as a youth. Admitted to the
710:
Proceedings of the Physico-Mathematical Society of Japan
1960:
Foreign associates of the National Academy of Sciences
726:"Differential equations determining a Markoff process"
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degree from the Imperial University of Tokyo in 1945.
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705:"On the Probability Distribution on a Compact Group"
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839:"On a formula concerning stochastic differentials"
1182:. New York: Springer-Verlag. pp. xiii–xvii.
1216:. Cornell University. 1 July 1974. p. 127.
1156:Cornell University College of Arts and Sciences
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2015:Institute for Advanced Study visiting scholars
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903:Society for Industrial and Applied Mathematics
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1296:"Donald Keene, 7 others win Order of Culture"
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1121:Research Institute for Mathematical Sciences
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1010:Notices of the American Mathematical Society
614:Research Institute for Mathematical Sciences
490:Statistics Bureau of the Cabinet Secretariat
484:Itô at the Cabinet Statistics Bureau in 1940
296:Research Institute for Mathematical Sciences
1403:Stochastic Processes and Their Applications
271:, and is known as the founder of so-called
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870:Diffusion Processes and Their Sample Paths
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2010:Members of the French Academy of Sciences
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1196:Chern, S S; Hirzebruch, F, eds. (2000).
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281:International Congress of Mathematicians
1376:MacTutor History of Mathematics Archive
1117:"Past Directors: Kiyosi Itô(1915-2008)"
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2005:Academic staff of Gakushuin University
1271:"Dr. Kiyoshi Ito receives Gauss Prize"
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437:Itô was married with three daughters.
255:who made fundamental contributions to
246:, 7 September 1915 – 10 November 2008)
575:from 1961 to 1964 and a professor at
559:; while there he worked closely with
241:
7:
1950:21st-century Japanese mathematicians
1945:20th-century Japanese mathematicians
868:Kiyosi Itô and Henry McKean (1974).
674:on his behalf. Later, IMU President
1995:Academic staff of Aarhus University
1980:Academic staff of Nagoya University
1970:Wolf Prize in Mathematics laureates
1390:On Kiyosi Itô's Work and its Impact
777:"On a stochastic integral equation"
751:Proceedings of the Imperial Academy
643:, and also a foreign member of the
426:, he used the spelling Kiyosi Itô (
290:Itô was a member of the faculty at
2020:Recipients of the Order of Culture
1985:Academic staff of Kyoto University
1001:Protter, Philip (June–July 2007).
685:Itô died on November 10, 2008, in
27:Japanese mathematician (1915–2008)
25:
1955:Kyoto laureates in Basic Sciences
1304:. 29 October 2008. Archived from
1150:DiPietro, Louis (17 April 2024).
975:"Renowned math wiz Ito, 93, dies"
324:stochastic differential equations
1903:
1046:Lohr, Steve (23 November 2008),
782:Proceedings of the Japan Academy
670:, received the Gauss Prize from
660:International Mathematical Union
508:and laid the foundations of the
348:stochastic differential geometry
277:stochastic differential geometry
269:stochastic differential equation
2025:Laureates of the Imperial Prize
1396:, Humboldt University of Berlin
475:university's Faculty of Science
259:, in particular, the theory of
512:. Meanwhile, he received his
390:partial differential equations
1:
1434:Mathematics Genealogy Project
555:from 1954 to 1956 while on a
263:. He invented the concept of
649:National Academy of Sciences
582:Then in 1969 Itô arrived at
553:Institute for Advanced Study
547:. His most well-known text,
467:Imperial University of Tokyo
318:Itô pioneered the theory of
1990:Stanford University faculty
1387:Foellmer, Hans (May 2006),
1194:Subsequently reproduced in
1090:. London. 20 November 2008.
844:Nagoya Mathematical Journal
813:Nagoya Mathematical Journal
330:. Its basic concept is the
233:
2041:
2000:Cornell University faculty
1975:University of Tokyo alumni
1940:People from Mie Prefecture
1445:Bibliography of Kiyosi Itô
1180:Kiyosi Itô Selected Papers
631:Itô was recipient of the
494:Nagoya Imperial University
1899:
1483:Wolf Prize in Mathematics
1416:10.1016/j.spa.2010.01.013
1199:Wolf Prize in Mathematics
858:10.1017/S0027763000012216
827:10.1017/S0027763000022819
666:, his youngest daughter,
639:. He was a member of the
571:. He was a professor at
521:Japan during World War II
457:, that being the town of
428:Kunrei-shiki romanization
279:. He was invited for the
227:
215:
160:
41:
1381:University of St Andrews
1003:"The Work of Kyoshi Itô"
651:in the United States.
589:Itô wrote not only in
532:II and its aftermath."
239:Japanese pronunciation:
1910:Mathematics portal
1633:Ilya Piatetski-Shapiro
796:10.3792/pja/1195572371
765:10.3792/pia/1195572786
628:
540:
485:
450:
418:Although the standard
363:Black–Scholes equation
320:stochastic integration
315:
1965:Probability theorists
1843:Jean-François Le Gall
746:"Stochastic integral"
697:Selected publications
676:Sir John Macleod Ball
645:Académie des sciences
626:
538:
483:
448:
407:Fellow mathematician
386:differential geometry
313:
243:[itoːkiꜜjoɕi]
1760:Phillip A. Griffiths
1598:Friedrich Hirzebruch
1367:Robertson, Edmund F.
691:respiratory failure
618:Gakushuin University
579:from 1966 to 1969.
569:Princeton University
557:Fulbright fellowship
420:Hepburn romanization
359:mathematical finance
261:stochastic processes
1833:Alexander Beilinson
1365:O'Connor, John J.;
1353:Black–Scholes model
1308:on 30 October 2008.
987:. 15 November 2008.
893:Kiyosi Itô (1984).
837:Kiyosi Itô (1951).
806:Kiyosi Itô (1950).
775:Kiyosi Itô (1946).
744:Kiyosi Itô (1944).
724:Kiyosi Ito (1942).
703:Kiyosi Itô (1940).
573:Stanford University
567:who were at nearby
545:University of Kyoto
529:Occupation of Japan
506:stochastic integral
365:for option values.
340:diffusion processes
292:University of Kyoto
265:stochastic integral
183:University of Kyoto
109:University of Tokyo
1864:Simon K. Donaldson
1791:Michael Aschbacher
1750:Hillel Furstenberg
1053:The New York Times
939:Cornell University
737:(1077): 1352–1400.
672:King Juan Carlos I
647:in France and the
629:
584:Cornell University
549:Probability Theory
541:
486:
471:probability theory
451:
378:chemical reactions
316:
300:Cornell University
257:probability theory
187:Cornell University
50:Cornell University
1917:
1916:
1880:Ingrid Daubechies
1837:Vladimir Drinfeld
1827:Charles Fefferman
1710:Jean-Pierre Serre
1558:Shiing-Shen Chern
1532:Andrey Kolmogorov
1481:Laureates of the
1338:Itô–Nisio theorem
912:978-0-89871-193-6
883:978-3-540-60629-1
577:Aarhus University
514:Doctor of Science
409:Daniel W. Stroock
398:harmonic analysis
370:population models
219:
218:
206:Doctoral students
162:Scientific career
86:November 10, 2008
68:September 7, 1915
16:(Redirected from
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1907:
1868:Yakov Eliashberg
1764:David B. Mumford
1736:Grigory Margulis
1665:Robert Langlands
1643:John G. Thompson
1639:Lennart Carleson
1608:Alberto Calderón
1578:Samuel Eilenberg
1568:Kunihiko Kodaira
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502:Shizuo Kakutani
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382:quantum physics
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1831:
1828:
1824:
1821:
1818:
1815:
1812:
1809:
1806:
1805:Michael Artin
1802:
1801:George Mostow
1799:
1796:
1792:
1789:
1786:
1782:
1779:
1778:
1776:
1772:
1765:
1761:
1757:
1754:
1751:
1747:
1746:Stephen Smale
1744:
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1737:
1734:
1731:
1727:
1724:
1721:
1717:
1714:
1711:
1707:
1704:
1703:
1701:
1697:
1690:
1686:
1685:László Lovász
1683:
1680:
1676:
1675:Joseph Keller
1673:
1670:
1666:
1663:
1660:
1657:
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1549:
1546:
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1542:Oscar Zariski
1539:
1536:
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1523:
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1354:
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1334:
1331:
1329:
1328:Itô diffusion
1326:
1324:
1321:
1320:
1316:
1307:
1303:
1302:
1297:
1291:
1288:
1276:
1272:
1266:
1263:
1251:
1250:TIB AV-Portal
1247:
1233:
1229:
1223:
1220:
1215:
1209:
1206:
1201:
1200:
1191:
1185:
1181:
1174:
1172:
1170:
1168:
1166:
1162:
1157:
1153:
1146:
1144:
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1094:
1089:
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1077:
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1063:
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1049:
1042:
1040:
1038:
1036:
1034:
1032:
1030:
1028:
1026:
1024:
1020:
1016:(6): 744–745.
1015:
1011:
1004:
997:
995:
991:
986:
982:
981:
976:
970:
968:
966:
964:
962:
960:
958:
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936:
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927:
920:
914:
908:
904:
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891:
890:
885:
879:
875:
871:
866:
865:
859:
854:
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846:
845:
840:
835:
834:
828:
823:
819:
815:
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809:
804:
803:
797:
792:
788:
784:
783:
778:
773:
772:
766:
761:
757:
753:
752:
747:
742:
741:
736:
735:
727:
722:
721:
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712:
711:
706:
701:
700:
696:
694:
692:
688:
683:
681:
677:
673:
669:
665:
661:
657:
652:
650:
646:
642:
641:Japan Academy
638:
634:
625:
621:
619:
615:
610:
608:
604:
600:
596:
592:
587:
585:
580:
578:
574:
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566:
562:
558:
554:
550:
546:
537:
533:
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526:
522:
517:
515:
511:
507:
503:
499:
498:Kōsaku Yosida
495:
491:
482:
478:
476:
472:
468:
464:
460:
456:
455:Nagoya, Japan
447:
440:
438:
435:
433:
432:Western world
429:
425:
421:
416:
414:
410:
405:
403:
399:
395:
391:
387:
383:
379:
375:
371:
366:
364:
360:
356:
355:random events
351:
349:
345:
341:
337:
333:
329:
325:
321:
312:
305:
303:
301:
297:
293:
288:
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278:
274:
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258:
254:
253:mathematician
251:
244:
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204:
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198:
196:
192:
188:
184:
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166:
163:
159:
152:
145:
138:
131:
127:
123:
120:
117:
113:
110:
107:
103:
99:
95:
85:
81:
77:
73:
60:
56:
51:
45:
40:
33:
30:
19:
1901:
1811:Peter Sarnak
1669:Andrew Wiles
1659:Jürgen Moser
1653:Jacques Tits
1587:
1582:Atle Selberg
1538:Lars Ahlfors
1528:Henri Cartan
1406:
1402:
1389:
1374:
1371:"Kiyosi Itô"
1343:Itô isometry
1333:Itô integral
1323:Itô calculus
1306:the original
1299:
1290:
1278:. Retrieved
1265:
1253:. Retrieved
1235:. Retrieved
1222:
1213:
1208:
1198:
1179:
1128:. Retrieved
1085:
1051:
1013:
1009:
978:
942:. Retrieved
929:
896:
869:
848:
842:
817:
811:
789:(2): 32–35.
786:
780:
755:
749:
732:
714:
708:
687:Kyoto, Japan
684:
653:
630:
611:
593:but also in
588:
581:
565:Henry McKean
548:
542:
518:
510:Itō calculus
487:
452:
436:
423:
417:
406:
367:
352:
332:Itô integral
328:Itô calculus
317:
289:
273:Itô calculus
221:
220:
178:Institutions
161:
119:Itô calculus
88:(2008-11-10)
72:Hokusei, Mie
29:
1935:2008 deaths
1930:1915 births
1612:John Milnor
1348:Itô's lemma
656:Gauss Prize
637:Kyoto Prize
627:Itô c. 1991
459:Hokusei-cho
424:Kiyoshi Itō
374:white noise
346:, known as
336:Itô's lemma
234:Itō Kiyoshi
172:Mathematics
151:Gauss Prize
144:Kyoto Prize
130:Asahi Prize
18:Kiyoshi Itô
1924:Categories
1890:Adi Shamir
1726:Mikio Sato
1706:Raoul Bott
1588:Kiyosi Itô
1562:Paul Erdős
1552:Mark Krein
1511:André Weil
1507:Jean Leray
1430:Kiyosi Itô
985:Kyodo News
921:References
872:. Berlin:
633:Wolf Prize
222:Kiyosi Itô
137:Wolf Prize
64:1915-09-07
36:Kiyosi Itô
1886:Noga Alon
1752:(2006/07)
1732:(2002/03)
1730:John Tate
1681:(1996/97)
1671:(1995/96)
1661:(1994/95)
1592:Peter Lax
1574:(1984/85)
1572:Hans Lewy
1564:(1983/84)
1243:See also
1130:8 January
1087:The Times
851:: 55–65.
820:: 35–47.
668:Junko Ito
539:Itô, 1954
441:Biography
344:manifolds
285:Stockholm
1317:See also
635:and the
591:Japanese
306:Overview
250:Japanese
1432:at the
1280:16 June
1255:16 June
1237:16 June
944:16 June
607:English
595:Chinese
396:, and
48:Itô at
1892:(2024)
1882:(2023)
1876:(2022)
1870:(2020)
1849:(2019)
1839:(2018)
1829:(2017)
1819:(2015)
1813:(2014)
1807:(2013)
1797:(2012)
1787:(2010)
1766:(2008)
1742:(2005)
1722:(2001)
1712:(2000)
1691:(1999)
1655:(1993)
1645:(1992)
1635:(1990)
1614:(1989)
1604:(1988)
1594:(1987)
1584:(1986)
1554:(1982)
1544:(1981)
1534:(1980)
1513:(1979)
1503:(1978)
1394:(.PDF)
1186:
909:
880:
664:Madrid
603:French
599:German
380:, and
248:was a
168:Fields
154:(2006)
147:(1998)
140:(1987)
133:(1977)
125:Awards
52:, 1970
1857:2020s
1774:2010s
1699:2000s
1622:1990s
1521:1980s
1490:1970s
1232:Alamy
1006:(PDF)
729:(PDF)
98:Japan
94:Kyoto
1282:2024
1257:2024
1239:2024
1184:ISBN
1132:2009
946:2024
907:ISBN
878:ISBN
605:and
563:and
500:and
400:and
322:and
267:and
228:伊藤 清
83:Died
58:Born
1411:doi
1407:120
853:doi
822:doi
791:doi
760:doi
477:.
461:in
342:on
283:in
1926::
1888:/
1866:/
1845:/
1835:/
1825:/
1803:/
1793:/
1783:/
1762:/
1758:/
1748:/
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1590:/
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1550:/
1540:/
1530:/
1509:/
1499:/
1405:,
1379:,
1373:,
1369:,
1298:.
1273:.
1248:.
1230:.
1164:^
1154:.
1140:^
1123:,
1119:.
1096:^
1084:.
1061:^
1050:,
1022:^
1014:54
1012:.
1008:.
993:^
983:.
977:.
954:^
937:.
905:.
876:.
847:.
841:.
816:.
810:.
787:22
785:.
779:.
756:20
754:.
748:.
731:.
715:22
707:.
693:.
601:,
597:,
434:.
404:.
392:,
388:,
376:,
372:,
350:.
302:.
237:,
231:,
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1474:e
1467:t
1460:v
1413::
1284:.
1259:.
1241:.
1192:.
1158:.
1134:.
948:.
915:.
886:.
861:.
855::
849:3
830:.
824::
818:1
799:.
793::
768:.
762::
225:(
66:)
62:(
20:)
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