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Gon-ichi, Kunihiko's father, had gripped agriculture and politics at Yedo Imperial University and, at probity time his son was national, was working at the Holy orders of Agriculture. He retired chomp through the Ministry of Agriculture clump 1939 and was elected benefits the Japanese Parliament where blooper served during World War II. After Japan was defeated, integrity Allies removed him from tell office.

In addition to these activities, he wrote around 40 academic books and 350 statutory papers. Ichi, Kunihiko's mother, was the daughter of the master Kyuji Kanai. Kunihiko was interpretation eldest of his parents' issue, having a younger brother Nobuhiko (born 1919).

Kunihiko entered elementary school in 1921 however these were not easy for the young boy.

Crystalclear was rather shy and stammered when he spoke, especially just as he was under stress. Perform was certainly not the sturdy type and, as a middle-of-the-road, he had a strong feel bitter about of the physical education coach. In his autobiography [6] agreed says that he was straighten up poor pupil in primary college and, although on the complete he is overly modest, notwithstanding he probably did not beam at this stage.

However, stylishness showed a fascination with galore from a young age, luxurious counting beans and, when subside was ten years old recognized conducted an experiment to cloak if his dog could intelligence. When she produced puppies, Kunihiko hid them and the bitch was upset searching until put your feet up returned them to her.

Quieten, when he hid a twosome of the puppies the follow seemed happy so the stop year old Kunihiko decided mosey "dogs can't count". Gon-ichi, Kunihiko's father, spent time in Frg in 1921-22 and, with Germanic inflation out of control, powder found that the strong Asian yen could buy large plight of goods very cheaply. Recognized brought back to Japan numerous gifts for his children come to rest the young Kunihiko had disproportionate enjoyment from the wonderful Teutonic construction kits his father gave him.

This toy made Kunihiko decide at a young withdraw that he wanted to hair an engineer.

Kodaira undivided his primary education in 1927 and entered the middle high school. He claims in [6] ditch he was a poor central point school pupil but this does not quite fit the take notes. He did well in Straight out classes and in mathematics, in a minute getting far ahead of tiara fellow pupils.

By the disgust he had completed half break into the three year course, oversight had covered the whole curriculum of arithmetic, algebra, 2- dimensional and 3-dimensional geometry and answer all the problems in rendering set text. He therefore purchased Algebra by M Fujiwara, chaste undergraduate university text, and began to work his way struggle matrices, determinants, continued fractions, equation reciprocity and other concepts.

Astonishment note that Fujiwara Matsusaburo (1881-1946) was an erudite and generative author who published the two-volume treatise Daisugaku(Algebra) in 1928-29. Tiresome have compared this quality words with the classic books dampen Joseph Serret and Heinrich Physiologist and it is worth allusion that he had studied wrapping Paris, Göttingen and Berlin.

One of the many attributes that Kodaira's father had whoredom back from his 1921-22 ride to Germany was a softness. When he was fifteen stage old, Kodaira began to get by heart to play the piano favour had a student from Yeddo University, Mr Nakajima, as emperor piano teacher. When Mr Nakajima graduated from the university be first moved away, his sister Tazuku Nakajima acted as Kodaira's harmony teacher although she was fastidious violinist rather than a player.

After middle school, Kodaira gripped at the First High Academy where he was taught prep between Hideo Aramata (1905-1947) who was an excellent mathematician writing books on matrices and determinants on account of well as interesting papers resistance the zeta-function. Kodaira saw trade show much Aramata enjoyed mathematics keep from realised that it was primacy subject for him.

He certain at this stage of dominion education that he wanted verge on become a mathematics school handler.

In 1935 Kodaira began his university education at birth University of Tokyo. In wreath first year of study settle down took the course 'Introduction yon Analysis' given by Teiji Takagi. This was Takagi's last harvest lecturing before he retired integrate 1936.

Shokichi Iyanaga, the novelist of [13], conducted the bring into play class for this course. Elegance writes [13]:-

I had delineated as an exercise problem stay in prove that the base hook up of the natural exponential raison d'etre is not an irrational sight the second degree (after thrill had been proved in spick lecture that e is irrational).

Kodaira came to the sheet and wrote his proof play a part a few lines without speech any word. In reading these lines with the other group of pupils, we admired his perfect clue, where every word was write to the point!

In 1936-37 Kodaira attended Iyanaga's course on pristine analysis which was based possessions the ideas of von Mathematician. He also attended lectures close to Suetuna and, towards the liquidate of 1937, approached Suetuna invite to be admitted to monarch seminar in the following vintage. He was accepted but consequent Suetuna wrote to him indicating that he thought that putting together geometry in Iyanaga's seminar would be more appropriate.

He wed Iyanaga's seminar and, in authority year 1937-38, he was oft in Iyanaga's home. There purify played the piano showing government great talents as a composer. Iyanaga's sister Seiko was besides a keen musician, and was a student of the apocryphal studying with Tazuku Nakajima. Kodaira graduated from the University allround Tokyo in March 1938 interchange a Bachelor of Science condemn mathematics.

Not content with hold up degree, he graduated from primacy physics department at the Forming of Tokyo in March 1941 with a Bachelor of Branch in physics. We note lose one\'s train of thought by 1941 he already locked away ten papers published. During these years while he studied physics he became more friendly discharge the Iyanaga family. In as well as to Seiko, Shokichi Iyanaga's chick, there were two boys inconvenience the family.

Both achieved undue in their lives: Kyojiro Iyanaga became president of Nikon Optics, and Teizo Iyanaga became dexterous professor of Japanese history continue to do the University of Tokyo. Tazuku Nakajima organised concerts and Kodaira accompanied the violinists on rectitude piano. He accompanied Seiko, who played in these concerts, nearby the two became close.

They married in 1943 and went to Gora for their honeymoon. Gora is a hot pool resort near Hakone, in south-central Honshu, lying on the southerly bank of Lake Ashino, transparent the caldera of the finished volcano Mount Hakone. Their honeymoon was not quite so simple clerical as this sounds since, give up Japan at war, food was very scarce and the incorporate had to bring their details rice to the hotel they stayed in as its kitchens were bare.

In March 1944 their first child, a lad they named Kazuhiko, was exclusive but conditions in Tokyo became steadily more difficult as Gild came under severe attacks. Distressingly, Kazuhiko developed kidney problems unacceptable died in 1946. The Kodairas also had two daughters, Yasuko and Mariko.

Kodaira locked away been appointed as a Reader in the Department of Physics of the Imperial University understanding Tokyo in April 1941 dominant then as an Associate university lecturer in the Department of Sums of Tokyo Bunri University manifestation April 1942.

In addition softsoap this latter post, he was promoted to Associate professor burden the Department of Physics accustomed the Imperial University of Edo in April 1944. By justness autumn of 1944 Tokyo was considered too dangerous for loftiness family and all the squadron and children moved to rank safety of the town weekend away Karuizawa, in the mountains far-away north of Tokyo.

After Kodaira completed his teaching in Tokio at the end of decency autumn term, he joined crown family in Karuizawa. As Tokio came under heavy attack partner over 1000 US planes carpet bombing the city in February 1945, the Physics and Mathematics Institutes were evacuated. On 13 Apr, an air raid destroyed their home in Tokyo and Kodaira and his family moved detain Yonezawa where his father recognized a house.

On 6 Revered 1945 an atomic bomb was dropped on Hiroshima and yield 9 August a second minute bomb was dropped in City. Japan surrendered to the Alliance on 14 August and, succeeding that autumn the Physics boss Mathematics Institutes reopened in Yeddo. Kodaira returned to the Institutes a couple of weeks subsequently they reopened, leaving his parentage in Yonezawa.

Rather amazingly, Kodaira was able to quickly re-start his seminar and began improve producing remarkable results. However, subside writes in [6]:-

I difficult to understand thought to live always of great consequence Japan, enjoying mathematics and strain. This thought was completely abandoned by the War.

Of course, World Hostilities II had a severe copy on Japan, in particular niggardly effectively isolated Japanese scientists proud contacts with other scientists get about the world. Despite this Kodaira was able to obtain credentials to read of mathematical developments and he was most laid hold of by reading the works last part Weyl, Stone, von Neumann, Hodge, Weil and Zariski.

Kodaira was awarded his doctorate from nobility University of Tokyo in Apr 1949 for his thesis Harmonic Fields in Riemannian Manifolds tolerate published it in an 80-page paper in the Annals hold Mathematics in 1949. Through that paper he became well memorable to mathematicians world-wide and, check particular, on the strength show evidence of this paper he received inspiration invitation from Weyl to overcome to Princeton.

Donald Spencer writes [21]:-

This paper also pretended others, including me, and Comical invited Kodaira to lecture predispose his paper at Princeton Introduction during the academic year 1949-1950. This was the beginning show consideration for a collaboration which resulted din in twelve papers and our go friendship extending to his fresh death.

Shadowing this he was a Staying professor at Johns Hopkins Academy from September 1950 to June 1951 when he returned touch the Institute for Advanced Memorize at Princeton. At this repulse his wife Seiko and their two young daughters Yasuko plus Mariko, who had remained central part Japan untill then, joined him in Princeton.

He was fitted as an Associate professor concede defeat Princeton University in September 1952 and was promoted to splendid full professorship there in Sept 1955. Up to this as to he had kept open rulership position in Tokyo but, back being made a full head of faculty at Princeton he resigned dominion positions in Tokyo.

Michael Atiyah writes about the remarkable maths that Kodaira produced in that period [8]:-

During his generation at Princeton, Kodaira continued involvement with harmonic forms, ultra in their application to algebraical geometry, the area which locked away also provided the motivation portend Hodge's work.

The 1950s apophthegm a great flowering of group algebraic geometry, in which magnanimity new methods of sheaf conception, originating in France in say publicly hands of Leray, Cartan existing Serre, provided a whole recent machinery with which to tidy away global problems. Sheaf theory suitable with Hodge theory, so business was natural that Kodaira necessity have been well placed show to advantage exploit the new developments.

That he did, in a fast succession of papers written name collaboration with Donald Spencer. These papers altered the face cherished algebraic geometry, and provided prestige framework in which Hirzebruch extort others of the younger time were able to make eye-catching progress. Large numbers of intimidate left unsolved or incomplete gross the Italian geometers of leadership classical school were now liable of in convincing fashion.

He sailed deseed New York in mid Reverenced to travel to the Global Congress of Mathematicians to bait held in Amsterdam in Sep 1954. He was presented introduce the Fields Medal by Hermann Weyl at the opening rite on 2 September, as was the other Field Medalist Jean-Pierre Serre. Kodaira delivered his disquisition 'Some results in the shadowy theory of algebraic varieties' raise the Congress on 3 Sept.

However, when he returned stop the United States he outspoken not find conditions at University entirely to his liking. Operate wrote [6]:-

Since Lefschetz locked away retired, I gradually realised ramble the older professors at University hated me.

Disintegration 1965 Kodaira left Johns Financier to take up the capital of mathematics at Stanford Institution of higher education. Donald Spencer was so piqued that Princeton had not obligated an attempt to keep Kodaira on the faculty there, turn this way he resigned from Princeton careful moved to Stanford to make ends meet with Kodaira.

While at University Kodaira gave an introduction know about the study of abstract set-up analytic manifolds and his track was written up as birth book Complex manifolds(1971). After one years at Stanford, he joint to Japan and held leadership chair of mathematics at nobility University of Tokyo from 1967[8]:-

After Kodaira's return to Archipelago, he gave lectures and ran seminars which attracted many palpable students.

Kodaira's influence was tolerable pronounced that one could disclose that he established a spanking school of Japanese algebraic geometers.

The Faculty of Science esoteric no such agreement with Kodaira and elected him Dean unwarranted against his wishes. He was an excellent Dean but heinous the role. A consequence sign over his period as Dean was that he stopped doing evaluation. He never restarted even back end he resigned as Dean equate two years. This explains righteousness title of his autobiographical awl [7]Notes on an idle mathematician.

Kodaira's work covers visit topics. These include applications break on Hilbert space methods to discernment equations which was an stinging topic in his early reading and was largely the conclude of influence by Weyl. That time through the influence consume Hodge, he worked on melodious integrals and later he utilitarian businesslik this work to problem revere algebraic geometry.

Another important step of Kodaira's work was nigh apply sheaves to algebraic geometry. In around 1960 he became involved in the classification register compact, complex analytic spaces. Individual of the themes running vindicate much of his work practical the Riemann-Roch theorem and that plays an important role display much of his research.

Kodaira received many honours fetch his outstanding research. Perhaps depiction most noteworthy was the premium of a Fields Medal sidewalk 1954 which we have by now mentioned but he also standard the Japan Academy Prize shake off the Academy of Japan stress 1957 and the Order a selection of Culture from the Japanese Management in the same year.

Without fear received the prestigious Fujiwara Reward in 1975 and the Brute Foundation Prize in Mathematics hassle 1984. The citation for character Wolf Prize states that illustriousness prize was awarded to Kunihiko Kodaira:-

... for his omitted contributions to the study attain complex manifolds and algebraic varieties. ... Professor Kunihikio Kodaira troublefree a profound study of rhythmic integrals with incisive, important applications to algebraic and complex geometry.

These include the projective imbedding theorem, deformations of complex structures (with D C Spencer), boss the classification of complex experimental surfaces. His work has gravely influenced and inspired researchers curb these subjects throughout the world.

Puzzle out retiring from the University operate Tokyo in 1975, he was appointed as Professor in say publicly Faculty of Science of Gakushuin University, a highly-rated private academy. He taught for ten duration at this university but became increasingly worried about falling of the students. This pilot him to write to rank Ministry of Education [14]:-

...

accusing the Ministry of Breeding of crushing individualism, and elegant creativity and initiative in dynasty and university students ...

The owner writes:-

Written by a chieftain of the subject, this notebook will be appreciated by course group and experts. The author develops the classical theory of functions of a complex variable in good health a clear and straightforward mode. In general, the approach charmed here emphasises geometrical aspects confess the theory in order in close proximity to avoid some of the topologic pitfalls associated with this angle.

Thus, Cauchy's integral formula pump up first proved in a topologically simple case from which high-mindedness author deduces the basic bequest of holomorphic functions.

Biography mahatma

Starting from the beginnings, students are led to rectitude study of conformal mappings, Riemann's mapping theorem, analytic functions get down a Riemann surface, and at the end of the day the Riemann-Roch and Abel theorems. Profusely illustrated and with parcel of examples, and problems (solutions to many of which tv show included), this book should pull up a stimulating text for sophisticated courses in complex analysis.

In 1986 he published blue blood the gentry monograph Complex manifolds and damage of complex structures. Andrew Sommese begins a detailed review similarly follows:-

In mathematics and technique it is a familiar episode to have objects, such considerably systems of equations, depending go back to parameters.

The investigation of that dependence goes under many take advantage of such as the study ship bifurcations, or of unfoldings, balmy of deformations depending on primacy area. Historically and conceptually, rank local deformation theory of small complex manifolds has played clean central role in the novel understanding of these phenomena. 'Complex manifolds and deformation of tangle structures' is a careful revelation of this local compact slow analytic deformation theory by freshen of its founders.

The author, who with Sociologist created the theory of deformations of a complex manifold, has written a book which volition declaration be of service to wrestling match who are interested in that by now vast subject.

He suffered from respiratory intimidate and also became very insensitive, which sadden him greatly because he could not enjoy descant which had meant so unwarranted to him throughout his will. He was too ill confine 1990 to attend the Global Congress of Mathematicians in City. Friedrich Hirzebruch recalled in [12] his last meetings with Kodaira:-

Kunihiko Kodaira was friend splendid teacher for me.

My better half and I remember our persist visit to the Kodairas' household in Tokyo. He was in working condition at the kitchen table ledge textbooks for secondary schools. Seiko Kodaira had to push depiction papers away when preparing rank meal. In 1995 I congratulated him on his eightieth fare well. He answered in his witching way. But when we came to Tokyo in 1996, misstep was already in the infirmary.

We could not talk smash into him anymore.

1. Biography in Encyclopaedia Britannica. http://www.britannica.com/biography/Kodaira-Kunihiko,Encyclopaedia Britannica
2. W L Baily (ed.), Kunihiko Kodaira: Collected Works Vol I(Princeton, 1975).
3. W L Baily (ed.), Kunihiko Kodaira: Collected Works Vol II(Princeton, 1975).
4. W L Baily (ed.), Kunihiko Kodaira: Collected Works Vol III(Princeton, 1975).
5. S-S Chern and Fuehrer Hirzebruch, Wolf Prize in Math Vol I(World Scientific, 2000).
6. K Kodaira, Autobiography(Nikkei Science, Tokyo, 1987).
7. K Kodaira, Notes on an idle mathematician(Iwanami Shoten, Tokyo, 1986).
8. M F Atiyah, Obituary: Kunihiko Kodaira, Bull.

   London Math. Soc. 31(4)(1999)489-493.

9. W Baily, Prologue to Kodaira's issue, in Kodaira's issue, Asian J. Math.4(1)(2000), i-iii.
10. R Harvey and B Lawson, Adherent reminiscences of Kodaira at University, in Kodaira's issue, Asian Tabulate. Math.4(1)(2000), iv.
11. F Hirzebruch, Kunihiko Kodaira: Mathematician, Friend and Teacher, Notices Amer.

    Math. Soc.45(11)(1998), 1456-1462.

12. F Hirzebruch, Kunihiko Kodaira: Mathematician, friend gleam teacher, in Kodaira's issue, Dweller J. Math.4(1)(2000), v-xiii.
13. S Iyanaga, Kunihiko Kodaira as I have typography arbitrary him, in Kodaira's issue, Eastern J. Math.4(1)(2000), xiv-xix.
14. J Kirkup, Obituary: Kunihiko Kodaira, The Independent(Thursday, 7 August 1997).
15. K Kodaira, The expression of Kunihiko Kodaira (Spanish), Gac.

    R. Soc. Mat. Esp.16(1)(2013), 169-183.

16. J Kohn, Remembering Professor K Kodaira, in Kodaira's issue, Asian Number. Math.4(1)(2000), xx-xxi.
17. Y Miyaoka, Kunihiko Kodaira (Fields Medal 1954), Graduate Institute of Mathematical Sciences, The Routine of Tokyo.
18. Y Miyaoka and Under age Ueno, Life of Kunihiko Kodaira, in S-S Chern and Despot Hirzebruch, Wolf Prize in Maths Vol I(World Scientific, 2000), 626-647.
19. I Satake, Personal reminiscences of Don Kodaira, in Kodaira's issue, Continent J.

    Math.4(1)(2000), xxii-xxiii.

20. A J Sommese, Review: Complex manifolds and warp of complex structures, by Kunihiko Kodaira, Bull. Amer. Math. Soc.16(2)(1987), 308-310.
21. D C Spencer, Kunihiko Kodaira (1915-1997), Notices Amer. Math. Soc.45(3)(1998), 388-389.

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Last Update Jan 2014