7 Chome-3-1 Hongo, Bunkyo City, Tokyo 113-8654, Japan

In 1935 Kodaira began his university education at the University of Tokyo. Kodaira graduated from the University of Tokyo in March 1938 with a Bachelor of Science in mathematics. Not content with one degree, he graduated from the physics department at the University of Tokyo in March 1941 with a Bachelor of Science in physics. Kodaira was awarded his doctorate from the University of Tokyo in April 1949 for his thesis Harmonic Fields in Riemannian Manifolds and published it in an 80-page paper in the Annals of Mathematics in 1949.

7 Chome-3-1 Hongo, Bunkyo City, Tokyo 113-8654, Japan

In 1935 Kodaira began his university education at the University of Tokyo. Kodaira graduated from the University of Tokyo in March 1938 with a Bachelor of Science in mathematics. Not content with one degree, he graduated from the physics department at the University of Tokyo in March 1941 with a Bachelor of Science in physics. Kodaira was awarded his doctorate from the University of Tokyo in April 1949 for his thesis Harmonic Fields in Riemannian Manifolds and published it in an 80-page paper in the Annals of Mathematics in 1949.

(This volume serves as an introduction to the Kodaira-Spen...)

This volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kähler manifolds called Hodge manifolds is algebraic. Included are the semicontinuity theorems and the local completeness theorem of Kuranishi. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds.

(Kunihiko Kodaira's influence in mathematics has been fund...)

Kunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis.

(Kunihiko Kodaira's influence in mathematics has been fund...)

Kunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis. These three volumes contain Kodaira's written contributions, published in a large number of journals and books between 1937 and 1971.

(Kunihiko Kodaira's influence in mathematics has been fund...)

Kunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis. These three volumes contain Kodaira's written contributions, published in a large number of journals and books between 1937 and 1971.

Kunihiko Kodaira was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds and as the founder of the Japanese school of algebraic geometers.

Background

Kunihiko Kodaira was born on March 16, 1915, in Tokyo. Kunihiko Kodaira's parents were Gon-ichi (1884-1976) and Ichi Kodaira (1894-1993). Gon-ichi, Kunihiko's father, had studied agriculture and politics at Tokyo Imperial University and, at the time his son was born, was working at the Ministry of Agriculture. He retired from the Ministry of Agriculture in 1939 and was elected to the Japanese Parliament where he served during World War II. After Japan was defeated, the Allies removed him from public office. In addition to these activities, he wrote around 40 academic books and 350 academic papers. Ichi, Kunihiko's mother, was the daughter of the schoolmaster Kyuji Kanai. Kunihiko was the eldest of his parents' sons, having a younger brother Nobuhiko (born in 1919).

Education

Kodaira entered elementary school in 1921. Kodaira completed his primary education in 1927 and entered the middle school. He did well in English classes and in mathematics, soon getting far ahead of his fellow pupils. In 1935 Kodaira began his university education at the University of Tokyo. Kodaira graduated from the University of Tokyo in March 1938 with a Bachelor of Science in mathematics. Not content with one degree, he graduated from the physics department at the University of Tokyo in March 1941 with a Bachelor of Science in physics. Kodaira was awarded his doctorate from the University of Tokyo in April 1949 for his thesis Harmonic Fields in Riemannian Manifolds and published it in an 80-page paper in the Annals of Mathematics in 1949.

From 1944 to 1951, Kodaira was an associate professor of physics at the University of Tokyo. Kodaira was invited to lecture at Princeton University during the academic year 1949–1950. Kodaira continued his work on manifolds. He discovered that, by using a type of integral known as a harmonic integral, he could more completely define the Riemann manifolds, and he sought to generalize this knowledge. Complex manifolds, which are those involving complex numbers, form the basis of much of modern calculus; however, at the time, little was understood about their properties because many were not defined. Therefore, Kodaira’s studies were critical to the advancement of the field of calculus. After a great deal of work on Riemann manifolds, he turned to another type of manifold called the Kahlerian manifolds, where he would produce his most spectacular results.

Kodaira wanted to prove that the Kahlerian manifolds, like the Riemann manifolds, were analytic in nature - in other words, that calculus could be used to solve or define them. He began to examine a small subset of the Kahlerian manifolds known as the Hodge manifolds. Using a theorem he had created earlier, called the vanishing theorem, he successfully proved the existence of meromorphic functions, a type of analytic function, on the Hodge manifolds. These meromorphic functions could be solved using algebraic varieties, a set of points that satisfy certain polynomial equations, thus making the Hodge manifolds analytic. By extension, then, in a theorem Kodaira labeled the embedding theorem, he proved that if the Hodge manifolds were analytic, then all Kahlerian manifolds were analytic as well.

Because each manifold is different and because they are so crucial to the theory of modern calculus, any theory or set of theories that can classify an entire group of them constitutes a major advance. For his work on algebraic varieties and Kahlerian manifolds, Kodaira received the Fields Medal in 1954, which was presented to him in Amsterdam by Kodaira’s friend and mentor, Hermann Weyl. Three years later, his native country followed with two of their most prestigious awards: the Japan Academy Prize and the Cultural Medal, given by the government of Japan.

Kodaira’s research continued in the midst of all the attention he received. Between 1953 and 1960, he further examined complex manifolds with D. C. Spencer, using the idea of deformations to refine his definitions. A deformation is a function which twists or bends a surface without tearing it; this function is important for both theoretical and practical reasons. Theoretically, deformations are one of the fundamental ideas of topology; practically, they are applied in mechanical engineering to describe the bending of metals. Therefore, Kodaira was applying an extremely practical and concrete concept to a very abstract theory of surfaces.

Much in demand because of his high reputation, Kodaira spent the next several years as a visiting professor at prestigious American universities. He remained at The Institute of Advanced Studies and Princeton until 1961, then spent a year at Harvard, and two years at Johns Hopkins; he taught at Stanford from 1965 to 1967. In 1967 he returned to Japan, accepting a position as a full professor at the University of Tokyo.

Although Kodaira continued his research after his return to Japan, he became increasingly interested in the teaching of mathematics. In 1971 he collaborated with James Morrow on a textbook based on his research into complex manifolds, the first of several such works. In 1975 he took on additional teaching responsibilities at Gakushuin University in Tokyo. Also in that year, Kodaira’s collected works appeared and he was granted emeritus status at the University of Tokyo. As an additional honor in a long list, he won the Fujihara Foundation of Science Prize for his theory of complex manifolds.

In the early 1980s, Kodaira joined a government-sponsored project to produce mathematics textbooks for students from grades seven to eleven. Kodaira produced the compulsory curriculum for grades seven through nine. These texts provided a weighty mathematics background with the intent of preparing Japanese students for any career. Kodaira’s texts appeared in 1984 and were later published in translation in the United States in 1992 as an example of the high quality of foreign texts.

Just before his retirement from teaching in 1985, the Wolf Foundation of Israel awarded Kodaira their mathematics prize for his contributions to the field of complex manifolds. Even after retirement, Kodaira remained interested in mathematics, and he published another work that summarized his theory of complex manifolds in 1986.

The last ten years of Kodaira's life were ones during which he battled against health problems. He suffered from respiratory problems and also became very deaf, which sadden him greatly since he could not enjoy music which had meant so much to him throughout his life. He was too ill in 1990 to attend the International Congress of Mathematicians in Kyoto. Kodaira died in Kofu on 26 July 1997.

Kodaira protested against the standardization and regimentation of the young in Japan's grinding new education system, accusing the Ministry of Education of crushing individualism, and eliminating creativity and initiative in children and university students, the full horror of which development is all too plain to see today in Japan.

Membership

Mathematical Society of Japan

American Association for the Advancement of Science

London Mathematical Society

Personality

As a child, Kodaira was rather shy and stammered when he spoke, especially when he was under stress. In his autobiography, he says that he was a poor pupil in primary school and, although on the whole, he is overly modest, nevertheless he probably did not shine at this stage. However, he showed a fascination with numbers from a young age, loved counting beans and, when he was ten years old he conducted an experiment to see if his dog could count. When she produced puppies, Kunihiko hid them and the dog was upset searching until he returned them to her. However, when he hid a couple of the puppies the dog seemed happy so the ten-year-old Kunihiko decided that "dogs can't count".

Physical Characteristics:
Kodaira was certainly not the athletic type and, as a consequence, he had a strong dislike of the physical education classes.

Quotes from others about the person

"I had given as an exercise problem to prove that the base e of the natural exponential function is not an irrational of the second degree (after it had been proved in a lecture that e is irrational). Kodaira came to the blackboard and wrote his proof in a few lines without speaking any word. In reading these lines with the other students, we admired his perfect proof, where every word was to the point!" - Shokichi Iyanaga

Interests

music

Connections

Kodaira wife Seiko was a violinist. They married in 1943 and went to Gora for their honeymoon. In March 1944 their first child, a boy they named Kazuhiko, was born but conditions in Tokyo became steadily more difficult as Japan came under severe attacks. Sadly, Kazuhiko developed kidney problems and died in 1946. The Kodairas also had two daughters, Yasuko and Mariko. Kodaira's wife, Seiko, died in January 2000, two and a half years after her husband.