Obituary: Kunihiko Kodaira

A natural bent for mathematics can be seen at all levels of daily life in Japan. In fish and vegetable markets, sellers tot up figures at high speeds: calculators are too slow and clumsy for them. Children practice the soroban (abacus) and partake in nationwide competitions, in which their ability triumphs over the computer. Japan has produced many mathematical geniuses, none more renowned that Kunihiko Kodaira. But their excellence in that branch of science finds recognition abroad rather than at home, especially when they work in the field of pure mathematics.

Certain younger mathematicians, after emigrating to major American universities, played a significant part in the almost never-ending progress of finding a solution to Fermat's theorem, a task in which they were encouraged by the much older Kodaira. This problem had baffled scholars of number theory ever since the mid-17th century, when Pierre de Fermat first posed it in a scribbled note in the margin of one of his books. Amir D. Aczel's book Fermat's Last Theorem: unlocking the secret of an ancient mathematical problem, clearly and elegantly written, was deservedly one of the best- sellers when it was first published in the United States in 1996. It reads like a brilliant thriller.

Among Kodaira's "disciples" involved in the solving of this theorem were Goro Shimura and his close friend Yutaka Taniyama, who were both at the Princeton Institute for Advanced Studies with Kodaira, and posited the Shimura-Taniyama conjecture that was an important step towards the solution of the problem.

There was a good deal of rather underhand in-fighting among the contestants for the honour of being the first to discover the answer, particularly among ambitious and highly gifted French mathematicians and this may have contributed to Taniyama's suicide on his 35th birthday. Certainly all the researchers were under very great strain and Andrew Wiles, who eventually cracked the formula almost by accident after years of struggle, spent the previous months in a nervous daze.

Modern Japanese mathematics may be said to date from the founding in 1877 of the Tokyo Mathematical Society. One of its latest fruits is Sugaku Jiten (1985), published in English in 1990 as Encyclopaedic Dictionary of Mathematics. Kodaira played a prominent role in its editing and publication.

He had already published a large number of books and scholarly papers on such themes as harmonic analysis, differential operators, complex analytic manifolds and above all algebraic geometry, a field in which he helped Japan to become a world leader. He was the first Japanese to be awarded the prestigious Fields Medal, and another of his students, Shigefumi Mori, won the same distinction in 1990 for solving problems in the classification of three dimensional algebraic varieties.

Another of the younger mathematicians, Heisuke Hironaka, won the Fields Prize in 1970 for research into algebraic manifolds and the resolution of singularities in analytic spaces. Much of this innovative work would not have been accomplished without Kunihiko Kodaira's exemplary groundbreaking work.

Kodaira took a degree in Mathematics at Tokyo University in 1938 and followed it with a degree in Physics in 1941. In 1944 he became an Assistant Professor of Mathematics at his Alma Mater. After the Second World War, Japanese mathematicians despaired of any kind of official advancement in Japanese academe and soon there was a steady "brain drain" in all fields of scholarly endeavour to Europe and the US. Kodaira got the call from Princeton in 1949 and was one of the first Japanese to take up a post there. He became a basic influence on 20th-century mathematics. He taught also at Harvard, Stanford, John Hopkins.

He did not return to Japan until 1957, to accept the Order of Culture Prize from the Emperor, and the Japan Academy Prize in the same year. In 1967 he became full professor at Tokyo University and also taught at Gakushin University.

He was elected a Japan Academy Member and "Foreign Member" of the American Science Academy. He had played the piano since childhood, to concert standard, and married the girl with whom he used to play duets, a gifted young violinist. In later years, he protested against the standardisation and regimention 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.

Kodaira wrote some good popular books about mathematics including Journal of a Lazy Mathematician and I Could Only Do Maths.

Kunihiko Kodaira, mathematician: born Tokyo 1915; died 26 July 1997.