The Laureates

Copyright © Klaus Tschira Stiftung / Peter Badge

Heisuke Hironaka

Born 9 April 1931, Yamaguchi-ken, Japan

Fields Medal (1970) “for his work in algebraic geometry, including the resolution of certain singularities and torus imbeddings with implications in the theory of analytic functions, and complex and Kähler manifolds.”

Heisuke Hironaka comes from a very large family of fifteen children and grew up working in his father’s textile factory. His family took shape in a rather tumultuous way; both his father and mother had been married before and had lost their spouses. When they got married, they had five children by their previous marriages, as his father had four children while Hironaka’s future mother already had a child of her own. Together, they had ten children and Hironaka was the oldest of the boys. At a young age, Hironaka dreamt of being a naniwabushi, or traditional storyteller, but that was soon overridden by the desire to be a pianist. He began playing piano in his middle school without a special instructor to speak of. Hironaka would take the early train to school so that he could practice before school began. He was later advised not to pursue the profession of a musician, which he heeded but it did not squelch his love of classic music.

Hironaka exhibited confidence and talent in mathematics at an early age, but did not seriously consider the subject until senior high school. After dabbling in the sciences, predominantly physics, at Kyoto University for the first two years, by the third year he recognized his strengths in mathematics and that his future lay in this field. Even though the western world was advancing rapidly in the various areas of mathematics, Japan’s strong suit at the time was abstract algebra, and Hironaka focused his efforts on algebraic geometry. His heart was caught by one problem in particular, the resolution of singularities. It was the fruit of those efforts with the resolution of singularities that landed him at Harvard in 1957 to study under Oscar Zariski, who had previously visited Kyoto University and was impressed by Hironaka. During his time at Harvard as a graduate student, Hironaka worked with and befriended some of the greatest minds in mathematics, such as Michael Artin, Steve Kleiman, and David Mumford, who heavily influenced his research.

A standout bond that he forged was with Alexander Grothendieck, who received the Fields Medal in 1966. Grothendieck encouraged him to come to Paris and their collaboration made great steps towards to Hironaka being able to prove the problem of resolution of singularities. Hironaka was able to work out the problem at the local level and it was Grothendieck’s ability to think globally that opened the door for him. It was Hironaka’s induction skills and selectively compiling the knowledge he had acquired in Kyoto, Cambridge and Paris that eventually led to his proof. Hironaka went back to the United States in 1960 and received his PhD from Harvard, and then he started to teach at Brandeis University. With the added security of his new position, Hironaka wholly immersed himself into completing his proof and was finally able to inform Zariski in 1962 that he had solved the problem of the resolution of singularities. In 1970, Heisuke Hironaka was honored with the Fields Medal for his work in algebraic varieties.

It was at Brandeis University that Hironaka met a young anthropology grad student named Wakako, and they married in 1960. Together, they have two children, their daughter Eriko and their son Jo. Wakako Hironaka is an accomplished author/translator and has risen through the ranks of Japanese politics. She served as Minister of Environment in the Hosokawa Reform Government from 1993-94.

Hironaka taught at Columbia (1964-68), then Harvard before returning to Kyoto University in 1975, where he eventually became Director of the Research Institute in 1983. His recognition continued by being made Professor Emeritus of Kyoto University in 1991, and he was president of Yamaguchi University from 1996-2002. Hironaka established the Japan Association of Mathematical Sciences foundation which organizes seminars to give young people the opportunity to exercise their creativity and exchange ideas. He is still teaching some younger students, though on a much less rigorous schedule and purely appreciates seeing the world through the eyes of a mathematician. Hironaka is still actively doing mathematics, yet on his own terms and at a pace free from the constraints of pressure.