Heisuke Hironaka

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Heisuke Hironaka

広中平祐

Born

April 9, 1931

Yuu-chō, Kuga-Gun,

, Japan

(modern-day

, Japan)

Died

March 18, 2026

(aged 94)

Tokyo, Japan

Alma mater

(

)

(

)

Spouse

(

1960)

Awards

(1967)

(1970)

(1975)

(2004)

Scientific career

Fields

Mathematics

Institutions

(1960)

Doctoral

students

José Manuel Aroca Hernández-

Ros

Charles Barton, III

Bruce Bennett

Max Benson

Jerome Hoffman

Audun Holme

Monique Lejeune-Jalabert

Takehiko Miyata

Loren Olson

Andrew Schwartz

[

]

Philip Wagreich

Boris Youssin

Heisuke Hironaka

(

広中平祐

Hironaka Heisuke

; April 9, 1931 – March 18,

2026)

was a Japanese mathematician who was awarded the

in 1970

for his contributions to

Early life and education

[

]

Hironaka was born in

, Japan on April 9, 1931. He was inspired to

study mathematics after a visiting

mathematics professor

gave a lecture at his junior high school. Hironaka applied to the

undergraduate program at Hiroshima University, but was unsuccessful. However,

the following year, he was accepted into

to study physics,

entering in 1949 and receiving his Bachelor of Science and Master of Science

from the university in 1954 and 1956. Hironaka initially studied physics,

chemistry, and biology, but during his third year as an undergraduate, he

chose to move to taking courses in mathematics.

The same year, Hironaka was invited to a seminar group led by

who would have a major influence on Hironaka's mathematical development. The

group, informally known as the Akizuki School, discussed cutting-edge research

developments including the

problem for which

Hironaka later received the Fields Medal.

Hironaka has described his

interest in this problem as having the logic and mystery of "a boy falling in

love with a girl."

In 1956, Akizuki invited then Harvard professor

to Kyoto University. Hironaka took the opportunity to present his own

research to Zariski, who suggested that Hironaka move to

continue his studies.

In 1957, Hironaka moved to the United States to attend Harvard University as a

doctoral student under the direction of Zariski.

Hironaka's

background, developed under Akizuki, allowed him to bring fresh insights into

mathematics discussions in Harvard, which placed a greater emphasis on

geometric perspectives. From 1958 to 1959,

visited

Harvard University and was another important influence on Hironaka, inviting

him to the

(IHES) in Paris.

Returning to Harvard in 1960, Hironaka received his

for his thesis

On the

Theory of Birational Blowing-up.

Career

[

]

Hironaka was an Associate Professor of Mathematics at

from

1960 to 1963. He taught at

from 1964 to 1968 and became a

professor of mathematics at

from 1968 until becoming

in 1992.

He returned to Japan for a joint professorship at the

and

from 1975 to 1983 and was the

Institute Director from 1983 to 1985.

Hironaka was the president of

from 1996 to 2002.

Research

[

]

In 1960, Hironaka introduced

, showing that a deformation of

need not be Kähler. The example is a 1-parameter family of

such that most fibers are Kähler (and even

projective), but one fiber is not Kähler. This can be used to show that

several other plausible statements holding for smooth varieties of dimension

at most 2 fail for smooth varieties of dimension at least 3.

In 1964, Hironaka proved that

admit

. Hironaka was able to give a general

solution to this problem, proving that any

can be replaced by (more precisely is

to) a similar variety that has no singularities.

Hironaka recalled that he felt very close to approaching the solution while studying in Harvard. Then, soon after

getting his first teaching position at Brandeis, he realized that if he combined his

experience

from Kyoto, geometry of polynomials from Harvard, and globalization technique from IHES, he had everything he needed

to solve the problem.

In 2017 he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of

singularities in a positive characteristic.

Influence on Asian mathematics

[

]

Hironaka has been active in promoting mathematical education, particularly in Japan and South Korea. Hironaka wrote or

co-authored 26 books on mathematics and other topics.

In 1980, he started a summer seminar for Japanese high school students, and later created a program for Japanese and

American college students. In 1984 he established the Japanese Association for Mathematical Sciences (JAMS) to fund

these seminars, serving as executive director.

Additional funding was received from corporations and the Japanese

government. Harvard emeritus math professor

noted that "In the 1980s there were few domestic grant

opportunities for foreign travel or exchange [...] today, one can see the fruits of Hironaka’s efforts in the number

of former JAMS fellows who have become professors of mathematics across the United States and Japan."

As visiting professor at

from 2008 to 2009, Hironaka mentored undergraduate student

a former high school drop-out and aspiring poet, encouraging his interest in pursuing math for graduate school. Huh won

a Fields medal in 2022 for the linkages he found between

and

Personal life and death

[

]

Hironaka married

in 1960, a Brandeis Wien International Scholar who entered Japanese politics through

her election to the

in 1986. They had a son Jo, and daughter Eriko, who is also a

mathematician.

On his love for mathematics, Hironaka said "I accumulate anything to do with numbers. For instance, I have more than

10,000 photos of flowers and leaves. I like to just count the numbers and compare them. I am so pleased to be a

mathematician, because I can see the mathematical interest in things."

Hironaka died in Tokyo on March 18, 2026, at the age of 94.

Awards

[

]

Hironaka received a Fields Medal, the highest honor in mathematics, at the

Nice in 1970 at 39, just under the 40 year age limit.

List of awards:

(1967)

(1970)

(1971)

(1975)

Honorary doctor of the

(1981)

(2004)

(2011)

Selected publications

[

]

Hironaka, H. (1957).

Mem. College Sci.

Univ. Kyoto Ser. A Math.

(2): 177-195. DOI: 10.1215/kjm/1250777055

Hironaka, H. (1960).

Hironaka, H. (1964),

Annals of Mathematics

(1):109-203.

Hironaka, H.;

. (1967),

J. Math. Soc. Japan,

(1-

2): 52-82. DOI: 10.2969/jmsj/02010052

Hironaka, H. (1967), “

J. Math. Kyoto Univ.,

(1): 325–

327. DOI: 10.1215/kjm/1250524306

Hironaka, H. (1974),

J. Korean Math. Soc.

(5): 901–920.

Aroca, J. M.; Hironaka, Heisuke; Vicente, J. L. (1977). “

" Memorias de Matematica del

Instituto.

Hironaka, H. (1991),

In P. Hilton, F. Hirzebruch, and R. Remmert (Eds.),

(pp. 155-176)

Hironaka, H.; Janeczko, S. (Eds.). (2004). “

Aroca, J. M.; Hironaka, H; Vicente, J. L. (2018),

ISBN 978-4-431-70218-4