Interview with Heisuke Hironaka Heisuke Hironaka is one of the premier algebraic geometers of the twentieth century. He is best known for his 1964 work on the resolution of singularities of algebraic va- rieties over a field of characteristic zero, for which he received the Fields Medal in 1970. The fundamental nature of this problem was apparent to many mathematicians in the first part of the twentieth century, notably Oscar Zariski, who solved the prob- lem for curves and surfaces and had a profound influence on Hironaka. Taking a strik- ingly original approach, Hironaka created new algebraic tools and adapted existing ones suited to the problem. These tools have proved useful for attacking many other problems quite far removed from the resolution of singularities. Another major in- fluence was Alexandre Grothendieck, who in 1959 invited the young Hironaka for the first of his many visits to the Institut des Hautes Études Scientifiques (IHÉS) in Paris. In a 2002 news release about the establishment of the Heisuke Hironaka Fund to pro- mote ties between the IHÉS and Japanese mathematicians, IHÉS professor Mikhael Gro- mov is quoted as saying that Hironaka’s resolution of singularities “is unique in the history of mathematics. It is one of the most difficult in the world that has not, to this day, been surpassed or sim- plified.” Heisuke Hironaka was born on April 9, 1931, in Yamaguchi-ken, Japan. As a student at Kyoto University, he was a member of the school around Yasuo Akizuki, who was a pioneer of modern algebra in Japan. Hironaka received his Ph.D. in 1960 from Harvard University, under the direction of Zariski. After positions at Brandeis University and Columbia University, he became a professor at Harvard in 1968, and from 1975 to 1988 he jointly held a profes- sorship at Kyoto University. He served as director of the Research Institute of Mathematical Sciences at Kyoto Uni- versity from 1983 to 1985. He received the Japan Academy Award in 1970 and the Order of Culture of the Japan- ese government in 1975. The fame and esteem Hironaka is accorded in Japan would strike Westerners as quite remarkable. An average Japanese person without much background in mathematics or science is likely to know his name. Hironaka has contributed much time and effort to encouraging young people interested in mathematics. In 1980, he started a summer seminar for Japanese high school students and later added one for Japanese and American college students; the seminars ran for more than two decades under his direction and continue to this day. To sup- port the seminars he established a philanthropic foundation in 1984 called the Japan Association for Mathemati- cal Sciences. The association also provides fellowships for Japanese students to pursue doctoral studies abroad. From 1996 to 2002, Hironaka served as the president of Yamaguchi University, which is in the prefecture where he was born. Nowadays he continues his educational activities, particularly at the local level, and does mathematics research. What follows is the edited text of an interview with Heisuke Hironaka, conducted in December 2004 by Notices senior writer and deputy editor Allyn Jackson. —A. J. 1010 NOTICES OF THE AMS VOLUME 52, NUMBER 9 Family and Childhood cousin was in Notices: You were born in 1931 in Yamaguchi pre- school in Hi- fecture. I’m interested to hear about your life grow- roshima and got ing up there and what your family was like. radiation burns, Hironaka: The town I was born in is a very small but he recovered town. One of my brothers is still living there. Ya- and survived. maguchi prefecture is not far from Hiroshima. The Somehow, people town was on the east side of Yamaguchi prefecture in our area were and facing the inland sea. The population was lucky. But people something like 3,000. About half the people fished, were afraid that and the other half farmed. But my father was a mer- we would be bombed. When- chant, selling clothes. Heisuke Hironaka (second from right in ever we heard a Notices: How many children in your family? front) with parents and siblings, Japan plane coming, Hironaka: I had many sisters and brothers. Al- 1938. together fifteen. But fifteen is actually four plus one people started plus ten. My father’s first wife died, and his sec- spreading out. At ond wife died too after having four children. My that time, they didn’t say it was an atomic bomb. mother had one child before marrying my father, They said it’s a “special bomb.” At that time, the and her husband died. So when my father and American air force had complete control of the mother married, they had five children. My parents air—not the ground yet, but the air was completely then had ten children, and I am the oldest boy controlled. We would see planes coming, and a among them. I have one elder sister. During World rumor would start: “Maybe that’s a ‘special bomb’.” In that kind of situation, grownups are desper- War II the government promoted having many chil- ate about the future. But children are not. Children dren, particularly boys. But after the war, raising don’t know! We were quite happy, actually. The all the children was quite difficult. One brother, also Americans put a lot of mines in the seabed, and a son of my father, died in New Guinea fighting after the war the Japanese brought them up against the Americans. He was twenty-three. An- and detonated them. It was like huge, beau- other brother was in the war with China. He was tiful fireworks. We enjoyed it! injured and died in a hospital in Beijing. Notices: Were you interested in mathe- Incidentally, the mother of the four children, who matics from a very young age? my father married before he married my mother, Hironaka: When we are children, we was my mother’s elder sister. think of doing many, many things. In ele- Notices: I see—your father married two sisters. mentary school I wanted to be a nani- Hironaka: Yes. I think that my mother was try- wabushi, which is a kind of storyteller. He ing to help her sister, who was sick. I like that I was might tell a yakuza story, or samurai story, in a big family. When you are small, it’s good to have or a sad story, and the story is partly sung. many people around of the same age or somebody I liked that, and I wanted to be that! But then older whom you can depend on or learn some- Harvard graduate in middle school I think I started liking thing from. And with the younger children, you feel dorm, 1957. mathematics. Actually, I was confident with that you have some responsibility to take care of mathematics from the first grade. them. My father was not poor, but the war made Notices: Did you have a mathematics teacher at many things difficult. Before the war he had a tex- some point when you were young whom you found tile factory. He sent his first son to an engineering inspiring? school in Nagoya to learn about textiles. He sent Hironaka: It’s kind of silly, but if some teacher his second son to study commerce. So my father praises you, for instance, for doing well on an had big hopes for these two children. When he lost exam, you become very proud of it. I had experi- those two sons, he became completely disap- ences like that. pointed. He sold the factory, and he stopped work- Notices: Did you study music also? ing. After the war, of course, there were big changes. The economy was bad, and they changed the cur- Hironaka: When I was in junior high I wanted rency so that the old currency became useless. to be a pianist. But at that time only the school had There was also a big cultural reform. My father had a piano. Our school was in Yanai, which was then some peasants working for him, and he had to about thirty minutes’ ride by train. I would take an give all the land to them. In any place, when the early train to play the piano before school started. war ends, things go crazy! I played just as was written in the book. From time Notices: Was your area affected by the dropping to time the music teacher taught me something and of the atomic bomb? I would play, but not in any serious way. At some Hironaka: Actually, my father saw it, but it was point they asked me to play in a joint concert with some distance away, so he wasn’t affected. My other schools. They asked me to play Chopin’s OCTOBER 2005 NOTICES OF THE AMS 1011 Impromptu— lecture to the students. It was a bit technical, so I that’s pretty diffi- couldn’t understand everything. But he said at the cult. And I made a beginning of his talk something like, “Mathemat- mess! The girls ics is a mirror in which you can project everything played much bet- in the world.” I was very puzzled by that, but also ter. But in the very impressed. I applied to Hiroshima University boys’ school, no- because I wanted to study with him. But I didn’t body but me was study at all for the entrance exam, and I failed it! playing the piano, So I began to study the year after, and I applied so they asked me to play.