Heisuke Hironaka

Heisuke Hironaka (広中 平祐 Hironaka Heisuke; born April 9, 1931) is a Japanese mathematician, specializing in algebraic geometry. At the 1970 International Congress of Mathematicians, he was awarded the Fields Medal.

Quotes

... A roller coaster does not have singularities—if it did, you would have a problem! But if you look at the shadow that the roller coaster makes on the ground, you might see cusps and crossings. If you can explain a singularity as being the projection of a smooth object, then computations become easier. Namely, when you have a problem with singularities in evaluation or differentiation or whatever, you can pull back to the smooth thing, and there the calculation is much easier. So you pull back to the smooth object, you do the computation or analysis, and then pull back to the original object to see what it means in the original geometry.

• as quoted by Allyn Jackson: (October 2005)"Interview with Heisuke Hironaka". Notices of the American Mathematical Society 52 (9): 1010–1019. (quote from p. 1015)

• The notion of infinitely near singular points is classical and well understood for plane curves. We generalize the notion to higher dimensions and to develop a general theory, in terms of idealistic exponents and certain graded algebras associated with them. We then gain a refined generalization of the classical notion of first characteristic exponents. On the level of technical base in the higher dimensional theory, there are some powerful tools, referred to as Three Key Theorems, which are namely Differentiation Theorem, Numerical Exponent Theorem and Ambient Reduction Theorem.
  • (2005). "Three key theorems on infinitely near singularities". Singularités Franco-Japonaises 10: 87-126.

Quotes about Heisuke Hironaka

• Les théorèmes démontrés à l'aide du théorème de Hironaka ne se comptent plus. Pour la plupart, on a l'impression que la résolution des singularités est vraiment au fond du problème, et ne pourra être évitée par recours à des méthodes différentes.
• trans.: The theorems demonstrated using Hironaka's theorem are countless. For the most part, one has the impression that the resolution of singularities is really at the heart of the problem, and cannot be avoided by resorting to different methods.
  • Alexander Grothendieck: "Travaux de Heisouké Hironaka sur la résolution des singularités". Actes du Congrès international des mathématiciens. 1. 1970. pp. 7–9.  (quote from p. 8, vol. 1, pdf)

• ... I once was in Japan and eating alone. A Japanese couple came and wanted to practice their English. They asked me what I did. I said I was a mathematician but could not get the idea across until I said: “Like Hironaka”. Wow! It’s as though in America I’d said “Like Babe Ruth”, or Michael Jordan, or Tiger Woods. Perhaps Hironaka’s name is ... the only one known, but in America I don’t think any mathematician’s name would get any response.
  • John Tate, as quoted by Martin Raussen and Christian Skau: (March 2011)"Interview with Abel Laureate John Tate". Notices of the AMS 58 (3): 444–452. (quote from p. 452)

External links

• Media related to Heisuke Hironaka on Wikimedia Commons
• "Heisuke Hironaka", at the MacTutor History of Mathematics archive