Heisuke Hironaka

Heisuke Hironaka (広中 平祐 Hironaka Heisuke; April 9, 1931 – March 18, 2026) was 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 Cusp (singularity) cusps and Intersection (geometry) crossings. If you can explain a Mathematical singularity singularity as being the Projection (mathematics) 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 Pullback 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: https://www.ams.org/notices/200509/fea-hironaka.pdf Interview with Heisuke Hironaka Notices of the American Mathematical Society 52 9 October 2005 1010–1019 (quote from p. 1015) The notion of infinitely near Singular point of a curve 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. Three key theorems on infinitely near singularities Singularités Franco-Japonaises 10 2005 87-126 https://ftp.gwdg.de/pub/EMIS/journals/SC/2005/10/pdf/smf_sem-cong_10_87-126.pdf There is an eternal question or eternal mission of mathematics, and that is infinity. A human has two hands: one hand is in infinity, the other hand is in the finite real world. I think that the real task of the mathematician is to somehow connect these two. as quoted by Jackson (2026): Allyn Jackson. 2026. Heisuke Hironaka obituary: mathematician who smoothed out geometry’s complexities. Nature [ 10.1038/D41586-026-02688-X 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 1970 1 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: Interview with Abel Laureate John Tate Notices of the AMS 58 3 March 2011 444–452 https://www.ams.org/notices/201103/rtx110300444p.pdf?version=meter+at+null&module=meter-Links&pgtype=article&contentId=&mediaId=&referrer=&priority=true&action=click&contentCollection=meter-links-click (quote from p. 452) External links Hironaka Category:1931 births Category:2026 deaths Category:Academics from Japan Category:Mathematicians from Japan Category:Fields Medalists Category:Harvard University alumni Category:Harvard University faculty Category:Immigrants to the United States