Heisuke Hironaka

"as quoted by Allyn Jackson: (quote from p. 1015)"

"Les théorèmes démontrés à laide du théorème de Hironaka ne se comptent plus. Pour la plupart, on a limpression que la résolution des singularités est vraiment au fond du problème, et ne pourra être évitée par recours à des méthodes différentes."

"... 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 ”, or , or . Perhaps Hironaka’s name is ... the only one known, but in America I don’t think any mathematician’s name would get any response."

"trans.: The theorems demonstrated using Hironakas theorem are countless. For the most part, one has the impression that the is really at the heart of the problem, and cannot be avoided by resorting to different methods."

"The notion of infinitely near s is classical and well understood for s. We generalize the notion to higher dimensions and to develop a general theory, in terms of idealistic exponents and certain s 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."