|||

**Paul R. Halmos (1916-2006), a major figure in twentieth century mathematics, died on October 2 in Los Gatos, California. Of Hungarian descent, he came to the United States at age 13. He entered the University of Illinois at 16, and received his doctorate when he was 22. Upon receiving his PhD he spent two years at the Institute for Advanced Study as an assistant to John von Neumann. Over the course of his career he held positions at the University of Chicago, University of Michigan, Indiana University, the University of California, Santa Barbara, the University of Hawaii, and Santa Clara University.**

**When interviewed several years ago, he was asked: What is mathematics to you? He responded: "It is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing — one great, glorious thing." A few years later, he was asked about the best part of being a mathematician. He said: "I'm not a religious man, but it's almost like being in touch with God when you're thinking about mathematics."**

Some quotations from the book "I want to be a mathematician"

*I didn't spend every minute of my last student year on the thesis--but the measure of the set of exceptional minutes was very near to zero.*

Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."

I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.

The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me -- both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

*I Want to be a Mathematician*, Washington: MAA Spectrum, 1985.

https://m.sciencenet.cn/blog-213294-434681.html

上一篇：纪伯伦谈欢乐与悲哀

下一篇：迟到的母亲节祝福--爱你终久长

Archiver|手机版|**科学网**
( 京ICP备07017567号-12 )

GMT+8, 2023-9-23 05:32

Powered by **ScienceNet.cn**

Copyright © 2007- 中国科学报社