Monday, August 23, 2010

Excerpts from Adventures of a Mathematician

1. Like mathematics, chess is one of the things where constant practice, constant thinking, and imagining, and studying are necessary to achieve a mastery of the game.
2. It was most stimulating to watch him (Banach) work at the blackboard as he struggled and invariably managed to pull through.
3. In mathematical discussions, or in short remarks he (Banach) made on general subjects, one could feel almost at once the great power of his mind. He worked in periods of great intensity separated by stretches of apparent inactivity.
4. It is such persistence and habit of concentration which somehow becomes the most important prerequisite for doing genuinely creative mathematical work.
5. In those days I went to almost every available general talk.
6. I had an almost pathological aversion to examinations.
7. I worked for a week on the thesis, then wrote it up in one night, from about ten in the evening until four in the morning, on my father's long sheets of legal paper.
8. As for myself, ever since I started learning mathematics I would say that I have spent - regardless of any other activity - on the average two to three hours a day thinking and two to three hours reading or conversing about mathematics. Sometimes when I was twenty-three I would think about the same problem with incredible intensity for several hours without using paper or pencil.
9. I was so absorbed and almost perpetually drunk with mathematics that I was not really aware of it.
10. I already had a pronounced book-buying - or, at least, book-handling - mania.
11. The American accent took me by surprise, and I missed most of what was being said. Then after a week I understood everything. This is a common experience, not only with languages but also with mathematics - a discontinuous process. Nothing, nothing, at first, and suddenly one gets the hang of it.
12. I have often succeeded in obtaining rather original and not unimportant results in areas where I did not know the foundations or details of a theory too well.
13. As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself.
14. I talked with confidence - I don't remember ever being very nervous about giving talks because I always felt I knew what I was talking about.
15. What I dislike is the obligation to be at a given place at a given time - not being able to feel completely free. This is because one of my characteristics is a special kind of impatience. When I have a fixed date, even a pleasant dinner or party, I fret. And yet when I am completely free, I may become restless, not knowing what to do.
16. In our mathematical conversations, as always, I was the optimist, and had some general, sometimes only vague ideas. He supplied the rigor, the ingenuities in the details of the proof, and the final constructions.
17. Six or seven years younger that I, he (Feynman) was brilliant, witty, eccentric, and original.
18. Fermi was overwhelmingly rational. Let me explain what I mean: the special theory of relativity was strange, irrational, seen against the background of what was known before. There was no simple way to develop it through analogies with previous ideas. Fermi probably would not have tried to develop such a revolution.
19. What people think of as inspiration or illumination is really the result of much subconscious work and association through channels in the brain of which one is not aware at all.
20. "Mathematics is a language in which one cannot express unprecise or nebulous thoughts," said Poincare.

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