Monday, May 24, 2004 :::
Eugene Wigner was in the Princeton physics department for, I don't know, hundreds of years before he died around 1994. He was brilliant; the Wigner-Ekhart theorem, put out in the thirties, is one of my all-time favorite theorems, and while it's a bit hard to explain to a non-technical audience, it's assumed implicitly by physicists today — they'll use it without even realizing it. Princeton's graduate program doesn't require that the students take any classes, replacing them all with the generals exams, which are therefore the most difficult in the country; while most departments will give a cursory exam to make sure the students haven't forgotten everything, the Princeton exam is the only way they know you ever looked at, say, General Relativity, so they're going to ask you to do a real problem. And the story goes that these problems for which the grad students were given an hour each were first run by Wigner, and if he couldn't do one in five minutes it was deemed too difficult to put on the test.
(I related this once to an associate professor at Princeton who had also been a graduate student there, and asked whether it was true. The only response I ever got from her was, "Well, it's a good story, isn't it?" This sounds like an ambiguous "no", but she's right — it is a good story. So I choose to believe it.)
Anyway, in the forties and fifties John von Neumann was working in the Princeton math department, developing the fundament of pretty much all modern computer science — where "modern" comprises anything after Turing — and largely inventing game theory to boot. Another brilliant man. What's been floating through my head recently is a comment Wigner made; he said, "There are two kinds of people in the world: Johnny von Neumann and everybody else."
I had a professor of Real Analysis — the phrase "bat out of hell" was applied to him, but that's not particularly relevant — who commented once that one can't go into math merely because one is good at it, because there will always be someone better. Cauchy could have been quite intimidated by Riemann, had he cared to be, "and Riemann is looking at Gauss". So you have to do what you love, because you love it. Though you'd better be good enough at it to feed your family, too.
This is cross-posted, and I think would make a decent 3 minute graduation speech.
::: posted by dWj at 8:58 PM
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