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02/22/02 -- Vol. 20, No. 34

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THE MT VOID Mt. Holz Science Fiction Society 02/22/02 -- Vol. 20, No. 34 El Presidente: Mark Leeper, mleeper@optonline.net The Power Behind El Pres: Evelyn Leeper, eleeper@optonline.net Back issues at http://www.geocities.com/evelynleeper All material copyright by author unless otherwise noted. To subscribe, send mail to mtvoid-subscribe@yahoogroups.com To unsubscribe, send mail to mtvoid-unsubscribe@yahoogroups.com

**GATTACA** (announcement):

For those who live in the Central New Jersey area, the Leeperhouse Film Festival is returning on Thursday, March 7, 7:30 PM. The film we are showing is GATTACA, the film frequently considered to be the best science fiction film of the 1990s. More details about GATTACA will appear in the March 1 MT VOID. [-mrl]

**Mathematics... a young man's game?**
(comments by Mark R. Leeper):

A few weeks ago at our film festival we screened the play "Fermat's Last Tango" by Joanne Sydney Lessner and Joshua Rosenblum. In this play a mathematician based on Andrew Wiles is taunted by the spirit of Pierre de Fermat over the mathematician's near-miss at proving Fermat's Last Theorem. He suggested that the mathematician, in the play named Keane, would never actually prove the theorem. One reason for this is that he was getting older and "mathematics is a young man's game." This was really an observation from the great mathematician G. H. Hardy who said,

"No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game . . . . Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty."

After the play we had a discussion that went to late hours, and part of it was the question of whether it was true that mathematics is a young man's game. Mathematicians do not make blanket statements without looking for counter-examples. Are there major counter examples? Well one problem is that the statement is a little vague. What does it mean for mathematics to be one's game? Clearly there are people who are very clever in mathematics to very advanced years. Mathematician Paul Erdos (pronounced air-dish) lived to 83 and the last 25 years of his life were extremely productive. As a semi-related aside, he said, somewhat whimsically, "The first sign of senility is when a man forgets his theorems. The second sign is when he forgets to zip up. The third sign is when he forgets to zip down." In any case, he was remembering his theorems and zipping up and down pretty much to age 83. And he was a great enough mathematician that he was probably doing important work at advanced ages. But does one consider if a mathematician is doing merely good work at advanced ages it is still his or her "game?"

I guess this is a question of some current interest to me. I, myself, have recently retired and one of the first things I am doing is what I have wanted to do for years, mathematics. Actually I have never stopped doing mathematics, but the rate of my output has gradually slowed down over the years. One reason is I used to have lots of interesting ideas for what I would like to investigate. I get a lot fewer these days and am able to make progress on only a small fraction of those. I pride myself that at one time I filled one (admitedly minor) chink in humanity's mathematical knowledge. I asked myself the right question and was lucky enough to answer it while I still had real mathematicians around to discuss it with. It was not a big discovery, but it still is some justification that I have contributed to humanity's knowledge. There is also the joy of having "walked on new-fallen snow." (I will happily bore with my mathematics anyone who requests it.) Going back to mathematics I have no expectation to again find something new, but I do want the mental exercise and just the fun of playing with mathematics. I am not sure if I find more surprising how much I have forgotten or how much I remember. Both seem substantial.

The good news for the young is that mathematics is a field where you do not need a lot of world knowledge to suggest to you what is really happening. In physics you probably have to know a great deal about physics theory before you can make substantial in- roads. In most cases in economics I assume you really have to have seen a lot of how economies flow. The amount of experience and world knowledge may be less in mathematics if you want to do something original. The bad news is that these days that is less and less true. What you may need to have is not real-world knowledge, but you may have to know about things like "modular forms" and "elliptical functions" and odd theorems with even odder names. Still back on the positive side, mathematics is one field where there seems to be low-hanging fruit. Mathematicians always stumble around in the dark, possibly right past something that is important. Something really new may be lying just one insight off the well-beaten path. Fermat may have had a one-page proof of his theorem that simply nobody has found. With my research, I was lucky and asked the right question in high school algebra. (Let me assure you that in theoretical mathematics circles, what you get in high school algebra is a very well-beaten path.) Ramanujan is another example. He was taught very little but the most rudimentary of established mathematics, discovered for himself much of what he knew, and did some very impressive work. He is an inspiration to every amateur mathematician. Mathematics also led to his early death.

I think there are some obvious counter-examples to Hardy's claim. Hardy himself said he was at his best at just after forty. Turing was said to be at the height of his powers when he was forty-one. If this is comfort it is pretty cold comfort. I am unlikely to see forty-one again. Other than from a distance, that is. There is a sort of prejudice in mathematics against age. Even the Fields Medal, the mathematical equivalent of the Nobel Prize, is awarded only to mathematicians under forty years of age, making it only very slightly less likely that I will ever receive one.

Once source I saw said, "Mathematicians make their best research contributions, on the average, at [age] 38.8 (biologists: 40.5; physicists 38.2; chemists 38.0)." This is hardly youth any more. I find that encouraging and discouraging at the same time. More encouraging is that Weierstrass was 70 when he discovered his polynomial approximation theorem. There is still hope. [-mrl]

Mark Leeper mleeper@optonline.net Quote of the Week: In heaven all the interesting people are missing. - Fredrich Nietzsche

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