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.
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Topics:
GATTACA (announcement)
Mathematics... a young man's game?
(comments by Mark R. Leeper)
===================================================================
TOPIC: 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]
===================================================================
TOPIC: 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
In heaven all the interesting people are missing.
- Fredrich Nietzsche
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