FOM: Rota's Interview

[Robert Tragesser]

In an interview with MIT Tech Talk, Professor Rota shared his ideas 
about
mathematicians, the mathematics profession and why they remain poorly
understood.

What's it like to be a mathematician?

It's the least rewarding profession except one: music. Musicians live an
impoverished life. Mathematicians -- for what they do -- are really 
poorly
rewarded. And it's a very competitive field, almost as bad as being a
concert pianist. You've got to be really an egoist. You've got to be 
terribly
self-centered.

Why are there so few women in the field?

Women are more realistic than men -- they can see that it's a flight 
from
reality. What they don't see is that it's a flight from reality that 
works.
The distribution of mathematics talent among men and women is exactly
the same. But in 40 years of teaching I've seen really good women
mathematicians leave the profession, including one very close friend, to
my great chagrin. I almost cried.

Why don't we hear about the work of mathematicians?

Mathematicians have bad personalities. They're snobs. Among them, and at
MIT, there's a tendency to judgment: people who don't write formulas are
tolerated. Mathematicians also make terrible salesmen. Physicists can
discover the same thing as a mathematician and say 'We've discovered a
great new law of nature. Give us a billion dollars.' And if it doesn't
change the world, then they say, 'There's an even deeper thing. Give us
another billion dollars.'

Are mathematicians really so different from other scientists and 
engineers?

The more experimental scientists and engineers are, the more common
sense they have, and so on until you get to the mathematicians, who are
totally devoid of common sense.

What do mathematicians do?

They work on problems. There are historical problems floating around. 
You
are in competition with people who came before you. Sometimes you 
discover
the competition wasn't that good after all.

How do they choose the problems?

People like to think that scientists see a need and try to solve that
problem. Engineers may work that way. But in math, you don't have an
application when you work on a problem. It's not the need prompting the
science. The reality is, it's the other way around. You say to yourself,
'I have a feeling there's something to this problem' and you work on it,
but not alone. Many people throughout history work on a single problem,
not a "lone genius." That's another phony-baloney theory.

And once the problem has been solved?

Applications are found after the theory is developed, not before. A math
problem gets solved, then by accident some engineer gets hold of it and
says, 'Hey, isn't this similar to...? Let's try it.' For instance, the 
laws
of aerodynamics are basic math. They were not discovered by an engineer
studying the flight of birds, but by dreamers -- real mathematicians --
who just thought about the basic laws of nature. If you tried to do it 
by
studying birds' flight, you'd never get it. You don't examine data 
first.
You first have an idea, then you get the data to prove your idea.

What is combinatorics?

Combinatorics is putting different-colored marbles in different-colored
boxes, seeing how many ways you can divide them. I could rephrase it in
Wall Street terms, but it's really just about marbles and boxes, putting
things in sets. Actually, some of my best students have gone to Wall
Street. It turns out that the best financial analysts are either
mathematicians or theoretical physicists.

We're also interested in the mathematical properties of knotting and
braiding. Someone in 1910 started with knots. You take one, cut it and 
you
get a braid. It's actually one of the hottest topics in math today and 
holds
the secret to a number of problems (I have a gut feeling). If we 
understand
braids well enough, we'll solve all the problems of physics.

Do these have applications for other sciences?

Protein folding is very closely related to this process. But biologists 
are
just at the beginning. As they get deeper and deeper into the DNA 
structure,
they'll need so much mathematical theory they'll have to become
mathematicians. There aren't more than two or three people right now who
know both math and biology. It takes a tremendous effort. But it's very
probable that an understanding of genetics is dependent on understanding
knotting.

What sorts of problems have combinatorics solved in the past?

One example is quantum mechanics, which was discovered 30 years ago.
The mathematics behind quantum mechanics had been worked out 20 years
before by a mathematician who didn't know what it was good for.

What would you like to tell the public about math and science?

Basic science is essential. The need for public relations is essential. 
We
won't survive -- continue to get funding -- without it. People think 
we've
got enough basic science. But the fact is, basic science costs so little
compared to, say, developing a new kind of submarine. It's a law of 
nature:
the things that get cut first are the least [expensive]. Take [the 
funding
for] the National Endowment for the Arts -- that was peanuts.
</quote>

APH




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