Behind most great science and engineering discoveries stands the work of a host of mathematicians. But their research, like the support of a silent consort, often goes unrecognized.

Gian-Carlo Rota, professor of applied mathematics and philosophy -- the sole MIT claimant to that title -- is not silent.

His interest in communicating with mathematicians, as well as the rest of us, has manifested itself in some very public ways. He spoke at Family Weekend this year ("Ten Predictions about Science") and last year ("Ten Lessons of an MIT Education"), was the Killian Lecturer in 1997 ("Mathematical Snapshots"), speaker at the Provost's Seminar in 1998 ("Ten Remarks on Husserl and Phenomenology"), and presenter of the 1998 American Mathematical Society (AMS) Colloquium Lectures -- a series of three talks presented each year by one of the world's most eminent mathematicians, according to the AMS.

Professor Rota also engages people, very graciously, on an individual level. He's known among students for his accessibility and his clear presentation of material in his math and philosophy courses. He's also respected for his deep understanding of those subjects and revered for his love of communicating.

"The first course of his I took changed my life. It's the only class at MIT that really has done that," said Eric "Krevice" Prebys, a senior in math and computer science. "He helped me to see the world in a totally different way. And that's what I wanted out of college." Mr. Prebys took Professor Rota's Introduction to Phenomenology (24.171) his sophomore year, and later, Probability (18.313) -- "the best probability course at MIT." He is currently enrolled in Professor Rota's phenomenology course on Martin Heidegger, Being and Time (24.172).

Professor Richard Stanley of mathematics, a former student of Professor Rota, credits his advisor with having transformed combinatorics, their mathematical specialty, from a "Mickey Mouse area" of research into a "respectable subject." Professor Stanley was one of the organizers of Rotafest, a four-day conference on combinatorics held at MIT in 1996 honoring Professor Rota's 64th birthday.

Of course, not everyone loves Professor Rota. His latest book, Indiscrete Thoughts (Birkhï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½user, 1997) includes essays that debunk the "myth of monolithic personality" through sketches of the lives of notable mathematicians. When first published, one mathematician wrote that he would not speak to Professor Rota again; another threatened a lawsuit.

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 toï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½? 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.

*A version of this article appeared in MIT Tech Talk on October 28, 1998.*