An Interview with NYU’s Peter D. Lax
The Abel Prize-winning mathematician talks about his life and career, from emigrating to the United States from Hungary to what he calls the “paradox of education.”
Published June 1, 2005
By Dorian Devins
Academy Contributor
Peter D. Lax is professor in the Mathematics Department at the Courant Institute of Mathematical Sciences, New York University. At age 15 he traveled to the United States from Hungary with his family. His career at Courant began in 1950, and has been interspersed with work at Los Alamos National Laboratory. Dr. Lax’s efforts have concentrated in the area of partial differential equations, and he is recognized for significant contributions to nonlinear equations of hyperbolic systems and for the Lax Equivalence Theorem, among other contributions. He is a member of the National Academy of Sciences and the recipient of many honors and awards, most recently the 2005 Abel Prize, often referred to as the “Nobel Prize of Mathematics.”
Was coming to the U.S. a difficult transition?
I didn’t know much English at first. My parents chose NYU because of Courant, who had the reputation of being very good with young people. At 18 I was drafted into the Army and, thanks to Courant, sent to Los Alamos. I spent a fantastic year there. After finishing my Ph.D. in ‘49, I went back to Los Alamos for a year and thereafter almost every summer into the sixties. That’s where I got involved with computing.
One advisor was John von Neumann. He realized that you couldn’t design nuclear weapons by trial and error – you had to calculate to make sure the design worked. He understood that traditional tools of applied mathematics wouldn’t work; there had to be massive computation. Being von Neumann, he realized this would work for other big engineering designs and for scientific understanding.
You must’ve met a lot of characters there.
I knew Richard Feynman during the war. He was maybe 25, but already legendary. I met Teller and Hans Bethe, who was a wonderful man and a spokesman for science. Feynman could have become that, but he had this terrible illness and died. Others who did very important work were Niels Bohr and Leo Szilard. Szilard liked to operate behind the scenes, but was extremely intelligent and could foresee the future.
How did you end up choosing the path of partial differential equations?
My teachers had done studies in that field. It’s very broad. The word partial just means that it deals with functions of many variables. Most physical theories are expressed as differential equations, like the propagation of sound, flow of fluids, and the way elastic material bends.
Did you approach the problems through mathematics or think about the applications first?
When I was at Los Alamos I thought about the applications, but back here I follow the mathematics.
What is the work you’ve done that you’re most proud of and has been your most important?
I’ve worked on five or six different things. I couldn’t say which one is my favorite. The work on dispersive equations I like very much. The work on shock waves and in scattering worked out very well. I’ve done something very interesting in what can be called harmonic analysis. I did lots of things in functional analysis.
You work in applied and pure mathematics. Is there usually a pretty clear-cut line between the two?
No, everybody mingles. You have to have a balance. Mathematics is taught to children in a way that is very numbers oriented.
Shouldn’t there be a better way to get kids engaged and show the relevance and beauty of math?
Many people think that mathematics theorems are something you memorize. One of the first things to impress on them is that mathematics is thinking. You don’t have to know anything; you can figure it out. Later you have to know a lot, but to get into it you can just figure it out in your head. I think once they get that, they lose their fear. There’s something I like to call the paradox of education: Science and mathematics evolve by leaps and bounds. But does that mean that what we teach in college and high school falls behind by leaps and bounds? The answer is not necessarily. New advances often simplify things tremendously, and whole branches of mathematics can be replaced by something much simpler.
What do you feel will be the most interesting or important areas of mathematics in the near future?
It’s hard to predict. Dispersive systems didn’t look so interesting until there was an astonishing discovery that nobody could have foreseen. Biologists are begging mathematicians to come in. The problems they have are somewhat different from the kinds that mathematicians have been working on before.
Is mathematics following other fields, in that the biological areas are booming?
Yes. I wish mathematics and computer science would move closer. It would be good for both.
On the connection between physics and mathematics: Was it Wigner who wrote the famous paper?
“The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” It was a lecture held here, part of a series of lectures in honor of Courant. One could make a biological point: Why is our brain capable of doing mathematics? Being able to recognize saber-toothed tigers is an evolutionary advantage. But formulating and solving differential equations? These are big questions that evolution isn’t yet ready to answer.
Has winning the Abel Prize changed your life in any way?
It brings interviews, and I get more email about it than about cheap pharmaceuticals. I’ll be happy to go back to my life. Life is mathematics; it’s wonderful
