From Budapest to Los Alamos, a Life in Mathematics
In the world of modern mathematics, Dr. Peter D. Lax, professor emeritus at New York University, ranks among the giants.
As a teenage refugee from the Nazis, he worked on the Manhattan Project at Los Alamos, where met the likes of Hans Bethe, Richard Feynman and Edward Teller.
As a young mathematician, he was a protégé of John von Neumann, a father of modern computing.
Dr. Lax's own work, at N.Y.U.'s Courant Institute of Mathematical Sciences, has often straddled the territory where theoretical mathematics and applied physics meet.
He is widely known for his work on wave theory, and his discoveries there are used for weather prediction, airplane design and telecommunications signaling.
This month, the Norwegian Academy of Science and Letters announced that Dr. Lax, who is 78, would receive its third Abel Prize, accompanied by $980,000, an honor created to compensate for the absence of a mathematics category among the Nobel Prizes.
"I don't know what I'll be doing with all that money," he said in an interview last week at his apartment in Manhattan. "I won't give it all away. I'm not rich. Some of it I will give to good causes, mainly in science."
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Q. When did you come to the United States?
A. My parents, my brother and I left Budapest in late November of 1941. I was 15 1/2. We were able to get out -- we are Jewish -- because my father was a physician. The American consul in Budapest was his friend and patient.
And so we went by train across Europe, through Germany in train compartments filled with Wehrmacht troops. We sailed for America from Lisbon on Dec. 5, 1941.
While we were on the high seas, the war broke out. So we left as immigrants and arrived in New York as enemy aliens. Within a month, my brother and I were in high school. I went to Stuyvesant.
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Q. In Hungary, you were a math prodigy. How did the New York public schools measure up?
A. I didn't take any math courses at Stuyvesant. I knew more than most of the teachers. But I had to take English and American history, and I quickly fell in love with America. In history, we had a text, and the illustrations were contemporary cartoons. I thought that was marvelous. I couldn't imagine a Hungarian textbook taking such a less-than-worshipful attitude.
Q. When were you drafted, and how did the Army affect your career?
A. In 1944. I was 18 and I spent six very pleasant months at Texas A&M, at an Army training program in engineering there. Later, I was sent to Los Alamos, and that was like science fiction. There were all these legends everywhere.
I arrived about six weeks before the A-bomb test. There was not too much secrecy inside the fence. That was Oppenheimer's policy. People told me, "We're building an atomic bomb, partly radium, but maybe plutonium, which doesn't exist in the universe, but we are manufacturing it at Hanford."
Q. Were the personality and policy clashes between Teller and J. Robert Oppenheimer evident even then?
A. I was the low man on the totem pole. But I understood what was going on. Looking back, there were two issues: should we have dropped the A-bomb and should we have built a hydrogen bomb?
Today the revisionist historians say that Japan was already beaten, and so the bomb wasn't necessary. I disagree. I remember being in the Army when the Germans surrendered, and we all assumed we were going to be sent to the Pacific next. I also think that Teller was right about the hydrogen bomb because the Russians were sure to develop it. And if they had been in possession of it, and the West not, they would have gone into Western Europe. What would have held them back?
Teller was certainly wrong in the 1980's about Star Wars. And that is still with us today. And it's draining a lot of money we don't have.
What I think was not right of Teller was to bring Star Wars to the White House though the back door, without going through the scientific community.
The system doesn't work. It's a phantasmagoria. But once you had Reagan charmed by it and Bush charmed by it, it became very hard to put an end of something that the president wants.
Q. What do you think your mentor John von Neumann would think about the ubiquity of computers today?
A. I think he'd be surprised. But nobody could have predicted that everybody and their cousin would have personal computers -- although I think of all people, he would have figured it out. Nobody can predict things, but you can see where something's heading.
He could see very far, very far. He saw the use of computers very broadly. But remember, he died in 1957 and did not live to see transistors replace vacuum tubes. Once you had transistors, you could miniaturize computers.
Q. Did you know John Nash, the protagonist of the film "A Beautiful Mind"?
A. I did, and I had enormous respect for him. He solved three very difficult mathematical problems and then he turned to the Riemann hypothesis, which is deep mystery. By comparison, Fermat's is nothing. With Fermat's -- once they found a connection to another problem -- they could do it. But the Riemann hypothesis, there are many connections, and still it cannot be done. Nash tried to tackle it and that's when he broke down.
Q. Do you believe that high school and college math are poorly taught?
A. By and large, that's correct. I would like to see the schools of education teach much more math than methods of teaching and educational psychology. In mathematics, nothing takes the place of real knowledge of the subject and enthusiasm for it.
Q. What do you consider your most significant contributions?
A. There are about five or six things that had an impact. Among them is my work on shock waves, where I clarified shock wave theory and combined it with practical numerical methods for calculating flows with shock waves.
At Los Alamos, this was important to understand how weapons work, but it is equally important in understanding how airplanes at high speed fly through the air.
Ralph Phillips and I came up with the Lax-Phillips semigroup in scattering theory that was a new idea and could be used in quite surprising number of directions. This helped understand radar pictures.
Recently Martin Kruskal and his collaborators have unexpectedly discovered brand new completely integrable systems, and I have helped clarify some things about such systems.
I was able to analyze, with my student Dave Levermore, what happens to solutions of dispersive systems when dispersion tends to zero.
It is a rather surprising new phenomenon, but not easy to express in layman's terms. In a report to the American Philosophical Society I put it into the form of haiku:
Speed depends on size
Balanced by dispersion
Oh, solitary splendor.
Q. Has mathematics become too complex for anyone to understand all of it?
A. Compared to physics or chemistry, mathematics is a very broad subject. It is true that nobody can know it all, or even nearly all. But it is also true that as mathematics develops, things are simplified and unusual connections appear.
Geometry and algebra for instance, which were so very different 100 years ago, are intricately connected today.
A Conversation With Peter Lax Correction: April 11, 2005, Monday A question-and-answer interview in Science Times on March 29 with the mathematician Peter D. Lax, who took part in the Manhattan Project as a young man, misstated a word in his comment recalling the first atomic bomb. The components included uranium, not radium.
