Adventures of a Mathematician

Prologue

At dusk the plane from Washington to Albuquerque approached the Sandia Mountain range at the foot of which nestles the city of Albuquerque. Some ten minutes before the landing, the lights of the city of Santa Fe became visible in the distance. On the Western horizon loomed the mysterious mass of the volcanic Jemez Mountains. It was perhaps the hundredth time I was returning from Washington, New York, or California, where Los Alamos affairs or some other government or academic business took me almost every month.

My thoughts traveled back to my first arrival in New Mexico in January of 1944. I was a young professor at the University of Wisconsin and had been called to participate in a project, the exact nature of which could not be divulged at the time. All I was told was how to get to the Los Alamos area — a train station named Lamy near Santa Fe.

If someone had prophesied some forty-five years ago that I, a young ’’pure” mathematician from Lwów, Poland, would spend a good part of my adult life in New Mexico — a state whose name and existence I was not even aware of when I lived in Europe — I would have dismissed the idea as inconceivable.

I found myself recollecting my childhood in Poland, my studies, my preoccupation with mathematics even at an early age, and how my interest in physics led me to enlarge my scientific curiosity, which in turn — by a series of accidents and chance — led to a call to join the Los Alamos Project. The nature of the work there I only vaguely guessed when my friend John von Neumann asked me to join him and other physicists at a strange place. “West of the Rio Grande,” was all he could tell me when I met him between trains at Union Station in Chicago.

The plane landed at Albuquerque. I took my bags, walked a hundred yards across a parking area, and climbed into the small plane that commuted several times a day between Albuquerque and a single runway at an altitude of 7300 feet on the Los Alamos mesa.

Von Neumann, one of the greatest mathematicians of the first half of the twentieth century, was the person who had been responsible for my coming to this country in 1936. We had corresponded since 1934 about some abstruse questions of pure mathematics. It was in this field that I early made a name for myself; von Neumann, working in similar areas, invited me to visit the newly established Institute for Advanced Studies in Princeton — a place well known to the general public because one of its first professors was Albert Einstein. Von Neumann himself was one of the youngest professors at Princeton. He was already famous for his work in the foundations of mathematics and logic. Years later, he was to become one of the pioneers in the development of electronic computers.

At one time I had undertaken to write a book on von Neumann’s scientific life. In trying to plan it, I thought of how I, along with many others, had been influenced by him; and how this man, and some others I knew, working in the purely abstract realm of mathematics and theoretical physics had changed aspects of the world as we now know it.

Memories of my own work in science, of my studies and early research, of the endless hours spent in cafés in my home town discussing mathematics with fellow mathematicians, of my coming to the United States, lecturing at Princeton and Harvard, became interwoven in an inextricable way with recollections of von Neumann’s life and later events.

When I started to organize my thoughts, I realized that up to that time — it was about 1966, I think — there existed few descriptions of the unusual climate in which the birth of the atomic age took place. Official histories do not give the real motivations or go into the inner feelings, doubts, convictions, determination, and hopes of the individuals who for over two years lived under unusual conditions. A set of flat pictures, they give at best only the essential facts.

Thinking of all this in the little plane from Albuquerque to Los Alamos, I remembered how Jules Verne and H. G. Wells had influenced me in my childhood in the books I read in Polish translation. Even in my boyish dreams, I did not imagine that some day I would take part in equally fantastic undertakings.

The result of all these reflections was that instead of writing a life of von Neumann, I have undertaken to describe my personal history, as well as what I know of a number of other scientists who also became involved in the great technological achievements of this age.

As I have already mentioned, I began as a pure mathematician. In Los Alamos I met physicists and other “natural” scientists, and consorted mainly, if not exclusively, with theoreticians. It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.

I became involved in the work on the atomic bomb, then in the work on the hydrogen bomb, but most of my life has been spent in more theoretical realms. My friend Otto Frisch, the discoverer of the possibility of chain reactions from fission, in an article in The Bulletin of the Atomic Scientists describing his first impressions of Los Alamos upon arriving there from embattled Britain, wrote:

“Certainly I have never found such a concentration of interesting people in one place. In the evening I felt I could walk into any house at random and would find congenial people engaged in music making or in stimulating debate…. I also met Stan Ulam early on, a brilliant Polish topologist with a charming French wife. At once he told me that he was a pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points!”

Little has been written about the lives of the people responsible for so much in science and in the birth of the nuclear age and the space age: von Neumann, Fermi, and numerous other mathematicians and physicists. But here I want to recount also the more abstract and philosophically decisive influences which came from mathematics itself. Names like Stefan Banach, G. D. Birkhoff, and David Hilbert are virtually unknown to the general public, and yet it is these men, along with Einstein, Fermi and a few others equally famous, who were indispensable to what twentieth-century science has accomplished.