A few weeks ago I was invited to give a Sunday talk at the Los Alamos Unitarian Church on the subject of "Pure Science in Los Alamos." The discussion that followed centered on problems that are of growing concern nowadays: the relation of science to morality; the good and the bad in scientific discoveries. Around 1910, Henri Poincaré, the famous French mathematician, had considered such dilemmas in his Dernières Pensées. The questions were less disturbing then. Now, the release of nuclear energy and the possibility of' gene manipulation have complicated the problems enormously.
I was asked what would have happened had the Los Alamos studies proved that it was impossible to build an atomic bomb. The world, of course, would be a less dangerous place in which to live, without the risk of suicidal war and total annihilation. Unfortunately, proofs of impossibility are almost nonexistent in physics. In mathematics, on the contrary, they provide some of the most beautiful examples of pure logic. (Think of the Greeks' proof that the square root of two cannot be a rational number, the quotient of two integers!) Humanity, it seems, is not emotionally or mentally ready to deal with these enormous increases in knowledge, whether they involve the mastery of energy sources or the inanimate and primitive life processes.
Someone in the audience wondered if some of the current research on the human brain might not ultimately lead to a wiser and better world. I would like to think so, but this possibility lies too far in the future to even guess at.
In the short span of my life great changes have taken place in the sciences. Seventy years amounts to some 2 percent of the total recorded history of mankind. I mentioned this once to Robert Oppenheimer at Princeton. He replied, "Ah! but one-fiftieth is really a large number, except to mathematicians!"
Sometimes I feel that a more rational explanation for all that has happened during my lifetime is that I am still only thirteen years old, reading Jules Verne or H. G. Wells, and have fallen asleep.
S.M.U.
SANTA FE
AUGUST 1982
Acknowledgements
This book could have been written without the help of my wife, Françoise, but it would have been merely a chaotic assemblage of items. That it may present some coherent features is the result of her intervention and collaboration. She managed to decrease substantially the entropy of this collection of reminiscences through several years' intelligent and systematic work. Thanks are also due to Gian-Carlo Rota, for our numerous conversations on some of the topics of this book; to Mrs. Emilia Mycielska, for her research on my deceased Polish colleagues; and to Mrs. Jane Richtmyer for going over some of the rougher spots of the text.
Grateful acknowledgment for permission to reproduce photographs is made to the following:
The Society of Fellows, Harvard (Harvard Junior Fellows, 1938)
Los Alamos Scientific Laboratory (all photographs so credited in the captions)
Harold Agnew (Enrico Fermi in the 1940s)
Nicholas Metropolis (Von Neumann, Feynman, and Ulam at Bandelier Lodge)
The Viking Press (George Gamow's cartoon of the "super" committee). From My World Line by George Gamow; copyright © 1970 by George Gamow.
Lloyd Shearer (Stan and Françoise Ulam at home, 1964)
All pictures not otherwise credited are the property of the author.
A Note on S. M. Ulam's Mathematics
by Jan Mycielski
Stanislaw Ulam belonged to a group of mathematicians who came to the United States from Poland before and during the Second World War and played a very important role in the life of mathematics in this country. Among them one can name Natan Aronszajn, Stefan Bergman, Samuel Eilenberg, Witold Hurewicz, Mark Kac, Otton Nikodym, Alfred Tarski, and Antoni Zygmund. They escaped the fate of many millions killed during the war, among whom were the important Polish mathematicians Jozef Marcinkiewicz, Stanislaw Saks, and Juliusz Schauder. The history of mathematics would have been very different if the war had not decimated the Polish youth and almost exterminated the Jewish youth of Europe.
Ulam wrote over 150 technical papers and three books: A Collection of Mathematical Problems, published in 1960, Mathematics and Logic (with Mark Kac), published in 1968, and this autobiography published in 1976. Selections of his papers were published in Sets, Numbers, Universes[1] (referred to as SNU), Science, Computers, and People[2] and Analogies Between Analogies[3] (referred to as ABA). A collection of articles about his contributions appeared in From Cardinals to Chaos.[4]
Françoise, his wife, had a great influence upon his life. She managed their various homes with incredible efficiency and helped in the organization of his many travels. In addition she edited this autobiography from tapes and was a coeditor of the collections of his papers published posthumously.
Endowed with exceptional charm and intelligence, Ulam had an unusual facility for establishing contacts with people. His most pleasant quality was his openness and spontaneity. Without hesitation he shared his ideas with all who were interested. Moreover he had a remarkable memory and a broad humanistic culture acquired in an excellent secondary school in Lwów.
Ulam had a unique ability to raise important unsolved problems. These problems exerted an exceptional influence upon the work of many scientists. In the years of our acquaintance which began in 1969, he preferred to invent open questions, especially those at the boundary of mathematics, physics, and biology, rather than to go into the details of mathematical work. He became a pioneer of computer applications to the heuristic study of dynamical systems. Although he encouraged younger mathematicians and liked to see the work of people from its best side, he looked at mathematics from the point of view of a scientist whose purpose is to study nature. He criticized these mathematical problems which do not appear to have a direct or natural motivation, calling them "Chinese puzzles." He preferred to think about physics and biology, and the mathematical problems that derive from them.
This gift is best illustrated by one of his conjectures which was soon proved by K. Borsuk. It is called "the antipodal theorem." To each continuous function f from the spherical surface to the plane, there exist two antipodal points on the sphere, x and — x, such that f(x) = f(-x).
A well-known consequence of the antipodal theorem was formulated by Steinhaus and is called "the ham and cheese sandwich theorem." It says that if you have a sandwich composed of bread, ham, and cheese, there is one plane which evenly divides the bread, the ham, and the cheese. In more formal language: For any three measurable sets in three-dimensional space, there exists a plane which halves each of them.
Ulam's work pertains to so many areas of mathematics and other sciences connected with it, and is so manifold, that only his most important contributions can be mentioned here.
Ulam's doctoral dissertation, written in 1931 (SNU, pp. 9–19), pertaining to the size of certain infinite cardinal numbers, contains results which are very important for the foundations of modern mathematics.