Stanislaw Ulam Quotes (1909-1984)

“Mathematics may be a way of developing physically, that is anatomically, new connections in the brain.”

“In conversations, some quite recent, on the present status of the foundations of mathematics, von Neumann seemed to imply that in his view, the story is far from having been told. Gödel's discovery should lead to a new approach to the understanding of the role of formalism in mathematics, rather than be considered as closing the subject.”

“One should remember that mathematical logic itself or the study of mathematics as a formal system can be considered a branch of combinatorial analysis. Metamathematics introduces a class of games—"solitaires"—to be played with symbols according to formal rules. One sense of Gödel's theorem is that some properties of these games can be ascertained only by playing them.”

“Quite aware that the criteria of value in mathematical work are, to some extent, purely aesthetic, he [von Neumann] once expressed an apprehension that the values put on abstract scientific achievement in out present civilization might diminish: "The interests of humanity might change, the present curiosities in science may cease, and entirely different things may occupy the human mind in the future." One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”

“The story that Dick Feynman could open safes whose combinations had been forgotten by their owners is true.”

“By an incredible coincidence, Gamow and Edward Condon, who had discovered simultaneously and independently the explanation of radioactivity (one in Russia, the other in this country), came to spend the last ten years of their lives within a hundred yards of each other in Boulder.”

“By an incredible coincidence, Gamow and Edward Condon, who had discovered simultaneously and independently the explanation of radioactivity (one in Russia, the other in this country), came to spend the the last ten years of their lives within a hundred yards of each other in Boulder.”

“[I]t was seeing the gist, the inner core of a problem, that enabled him to open so many new roads—roads that often led to new branches of mathematics. ...Cellular automata theory, which he proposed to von Neumann; the Monte Carlo method of solving intractable problems, not only in probability theory but in areas such as number theory where the method would not have been thought applicable; and his work on nonlinear processes that anticipated today's interest in solitons and "chaos." We still do not know—it remains a government secret—what jumped into Ulam's head that made it possible for Edward Teller to build the H-bomb.”

“I contributed; Ulam did not. I'm sorry I had to answer it in this abrupt way. Ulam was rightly dissatisfied with an old approach. He came to me with a part of an idea which I already had worked out and difficulty getting people to listen to. He was willing to sign a paper. When it then came to defending that paper and really putting work into it, he refused. He said, "I don't believe in it."”

“With his unusual looks and magnetic green eyes, he always seemed to stand out in a crowd. I remember a party years later when Georgia O'Keefe pointed an imperious finger in his direction and exclaimed "Who is that man?"”