Academics From Poland

"There are, roughly speaking, two kinds of mathematical creativity. One, akin to conquering a mountain peak, consists of solving a problem which has remained unsolved for a long time and has commanded the attention of many mathematicians. The other is exploring new territory."

"When one is young, and seventeen is very young, one lives in the present. The future, even the near future, is cloaked in unreality."

"I had a phenomenal memory and could recite long poems by Russian poets, mainly Pushkin. Except for an unusual memory, I was not precocious in any respect and somewhat later, to the chagrin of my father, I was inordinately slow learning the multiplication tables."

"In the summer of 1930 my academic future, however, was not uppermost in my mind. I had been stricken by an acute attack of a disease which at regular intervals afflicts all mathematicians and, for that matter, all scientists: I became obsessed by a problem."

"In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the “ordinary” and the “magicians.’’ An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon, in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students because they cannot be emulated and it must be terribly frustrating for a brilliant young mind to cope with the mysterious ways in which the magician’s mind works. Richard Feynman is a magician of the highest caliber. Hans Bethe, whom Dyson considers to be his teacher, is an “‘ordinary genius’’; so much so that one may gain the erroneous impression that he is not a genius at all. But it was Feynman, only slightly older than Dyson, who captured the young man’s imagination. To be a physicist must have meant to him to be like Feynman and this, alas, was impossible. And so Dyson fell back on the source of strength he always had in reserve: the mastery of mathematical technique."

"Creative people live in two worlds. One is the ordinary world which they share with others and in which they are not in any special way set apart from their fellow men. The other is private and it is in this world that the creative acts take place."

"Unrestricted abstraction tends to divert attention from whole areas of application whose very discovery depends of the features that the abstract point of view rules out as being accidental."

"There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians.’ an ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians... Feynman is a magician of the highest caliber."

"Mathematics is an ancient discipline. For as long as we can reliably reach into the past, we find its development intimately connected with the development of the whole of our civilization. For as long as we have a record of man's curiosity and his quest for understanding, we find mathematics cultivated and cherished, practiced and taught. Throughout the ages it has stood as an ultimate in rational thought and as a monument to man's desire to probe the workings of his own mind."

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

"Very soon I discovered that if one gets a feeling for no more than a dozen other radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships."

"Thanks to my memory, which enabled me to quote Latin and to discuss Greek and Roman civilization, it became obvious to some of my colleagues in other fields that I was interested in things outside mathematics. This lead quickly to very pleasant relationships."

"In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug."

"There may be such a thing as habitual luck. People who are said to be lucky at cards probably have certain hidden talents for those games in which skill plays a role. It is like hidden parameters in physics, this ability that does not surface and that I like to call "habitual luck"."

"I am always amazed how much a certain facility with a special and apparently narrow technique can accomplish."

"In mathematics, as in physics, so much depends on chance, on a propitious moment."

"With sixty professors there are roughly eighteen hundred pairs of professors. Out of that many pairs it was not surprising that there were some whose members did not like one another."

"As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self confidence."

"It is most important in creative science not to give up. If you are an optimist you will be willing to "try" more than if you are a pessimist."

"It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me."

"Ada came from Lwów. She was a very good looking girl who was studying mathematics at the University of Geneva. For a few years I had an off-and-on romance with her."

"For many years I was the youngest among my mathematical friends. It makes me melancholy to realize that I now have become the oldest in most groups of scientists."

"Thinking very hard about the same problem for several hours can produce a severe fatigue, close to a breakdown. I never really experienced a breakdown, but have felt "strange inside" two or three times during my life."

"I thought that the description of Don Quixote's fight with the windmills the funniest thing imaginable."

"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."

"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."

"Do not lose your faith. A mighty fortress is our mathematics. Mathematics will rise to the challenge, as it always has."

"I'm an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate..."

"Whatever is worth saying, can be stated in fifty words or less."

"The first sign of senility is that a man forgets his theorems, the second sign is that he forgets to zip up, the third sign is that he forgets to zip down."

"Engraved on my memory is the day when I found him at noon staring intensely out of a window in our living room with a strange expression on his face. Peering unseeing into the garden, he said "I found a way to make it work." "What work?" I asked. "The Super" he replied. "It is a totally different scheme, and it will change the course of history.""

"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?""

"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.""

"The mathematicians know a great deal about very little and the physicists very little about a great deal."

"Teller’s calculations were faulty; his prototype would have been a dud. This was first noticed by Stanislaw Ulam... Having shown that the Teller scheme was a nonstarter, Ulam produced, in his typically absent-minded fashion, a workable alternative. “I found him at home at noon staring intensely out of a window with a very strange expression on his face,” Ulam’s wife recalled. “I can never forget his faraway look as peering unseeing in the garden, he said in a thin voice—I can still hear it—‘I found a way to make it work.’”"

"[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 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."

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

"I am turned off when I see only formulas and symbols, and little text."

"Thoughts are steered in different ways."

"As one sharpens a knife on a whetstone, the brain can be sharpened on dull objects of thought. Every form of assiduous thinking has its value."

"It is not so much whether a theorem is useful that matters, but how elegant it is."

"In its evolution from a more primitive nervous system, the brain, as an organ with ten or more billion neurons and many more connections between them must have changed and grown as a result of many accidents."

"What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else."

"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."

"According to recent studies, at least one star out of three is multiple."

"Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?"

"I was still very hopeful that much work lay ahead of me. Perhaps because much of what I had worked on or thought about had not yet been put into writing, I felt I still had things in reserve. Given this optimistic nature, I feel this way even now when I am past sixty."

"Ty Boże, ty naturo! dajcie posłuchanie. Godna to was muzyka i godne śpiewanie. Ja mistrz! Ja mistrz wyciągam dłonie! Wyciągam aż w niebiosa i kładę me dłonie Na gwiazdach jak na szklannych harmoniki kręgach."

"Basically, this modern Yiddish literature detected and depicted a paradox that casts a sharp light on the situation of Yiddishkeit at the start of the new century: it was a literature of rupture that the rabbis rejected as impious, a literature turned towards the realities of life, towards the world of the underdog, but if it testifies in this way to the earthquakes that were shaking Yiddishland, it did not take flight beyond the linguistic and cultural frontiers of this world and set foot in universal culture. Though very many Jews in Poland were moved by reading Adam Mickiewicz, how many Polish intellectuals between the two wars were aware of Peretz? This literature remained entirely focused on the Yiddish world, its fund of religious mythology, its customs and traditions, a literature that prospered at the heart of the crisis this world was undergoing, for the exclusive use of those who were its direct witnesses or its agents. Curiously, it is only posthumously, one could say, decades after the disappearance in fire and blood of the world from which it arose, that this literature has begun to enter the pantheon of human culture in general, and, paradox of paradoxes, the broad non-Yiddish-speaking public has begun to discover Sholem Aleichem and Shalom Asch by way of Isaac Bashevis Singer."

"Sound as a burrow'd marmot he slept On the straw where he'd tumbled fully-dressed that night."