Mathematicians From The United States

"I would like to state at this time that I am not now and have never been... a member of the Boy Scouts of America. Their motto is, as you know, "Be Prepared!" and that is the name of this song."

"I find enough mystery in mathematics to satisfy my spiritual needs. I think, for example, that pi is mysterious enough (don't get me started!) without having to worry about God. Or if pi isn't enough, how about fractals? or quantum mechanics?"

"No one is more dangerous than someone who thinks he has "The Truth". To be an atheist is almost as arrogant as to be a fundamentalist. But then again, I can get pretty arrogant."

"Andrew Wiles gently smiles, Does his thing, and voila! Q.E.D., we agree, And we all shout hurrah! As he confirms what Fermat Jotted down in that margin, Which could've used some enlargin'."

"Political satire became obsolete when Henry Kissinger was awarded the Nobel Peace Prize."

"Alas, irreverence has been subsumed by mere grossness, at least in the so-called mass media. What we have now — to quote myself at my most pretentious — is a nimiety of scurrility with a concomitant exiguity of taste. For example, the freedom (hooray!) to say almost anything you want on television about society's problems has been co-opted (alas!) by the freedom to talk instead about flatulence, orgasms, genitalia, masturbation, etc., etc., and to replace real comment with pop-culture references and so-called "adult" language. Irreverence is easy — what's hard is wit."

"I’ve always kind of considered him the J. D. Salinger of demented music."

"Lehrer is that rarest of beasts a performer who was never seduced by the roar of the crowd and who rejected show business well before it had a chance to do the same to him. His concert tours were brief and motivated either by a desire to visit a new place (such as Australia, in 1960) or to test and polish material for a recording."

"Mr. Lehrer's muse is not fettered by such inhibiting factors as taste."

"Lehrer was able to express and to expose, in humorous verse and lilting music, some of the most powerful dangers of the second half of the century … Many of the causes of which Lehrer sang became, three decades later, part of the main creative impulse of mankind."

"The best musical satirist of the 20th Century."

"Dear Mr. Lehrer:"

"You can make fun with Saddam Hussein jokes … but you can't make fun of, say, the concentration camps. I think my target was not so much evil, but benign stupidity people doing stupid things without realising or, instead, thinking they were doing good."

"The audience usually has to be with you, I'm afraid. I always regarded myself as not even preaching to the converted, I was titillating the converted. The audiences like to think that satire is doing something. But, in fact, it is mostly to leave themselves satisfied. Satisfied rather than angry, which is what they should be."

"I could prove God statistically. Take the human body alone — the chances that all the functions of an individual would just happen is a statistical monstrosity."

"You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers."

"The tools introduced by Nash gave rise to new powerful theories (convex integration, Nash-Moser scheme) which later would allow to attack many mathematical problems."

"[W]hile the book and the movie probed the conflicting complexities in Nash the man, neither delved deeply into Nash's math. So for most people today, his accomplishments remain obscure. Within the world of science, though, Nash's math now touches more disciplines than Newton's or Einstein's. What Newton's or Einstein's math did for the physical universe, Nash's math may now be accomplishing for the biological and social universe."

"When Freeman Dyson, the physicist, greeted John Forbes Nash, Jr. at the Institute for Advanced Study one day in the early 1990s, he hardly expected a response. A mathematics legend in his twenties, Nash had suffered for decades from a devastating mental illness. A mute, ghost-like figure who scrawled mysterious messages on blackboards and occupied himself with numerological calculations, he was known around Princeton only as “the Phantom.” To Dyson’s astonishment, Nash replied. He’d seen Dyson’s daughter, an authority on computers, on the news, he said. “It was beautiful,” recalled Dyson. “Slowly, he just somehow woke up.” Nash’s miraculous emergence from an illness long considered a life sentence was neither the first, nor last, surprise twist in an extraordinary life."

"As I said, I spent a great deal of time in the common room, and so did Nash. He was a very interesting character and full of ideas. He also used to wander in the corridors whistling things like Bach, which I had never really heard before — a strange way to be introduced to classical music! I saw quite a bit of him over those years and I also became interested in game theory, in which he was an important contributor. He was a very interesting person."

"He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well. However, my most vivid memory of this time is of the many games which were played in the common room. I was introduced to Go and Kriegspiel, and also to an ingenious topological game which we called Nash in honor of the inventor."

"... he gave his name to the Nash equilibrium – a position in a situation of competition or conflict in which both sides have selected a strategy, but where neither side can then independently change their strategy without ending up in a less desirable position. Such positions are common in everyday life, and in the interactions of business people, politicians and nations. He earned his early reputation, and his 1994 Nobel prize in economics, by proving mathematically that there is at least one Nash equilibrium lying in wait to trap us in every situation of competition or conflict where the parties are unwilling or unable to communicate."

"This man is a genius."

"People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person in the world."

"Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person."

"Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future."

"At the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos."

"Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort."

"As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "," also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph. D. thesis with the other results."

"By the time I was a student in high school I was reading the classic Men of Mathematics by E. T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself p times where p is a prime."

"I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia."

"We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other."

"The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation. The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games."

"A less obvious type of application (of non-cooperative games) is to the study of . By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration."

"If it is really true that you cannot resist them, then you are not sinning of your own free will and hence (at least according to me) not sinning at all."

"Why should I worry about dying? It's not going to happen in my lifetime!"

"I believe that either Jupiter has life or it doesn't. But I neither believe that it does, nor do I believe that it doesn't."

"Of course the falsity of the fact that you believe it is red implies that you don't believe it is red. But this does not mean that you believe it is not red!"

"Metaphysical problems about "mind" versus "matter" arise only from epistemological confusions."

"I have free will, but not of my own choice. I have never freely chosen to have free will. I have to have free will, whether I like it or not!"

"Humor could not flourish in a wholly serious and rational atmosphere."

"From what little was known about the subject, insincerity itself was regarded as another form of psychosis but one which was exceedingly rare."

"Medical opinions differed as to the cause of this "humor" disease."

"There is nothing like a naturalistic orientation to dispel all these morbid thoughts of "sin" and "free will" and "moral responsibility.""

"Centralization of society's vital services in giant computer centers, reservoirs, nuclear power plants, air- traffic control centers, 100-story skyscrapers, and government compounds increases its vulnerability. ... choosing his targets, today's saboteur could pollute a city's water supply, dynamite power transmission towers, cripple an airport control center, destroy a corporate or government computer center."

"The outstanding feature of behavior is that it is often quite easy to recognize but extremely difficult or impossible to describe with precision."

"If Korzybski cannot be said to have established an empirical science, what then has he done? He has pointed a way toward the establishment of such a science. He was a precursor of an intellectual revolution which is just now beginning and which promises to match that of the Renaissance. If Korzybski is seen in this role, then the question of his originality or erudition is not important. He might have something of a dilettante in him. He might have pretended to have more specialized knowledge than he actually had. Great portions of his outlook might be found in the works of more modest and more meticulous workers, That is not important. He was a man of vision and an apostle. Such men are all too rare in our age of specialization."

"The accusations of cultism leveled against Korzybski's followers are not altogether unfounded. In the United States there is a large floating population of 'truthseekers'. Many of them lack the capacity of strenuous intellectual effort required in a fruitful pursuit of knowledge and wisdom; others lack the power of critical evaluation, which would enable them to tell the genuine from the false. Still others cannot be comfortable until they find a panacea to believe in. These people support 'movements' and cults. They are as likely to 'go for' Christian Science as for technocracy, for psychoanalysis as for theosophy, for the Great Books programme as for dianetics. And so inevitably one finds some of them among the adherents of general semantics ... Whether they were actually helped by general semantics or by other factors cannot be determined without sufficient controls. But they went about spreading the faith, thus giving a cultist flavour to the 'movement'."

""What is good in Korzybski's work," they say, "is not new, and what is new is not good." On the other hand, many "Korzybski-ites" proclaim that Korzybski's work has "nothing to do" with semantics. They go so far as to say that the very term "general semantics" was an unfortunate choice; that had Korzybski known what confusion would arise between semantics and general semantics he would not have used it at all. Korzybski himself has maintained that while semantics belongs to the philosophy of language and perhaps to the theory of knowledge, general semantics belongs to empirical science: that it is the foundation of a science of man, the basis of the first "non-aristotelian system," which has had no predecessor and which no academic semanticist has ever achieved."

"For a general semanticist, communication is not merely words in proper order properly inflected (as for the grammarian) or assertions in proper relation to each other (as for the logician) or assertions in proper relation to referents (as for the semanticist), but all these together, with the chain of 'fact to nervous system to language to nervous system to action."