Mathematicians From Poland

"Various threats come along with the development of information technologies. Connecting people with machines, such a cyborgization of societies, creates a new type of threats – such threats that bring us back a little bit to the Orwellian universe of Nineteen Eighty-Four, in which someone gets very strong tools to control everything. If every human being will be appropriately chipped and our nervous systems, or even our minds, will be incorporated into a global network – one can imagine that sooner or later someone would like to take these technological possibilities in order to get some unprecedented concentration of power and domination. The possibilities of direct physical control may be created, especially if we are connected to a network in a way that interferes with the structure of our nervous system – then we can imagine different possibilities of exerting direct influence. For now, this is the field of speculation."

"My cousin Zygmunt found a distant relative in Italy, Professor Vettolani, who works as an astrophysicist in Bologna. When we contacted him, it turned out that our family traditions are quite compatible. So I think we are really connected by Etruscan blood. Although Zygmunt, who is a tireless researcher of family history, has several other theories about our origins. It turns out that in Italy there were two, no longer existing, settlements called Vetulani: one in Lazio, and the other in Tuscany, near Pisa."

"In some individual actions a very high level of simulation was achieved, e.g. in chess or Go. However, we are still very far from being able to model all human behaviors, even very primitive ones. The number of decisions made every day turns out to be so huge that it will take a long time until a device capable of dealing with all the problems, a device of which actions would be indistinguishable from human ones, will be created. We cannot predict if and when this will happen, because from previous experience it appears that no forecast in this area managed to meet the reality."

"The fact that a computer player wins a game of chess or bridge with a human does not necessarily mean that the device is intelligent. The victory results from the fact that in the final analysis the device has been applied appropriate algorithms developed by man, e.g. using the properties of artificial neural networks. It is not the device that wins with a man, e.g. a chess player, but a man – the designer of the device. It is simply the rivalry of one intellect with another through the medium of computer science."

"A man who crosses the street must be careful not to be hit by a car, even if the car is an automatic vehicle without a driver, because the car is stronger than a man. We should be afraid of devices that function in a dangerous way for us. The robot will become such a device if we manage to equip it not so much in intelligence as in mechanisms imitating the effects of a certain human functionality. I mean equipping robots with mechanisms that function in a similar way to consciousness of existence and the instinct of self-preservation of a human being. I do not mean to say that the device will be conscious, but that its behavior will be similar to the behavior of a rational unit, such as a man aware of his existence. The machine will not receive consciousness, but it will behave as if it did."

"How does artificial intelligence refer to social relationships – for example, the functioning of one or another political system? Well, the evolution of the world is not a closed and completed process. For sure, we are awaiting a change in social relations due to moving of the labor market, especially as a result of transferring the burden of performing various activities on the devices. The invention of machines during the English Industrial Revolution of the eighteenth and early nineteenth centuries resulted in mass strikes and revolts, because many workers were afraid that they would be replaced by the machines. The societies has somehow coped with it. Will they defend themselves in the situation of the next step towards the automation of everything? It's an open matter."

"The words "routine analyses" are used to denote the analyses performed by laboratories, frequently attached to industrial plants, and distinguished by the following characteristics: (1) All the analyses or measurements of the same kind, for example, are designed to measure the sugar content in beets or to determine the coordinates of a star. (2) The analyses are carried out day after day using the same methods and the same instruments. (3) While all the analyses are of the same kind, the quantity n varies from time to time, where n represents some small number, 2, 3, 4, 5."

"The future mathematical statistician needs early contacts with experimental sciences. He needs them because, at this stage of the development of statistics, the expeimental sciences are sources of theoretical problems. Also, he needs them because in almost any imaginable job which he may get after graduation, he will be called upon to apply his theory to experimental or observational problems."

"Suppose it is desired to test the efficiency of several treatments intended to destroy certain larvae on a field. The experiments are arranged in the usual way. The treatments compared are applied to particular plots with several replications and then the plots (or smaller parts of them) are inspected and all the surviving larvae are counted. Thus the observations represent the numbers of surviving larvae in several equal areas. It happens frequently that, while there is room for doubt as to whether there is any significant difference between the average number of survivors corresponding to particular treatments, there is no doubt whatever that the variablitity of the observations differs from treatment to treatment."

"The development of modern science is marked by a pronounced tendency toward indeterminism. A somewhat brutal description of this tendency may be states as follows. In relation to some phenomena, instead of trying to establish a (deterministic) functional relationship between a variable y, and some other variables x1, x2, ... , xn, we try to build a (stochastic or probabilistic) model of these phenomena, predicting frequencies with which, in specified conditions, the same variable y will assume all of its possible values."

"A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies."

"Stalin invented Slonimsky! Then he must have also invented the genetic content of one-quarter of me, for Z. Y. Slonimsky, known to the world of Jewish scholarship as Chaim Selig Slonimsky, was my paternal grandfather. A swarm of childhood memories invaded my brain. Ever since I could remember, my mother used to tell me amazing tales about my grandfather, who was a genius, but an impractical one. "Don’t follow in his footsteps," she cautioned me."

"Where there is independence there must be the normal law."

"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."

"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."

"Independence is the central concept of probability theory and few would believe today that understanding what it meant was ever a problem."

"I then reached for a time honored tactic used by mathematicians: if you can't solve the real problem, change it into one you can solve."

"There was hardly a page in Markov's book which did not feature the normal law and it cast a spell over me from which I have never fully recovered. Adding to the fascination was the impression that somehow the normal law was the key to mysterious and elusive world of chance phenomena."

"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."

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

"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."

"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."

"I didn't even try to penetrate the comics, though many years later I came, somewhat grudgingly, to admire Pogo."

"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."

"As an introduction to America, my ten months in Baltimore were superb. I find it difficult to find words to convey the feeling of decompression, of freedom, of being caught in a sweep of unimagined and unimaginable grandeur. It was a life on a different scale with more of everything - more air to breathe, more things to see, more people to know."

"I prefer concrete things and I don't like to learn more about abstract stuff than I absolutely have to."

"Actually, my solution generated considerable further work and the "dog-flea" model keeps cropping up from time to time in unexpected contexts."

"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."

"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."

"As a mathematician Erdös is what in other fields is called a "natural". If a problem can be stated in terms he can understand, though it may belong to a field with which he is not familiar, he is as likely as, or even more likely than, the experts to find a solution."

"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."

"Thoughts are steered in different ways."

"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."

"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."

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

"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."

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

"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?"

"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."

"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"."

"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."

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

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

"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."

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

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

"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."

"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."