Jews From Hungary

"The volume of the cone was discovered by Democritus... He did not prove it, he guessed it... not a blind guess, rather it was reasoned conjecture. As Archimedes has remarked, great credit is due to Democritus for his conjecture since this made proof much easier. Eudoxes... a pupil of Plato, subsequently gave a rigorous proof. Surely the labor or writing limited his manuscript to a few copies; none has survived. In those days editions did not run to thousands or hundreds of thousands of copies as modern books—especially, bad books—do. However, the substance of what he wrote is nevertheless available to us. ...Euclid's great achievement was the systematization of the works of his predecessors. The Elements preserve several of Eudoxes' proofs."

"Good approximations often lead to better ones."

"In my presentation I... follow the genetic method. The essential idea... is that the order in which knowledge has been acquired by the human race will be a good teacher for its acquisition by the individual. The sciences came in a certain order; an order determined by human interest and inherent difficulty. Mathematics and astronomy were the first sciences really worth the name; later came mechanics, optics, and so on. At each stage of its development the human race has had a certain climate of opinion, a way of looking, conceptually, at the world. The next glimmer of fresh understanding had to grow out of what was already understood. The next move forward, halting shuffle, faltering step, or stride with some confidence, was developed upon how well the [human] race could then walk. As for the human race, so for the human child. But this is not to say that to teach science we must repeat the thousand and one errors of the past, each ill-directed shuffle. It is to say that the sequence in which the major strides forward were made is a good sequence in which to teach them. The genetic method is a guide to, not a substitute for, judgement."

"For many of the stories told the final form resulted from a sort of informal psychological experiment. I discussed the subject with several different classes... Several passages... have been suggested by answers of my students, or... modified... by the reaction of my audience."

"I... present also examples of historic interest, examples of real mathematical beauty, and examples illustrating the parallelism of the procedures in other sciences, or in everyday life."

"I shall often discuss mathematical discoveries... I shall try to make up a likely story how the discovery could have happened. I shall try to emphasize the motives underlying the discovery, the plausible inferences that led to it... everything that deserves imitation."

"The efficient use of plausible reasoning is a practical skill and it is learned... by imitation and practice. ...what I can offer are only examples for imitation and opportunity for practice."

"The general or amateur student should also get a taste of demonstrative reasoning... he should acquire a standard with which he can compare alleged evidence of all sorts aimed at him in modern life."

"In plausible reasoning the principal thing is to distinguish... a more reasonable guess from a less reasonable guess."

"The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference."

"Everyone knows that mathematics offers an excellent opportunity to learn demonstrative reasoning, but I contend also that there is no other subject in the usual curricula of the schools that affords a comparable opportunity to learn plausible reasoning. ...let us learn proving, but also let us learn guessing."

"Demonstrative reasoning penetrates the sciences just as far as mathematics does, but it is in itself (as mathematics is in itself) incapable of yielding essentially new knowledge about the world around us. Anything new that we learn about the world involves plausible reasoning, which is the only kind of reasoning for which we care in everyday affairs."

"The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. … Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information."

"To write and speak correctly is certainly necessary; but it is not sufficient. A derivation correctly presented in the book or on the blackboard may be inaccessible and uninstructive, if the purpose of the successive steps is incomprehensible, if the reader or listener cannot understand how it was humanly possible to find such an argument...."

"Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. … To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery."

"We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building."

"The best of ideas is hurt by uncritical acceptance and thrives on critical examination."

"Euclid's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument."

"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."

"There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann."

"Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper."

""Groping" and "muddling through" is usually described as a solution by trial and error. ...a series of trials, each of which attempts to correct the error committed by the preceding and, on the whole, the errors diminished as we proceed and the successive trials come closer and closer to the desired final result. ...we may wish a better characterization ..."successive trials" or "successive corrections" or "successive approximations." ...You use successive approximations when ...looking for a word in the dictionary ...A mathematician may apply the term ...to a highly sophisticated procedure ...to treat some very advanced problem ...that he cannot treat otherwise. The term even applies to science as a whole; the scientific theories which succeed each other, each claiming a better explanation ...may appear as successive approximations to the truth. Therefore, the teacher should not discourage his students from using trial and error—on the contrary, he should encourage the intelligent use of the fundamental method of successive approximations. Yet he should convincingly show that for ...many ... situations, straightforward algebra is more efficient than successive approximations."

"[M]athematicians and physicists think alike; they are led, and sometimes misled, by the same patterns of ."

"The absence from the Dead Sea Scrolls of historical texts proper should not surprise us. Neither in the inter-Testamental period, nor in earlier biblical times, was the recording of history as we understand it a strong point among the Jews."

"If one had to single out the most revolutionary novelty furnished by Qumran, its contribution to our understanding of the genesis of Jewish literary compositions could justifiably be our primary choice."

"The account of the discovery of the Dead Sea Scrolls, as the manuscripts are inaccurately designated, and of the half a century of intense research that followed, is in itself a fascinating as well as an exasperating story."

"The historical Jesus can be retrieved only within the context of first-century Galilean Judaism.... Against this background, what kind of picture of Jesus emerges from the Gospels? That of a rural holy man, initially a follower of the movement of repentance launched by another holy man, John the Baptist. In the hamlets and villages of Lower Galilee and the lakeside, Jesus set out to preach the coming of the Kingdom of God within the lifetime of his generation and outlined the religious duties his simple listeners were to perform to prepare themselves for the great event."

"This is a simple and moving message, which Jesus formulated in his own language for his simple Galilean audience, about God, the heavenly Father, on the dignity of all human beings as children of God, on life turned into worship by total trust, on an overwhelming sense of urgency to do one’s duty without procrastination, on the sanctification of the here and now, and above all on the love of God through the love of one’s neighbour."

"Television is of great educational value. It teaches you while still young how to (a) kill, (b) rob, (c) embezzle, (d) shoot, (e) poison, and, generally speaking, (f) how to grow up into a Wild West outlaw or gangster by the time you leave school."

"On the Continent people have good food; in England, people have good table manners."

"Continental people have sex life; the English have hot-water bottles."

"In England everything is the other way round."

"An Englishman, even if he is alone, forms an orderly queue of one."

"Teach foreign how to be alive in England."

"When people say England, they sometimes mean Great Britain, sometimes the United Kingdom, sometimes the British Isles, – but never England."

"The trouble with tea is that originally it was quite a good drink. So a group of the most eminent British scientists put their heads together and made complicated biological experiments to find a way of spoiling it. To the eternal glory of British science, their labour bore fruit. To the eternal glory of British science their labour bore fruit. They suggested that if you do not drink it clear, or with lemon or rum and sugar, but pour a few drops of cold milk into it, and no sugar at all, the desired object is achieved. Once this refreshing, aromatic, oriental beverage was successfully transformed into colourless and tasteless gargling-water, it suddenly became the national drink of Great Britain and Ireland – still retaining, indeed usrping, the high-sounding title of tea."

"- Driver: "How many kids do you have ?" - Sallah: "Six." - Driver: "It says here that you have seven." - Sallah: "Seven ?" [counting] "OK, seven kids." (from Sallah Shabati)"

"If you start looking like vour passport photo, it's high time you went abroad."

"What's the use of having a gorgeous outfit if you are not happy?"

"I believe in loyalty. When a woman reaches a certain age she likes, she should stick with it."

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."

"A deep sense of humor and an unusual ability for telling stories and jokes endeared Johnny even to casual acquaintances. He could be blunt when necessary, but was never pompous. A mind of von Neumann's inexorable logic had to understand and accept much that most of us do not want to accept and do not even wish to understand. This fact colored many of von Neumann's moral judgments. "It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature." Only scientific intellectual dishonesty and misappropriation of scientific results could rouse his indignation and ire — but these did — and did almost equally whether he himself, or someone else, was wronged."

"Where in the Schrödinger equation do you put the joy of being alive?"

"In science, it is not speed that is the most important. It is the dedication, the commitment, the interest and the will to know something and to understand it — these are the things that come first."

"A possible explanation of the physicist's use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection."

"I know that my retirement will make no difference in its [my newspaper's] cardinal principles, that it will always fight for progress and reform, never tolerate injustice or corruption, always fight demagogues of all parties, never belong to any party, always oppose privileged classes and public plunderers, never lack sympathy with the poor, always remain devoted to the public welfare, never be satisfied with merely printing news, always be drastically independent, never be afraid to attack wrong, whether by predatory plutocracy or predatory poverty."

"We will always fight for progress and reform, never tolerate injustice or corruption, always fight demagogues of all parties, always oppose privileged classes and public plunderers, never lack sympathy with the poor, always remain devoted to the public welfare, never be satisfied with merely printing news, always be drastically independent, never be afraid to attack wrong, whether by predatory plutocracy or predatory poverty."

"Every issue of the paper presents an opportunity and a duty to say something courageous and true; to rise above the mediocre and conventional; to say something that will command the respect of the intelligent, the educated, the independent part of the community; to rise above fear of partisanship and fear of popular prejudice. I would rather have one article a day of this sort; and these ten or twenty lines might readily represent a whole day's hard work in the way of concentrated, intense thinking and revision, polish of style, weighing of words."

"There is not a crime, there is not a dodge, there is not a trick, there is not a swindle, there is not a vice, that does not live by secrecy."

"Our republic and its press will rise or fall together. An able, disinterested, public-spirited press, with trained intelligence to know the right and courage to do it, can preserve that public virtue without which popular government is a sham and a mockery. A cynical, mercenary, demagogic press will produce in time a people as base as itself. The power to mold the future of the Republic will be in the hands of the journalism of future generations."