Academics From The United States

"Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth."

"Ideality is preëminently the foundation of Mathematics."

"What is man? … What a strange union of matter and mind! A machine for converting material into spiritual force."

"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.""

"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."

"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."

"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..."

"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."

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

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

"I have no health for a soldier, and as I have no expectation of serving my country in that way, I am spending my time in the old trifling manner, and am so taken with optics, that I do not know whether, if the enemy should invade this part of the country, as Archimedes was slain while making geometrical figures on the sand, so I should die making a telescope."

"Commencement speakers have a good deal in common with grandfather clocks: Standing usually some six feet tall, typically ponderous in construction, more traditional than functional, their distinction is largely their noisy communication of essentially commonplace information. - Commencement address at University of Iowa."

"If our astronomer be judged by the original contributions which, under existing adverse circumstances, he actually did make to astronomy and mathematics, then it must be admitted that he can not be placed in the foremost rank of astronomers then living. Friends will judge him by what he might have done; the world at large will judge him by what he actually accomplished. Our greatest indebtedness to Rittenhouse lies not in the original contributions he made to science, but rather in the interest which he aroused in astronomical pursuits, and in the diffusion of scientific knowledge in the New World which resulted from his efforts."

"Only two transits of Venus had been observed before his time, and of these, the first, in 1639, had been seen by only two persons. These transits happen so seldom that there cannot be more than two in one century, and in some centuries none at all. But the transits of Venus are the best means we have for determining the parallax of the sun. ...The observations were a success and established for Rittenhonse the reputation of an exact and careful astronomer. ...During the transit Rittenhouse saw one phenomenon which escaped the notice of all other astronomers. When the planet had advanced about half of its [Venus'] diameter upon the sun, that part of the edge of the planet which was off the sun's disc appeared illuminated, so that the outline of the entire planet could be seen. But a complete circle of light around Venus would indicate that more than half of Venus is illuminated. This can happen... only when the rays of light are refracted by an atmosphere. Hence... Venus is surrounded, like the earth, by an atmosphere. But this appearance of a ring of light was not confirmed by other astronomers, and the statement of Rittenhouse excited no attention for nearly a century, until his observation was at last confirmed by other astronomers."

"As a mechanic, Rittenhouse became celebrated for the extreme exactness and finish of his workmanship. Especially celebrated were his chronometer clocks. It was while thus engaged in the manufacture of clocks that he planned and executed an instrument which brought into play both his mechanical and mathematical skill. ...the orrery. It was, indeed, intended to be a sort of a perpetual astronomical almanac, in which the results, instead of being exhibited in tables, were to be actually exhibited to the eye. His orrery greatly exceeded all others in precision. It attracted very general attention among well informed persons... There arose a lively competition between different colleges in this country for the possession of this orrery."

"His invention, whatever it may have been, was not of sufficient importance to deserve the name of an "invention of fluxions." If Rittenhouse actually made an invention of such transcending magnitude before the age of twenty, and at a time when he had hardly begun his scientific studies, how is it that he made not the slightest approach to any similar discovery during the forty-four years of his maturer life? Though always a passionate lover of scientific pursuits, he made no original contributions whatever to the science of pure mathematics. Science is indebteded to him chiefly for his orreries and the observations of the transit of Venus. ...the alleged invention of fluxions was little more than a "rumor set afloat by idle gossip." It serves to show us, however, in what unbounded admiration he was held by his countrymen."

"The most noted mathematician and astronomer of early times [in the U.S.] was not a professor in a college, nor had he been trained within college walls. We have reference to David Rittonhouse."

"Among the books he inherited from his uncle was an English translation of the "Principia" of Newton. Such was the progress which he made in mathematical knowledge, although now destitute of any aid, that he was enabled to accomplish the perusal of this work, for the proper understanding of which so much acquaintance with geometry and algebra is necessary, before he had attained his nineteenth year. Newton, as is well known, from deference to the practice of the ancient philosophers, adopts in this work the synthetic method of demonstration, and gives no clue to the analytic process by which the truth of his propositions was first discovered by him. Unlike the English followers of this distinguished philosopher, who contented themselves, for a time, with following implicitly in the path of geometric demonstration, which he had thus pointed out, Rittenhouse applied himself to search for an instrument, which might be applied to the purpose of similar discoveries, and in his researches attained the principles of the method of fluxions. So ignorant was he of the progress which this calculus had made, and of the discussions in relation to its invention and improvement, that he for a time considered it as a new discovery of his own. In this impression, however, he could not have long continued; as he made, in his nineteenth year, an acquaintance who was well qualified to set him right in this important point."

"It was during the residence of our ingenious philosopher with his father in the country that he made himself master of Sir Isaac Newton's Principia, which he read in the English translation of Mr. Motte. It was here, likewise, he became acquainted with the science of fluxions; of which sublime invention he believed himself, for a while, to be the author, nor did he know for some years afterwards that a contest had been carried on between Sir Isaac Newton and Leibnitz for the honor of the great and useful discovery. What a mind was here! Without literary friends or society, and with but two or three books, he became, before he had reached his four and twentieth year, the rival of two of the greatest mathematicians in Europe."

"The year 1775 opened with a project intended to bring the abilities of Rittenhouse more effectually into the service of science. The Philosophical Society addressed the colonial legislature of Pennsylvania, praying it to establish a public observatory, and commit it to the care of Rittenhouse. Had the circumstances of the times permitted this project to be carried into effect, it would have enabled him to occupy a great space in the history of astronomy. He had already shown himself the equal, in point of learning and skill as an observer, to any practical astronomer then living; nothing was wanting to make him rank with the Flamsteads, the Halleys, and the Maskelynes, but that he should be permitted to devote his whole mind to this pursuit, and be furnished with those instruments and accommodations, for which no private fortune will suffice. Other men might have been found as well, nay, better qualified for the political pursuits and public offices in which it became his fate to spend the rest of his life; but America has never yet produced any individual who has manifested so great a capacity for extending the domain of practical astronomy. To arrange the details of a disorganized and depreciating currency, to collect and disburse a scanty and ill-paid revenue, were thereafter to be the pursuits of our philosopher; and he was to expend upon the estimates and returns of the tax-gatherer those powers of mind which were capable of grasping, and that mechanical skill which sufficed to imitate, the vast mechanism of the universe."