Mr Goulburn, Chancellor of the Exchequer, asked my opinion on the utility of Mr Babagge's calculating machine, and the propriety of spending further sums of money on it. I replied, entering fully into the matter, and giving my opinion that it was worthless.

(Sir George Airy, Astronomer Royal, 1842)

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Darwin's theory was presented to the Linnaean Society of London in 1858. It had rather little impact. The president (a dentist interested in reptiles) claimed that the year had not "been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear; it is only at remote intervals that we can reasonably expect any sound and brilliant innovation that shall produce a marked and permanent impression on the character of any brand of knowledge."

(Steve Jones in the New York Review of Books, July 17, 1997)

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Thinking is the great enemy of perfection.

(Joseph Conrad)

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...the thing of greatest importance to mathematics in Europe was the discovery by Tartaglia that you can solve a cubic equation--which, altho it is very little used, must have been psychologically wonderful because it showed a modern man could do something no ancient Greek could do, and therefore helped in the renaissance which was the freeing of man from the intimidation of the ancients...

(Richard Feynman)

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You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office. You are not nameless to me. Do not remain nameless to yourself--it is too sad a way to be. Know your place in the world and evaluate yourself fairly, not in terms of the naive ideals of your youth, nor in terms of what you erroneously imagine your teacher's ideals are.

Best of luck and happiness.

Sincerely,

Richard P. Feynman

(To a former student who was unhappy with his life as a scientist because he was not working on fundamental problems.)

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During the period of the mid-1940s and following, S. Chandrasekar used to drive some hundred miles between Yerkes Observatory in Williams Bay and the University of Chicago, week after week, to meet with a class of two students... When the Nobel Prize in physics was awarded in 1957, it went to the whole class, Messrs. Lee and Yang.

(John Wilson)

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The most exciting phrase to hear in science, the one that heralds new discoveries, is not "Eureka!", but "That's funny..."

(Isaac Asimov)

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When feeling burdened or downcast,... the human mind will gladly turn to the realms of Mathematics, where a lucid and precise grasp of objectivities is obtained and insight is gained so pleasantly through appropriate concept formation. Here the human spirit feels at home.

(Paul Bernays)

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I believe there exists, and I feel within me, an instinct for truth, or knowledge or discovery, of something of the same nature as the instinct of virtue, and that our having such an instinct is reason enough for scientific researches without any practical results ever ensuing from them.

(Charles Darwin)

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Philosophy is written in that great book which is ever before our eyes -- I mean the universe -- but we can never understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders hopelessly through a dark labyrinth.

(Galileo)

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It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that it is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

(Paul Dirac)

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From long experience, all working mathematicians know that there is a preliminary period of rapid advancement in ideas without worrying about exact definitions and proofs, after which there is very hard work to go from that level of accuracy to finished mathematics, where the bugs in definitions and proofs are gone, and concepts are quite clear. A lot of things change in the process. This is the essence of finishing mathematical work.

(Anil Nerode)

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I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

(Isaac Newton)

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Giuseppe Peano was one of the first to use what we now call symbolic logic, and he habitually wrote out all of his lecture notes in his new symbolism. He taught at a military academy, and his students were so incensed by his formalistic approach to mathematics that they rebelled (despite his promise to pass them all) and got him fired. Subsequently he found a more congenial setting at the University of Turin.

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Michael Faraday, after a public demonstration of an electrical experiment, was asked what was the use of electricity? He replied, "What use, madam, is a new-born baby?"

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Being a mathematician (as well as a logician, and perhaps a philosopher of a sort), I have had the opportunity to attend many discussions between specialists in mathematics, where the problem of applications is especially acute, and I have noticed on several occasions the following phenomenon: If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard-pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.

Speaking more seriously, I do not wish to deny that the value of a man's work may be increased by its implications for the research of others and for practice. But I believe, nevertheless, that it is inimical to the progress of science to measure the importance of any research exclusively or chiefly in terms of its usefulness and applicability. We know from the history of science that many important results and discoveries have had to wait centuries before they were applied in any field. And, in my opinion, there are also other important factors that cannot be disregarded in determining the value of a scientific work. It seems to me that there is a special domain of very profound and strong human needs related to scientific research, which are similar in many ways to aesthetic and perhaps religious needs. And it also seems to me that the satisfaction of these needs should be considered an important task of research. Hence, I believe, the question of the value of any research cannot be adequately answered without taking into account the intellectual satisfaction which the results of that research bring to those who understand it and care for it. It may be unpopular and out-of-date to say it -- but I do not think that a scientific result which gives us a better understanding of the world and makes it more harmonious in our eyes should be held in lower esteem than, say, an invention which reduces the cost of paving roads, or improves household plumbing.

(Alfred Tarski, "The Semantic Conception of Truth and the Foundations of Semantics," 1944.)

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Some years ago, someone wrote a book called "The Seven Laws of Money." One of the "laws" went something like this: "Do good work and don't worry about money; it will come along as a side effect." Whether or not that's true of money, I don't know, but in my experience, it's true of credit for scientific work. Just make sure you keep working at important problems, enjoying a life of science, and don't worry so much about credit. You will probably get what you deserve -- as a side effect.