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Erds, Paul Mathematics is not yet ready for such problems. [Attributed by Paul Halmos.] The American Mathematical Monthly, Nov. 1992
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Euler, Leonhard (1707 – 1783) If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
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Euler, Leonhard (1707-1783) Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate. In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
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Everett, Edward (1794-1865) In the pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven. Quoted by E.T. Bell in The Queen of the Sciences, Baltimore, 1931.
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Eves, Howard W. A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence. In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
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Eves, Howard W. An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity. In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
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Eves, Howard W. Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges. In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
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Eves, Howard W. One is hard pressed to think of universal customs that man has successfully established on earth. There is one, however, of which he can boast the universal adoption of the Hindu-Arabic numerals to record numbers. In this we perhaps have man’s unique worldwide victory of an idea. Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
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Ewing, John If the entire Mandelbrot set were placed on an ordinary sheet of paper, the tiny sections of boundary we examine would not fill the width of a hydrogen atom. Physicists think about such tiny objects; only mathematicians have microscopes fine enough to actually observe them. ‘Can We See the Mandelbrot Set?’, The College Mathematics Journal, v. 26, no. 2, March 1995.
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Feynman, Richard Philips (1918 – 1988) We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn’t any place to publish, in a dignified manner, what you actually did in order to get to do the work. Nobel Lecture, 1966.
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Finkel, Benjamin Franklin The solution of problems is one of the lowest forms of mathematical research, … yet its educational value cannot be overestimated. It is the ladder by which the mind ascends into higher fields of original research and investigation. Many dormant minds have been aroused into activity through the mastery of a single problem. The American Mathematical Monthly, no. 1.
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Fisher, Irving The effort of the economist is to ‘see,’ to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further. Transactions of Conn. Academy, 1892.
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Fisher, Ronald Aylmer (1890-1962) To call in the statistician after the experiment is done may be no more than asking hm to perform a postmortem examination: he may be able to say what the experiment died of. Indian Statistical Congress, Sankhya, ca 1938.
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Flaubert, Gustave (1821-1880) Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?
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Focus Newsletter (MAA) Sample recommendation letter: Dear Search Committee Chair, I am writing this letter for Mr. John Smith who has applied for a position in your department. I should start by saying that I cannot recommend him too highly. In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you. His dissertation is the sort of work you don’t expect to see these days. It definitely demonstrates his complete capabilities. In closing, let me say that you will be fortunate if you can get him to work for you. Sincerely, A. D. Visor (Prof.)
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Fontenelle, Bernard Le Bovier (1657-1757) Leibniz never married; he had considered it at the age of fifty; but the person he had in mind asked for time to reflect. This gave Leibniz time to reflect, too, and so he never married. Eloge de le Leibniz.
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For the things of this world cannot be made known without a knowledge of math.- Anonymous
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Forget committees. New, noble, world changing ideas always come from one person working alone.- H. Jackson Brown
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Frankland, W.B. Whereas at the outset geometry is reported to have concerned herself with the measurement of muddy land, she now handles celestial as well as terrestrial problems: she has extended her domain to the furthest bounds of space. Hodder and Stoughton, The Story of Euclid. 1901.
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Frayn, Michael For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems. Constructions. 1974.
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