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Karlin, Samuel (1923 – ) The purpose of models is not to fit the data but to sharpen the questions. 11th R A Fisher Memorial Lecture, Royal Society 20, April 1983.
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Kasner, E. and Newman, J. When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently it must first set its affairs in order at home. Mathematics and the Imagination, New York: Simon and Schuster, 1940.
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Keller, Helen (1880 – 1968) Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important… The knowledge doesn’t make life any sweeter or happier, does it? The Story of My Life. 1903.
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Kelley, John A topologist is one who doesn’t know the difference between a doughnut and a coffee cup. In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
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Kepler, Johannes (1571-1630) Where there is matter, there is geometry. (Ubi materia, ibi geometria.) J. Koenderink Solid Shape, Cambridge Mass.: MIT Press, 1990
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Keynes, John Maynard It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. The Application of Probability to Conduct.
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Kleinhenz, Robert J. When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain’s sheer face, encountering obstacles at every turn, often retracing one’s steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countrysideand then noting the automobile road up the other side!
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Kline, Morris A proof tells us where to concentrate our doubts. In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
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Kline, Morris Statistics: the mathematical theory of ignorance. In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
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Kline, Morris Universities hire professors the way some men choose wives – they want the ones the others will admire. Why the Professor Can’t Teach. St. Martin’s Press, 1977. p 92.
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Koestler, Arthur (1905- ) Nobody before the Pythagoreans had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred. The Sleepwalkers. 1959.
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Kovalevsky, Sonja Say what you know, do what you must, come what may. [Motto on her paper ‘On the Problem of the Rotation of a Solid Body about a Fixed Point.’]
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Kraft, Prinz zu Hohlenlohe-Ingelfingen (1827 – 1892) Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else. Attributed by Karl Schellbach. In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.
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Kronecker, Leopold (1823-1891) Number theorists are like lotus-eaters — having once tasted of this food they can never give it up. In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
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La Touche, Mrs. I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are permutations and aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of number which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then from the top down, the result is always different. Mathematical Gazette, v. 12.
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LaGrange, Joseph-Louis [said about the chemist Lavoisier:] It took the mob only a moment to remove his head; a century will not suffice to reproduce it. H. Eves An Introduction to the History of Mathematics, 5th Ed., Saunders.
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LaGrange, Joseph-Louis The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure. Preface to M’anique Analytique.
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LaGrange, Joseph-Louis When we ask advice, we are usually looking for an accomplice.
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Lakatos, Imre That sometimes clear … and sometimes vague stuff … which is … mathematics. In P. Davis and R. Hersh The Mathematical Experience, Boston: Birkh’ser, 1981.
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Lanczos, Cornelius Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose. In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
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