Kant, Emmanual (1724 - 1804)
The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.
The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.
Kant, Emmanual (1724 - 1804)
All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas.
Quoted in Hilbert's Foundations of Geometry.
Kaplan, Abraham
Mathematics is not yet capable of coping with the naivete of the mathematician himself.
Sociology Learns the Language of Mathematics.
Kaplansky, Irving
We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free , but when the chips are down we close the office door and compute with matrices like fury.
Paul Halmos: Celebrating 50 Years of Mathematics.
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.
Kasner, E. and Newman, J.
Mathematics is man's own handiwork, subject only to the limitations imposed by the laws of thought.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
Kasner, E. and Newman, J.
...we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
Kasner, E. and Newman, J.
Mathematics is the science which uses easy words for hard ideas.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
Kasner, E. and Newman, J.
Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
Kasner, E. and Newman, J.
Perhaps the greatest paradox of all is that there are paradoxes in mathematics.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
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.
Kasner, E. and Newman, J. R.
The testament of science is so continually in a flux that the heresy of yesterday is the gospel of today and the fundamentalism of tomorrow.
E. Kasner and J. R. Newman, Mathematics and the Imagination, Simon and Schuster, 1940.
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.
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.
Kepler, Johannes (1571-1630)
A mind is accustomed to mathematical deduction, when confronted with the faulty foundations of astrology, resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
Kepler, Johannes (1571-1630)
Where there is matter, there is geometry.
(Ubi materia, ibi geometria.)
J. Koenderink Solid Shape, Cambridge Mass.: MIT Press, 1990
Kepler, Johannes (1571-1630)
The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.
Kepler, Johannes (1571-1630)
Nature uses as little as possible of anything.
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.
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!
Kline, Morris
A proof tells us where to concentrate our doubts.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Kline, Morris
Statistics: the mathematical theory of ignorance.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Kline, Morris
Logic is the art of going wrong with confidence.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
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.
Koestler, Arthur (1905- )
In the index to the six hundred odd pages of Arnold Toynbee's A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur yet their cosmic quest destroyed the medieval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
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.
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."]
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.
Kronecker, Leopold (1823 - 1891)
God made the integers, all else is the work of man.
Jahresberichte der Deutschen Mathematiker Vereinigung.
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.
Famous Mathematics Quotes List
Following is the list of Mathematical Quotations:
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