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Poincare, Jules Henri (1854-1912)
The mind uses its faculty for creativity only when experience forces it to do so.
Poincare, Jules Henri (1854-1912)
Mathematical discoveries, small or great, are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
Source unknown
Poincare, Jules Henri (1854-1912)
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.
La Science et l'hypothese.
Poincare, Jules Henri (1854-1912) natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
Science and Method.
Poisson, Simeon (1781-1840)
Life is good for only two things, discovering mathematics and teaching mathematics.
Mathematics Magazine, v. 64, no. 1, Feb. 1991.
Polya, George (1887-1985)
Mathematics consists of proving the most obvious thing in the least obvious way.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Polya, George (1887-1985)
The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face the blackboard and to turn his back to the class. He writes a, he says b, he means c; but it should be d. Some of his sayings are handed down from generation to generation.
"In order to solve this differential equation you look at it till a solution occurs to you."
"This principle is so perfectly general that no particular application of it is possible."
"Geometry is the science of correct reasoning on incorrect figures."
"My method to overcome a difficulty is to go round it."
"What is the difference between method and device? A method is a device which you used twice."
How to Solve It. Princeton: Princeton University Press. 1945.
Polya, George (1887-1985)
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
D. J. Albers and G. L. Alexanderson, Mathematical People, Boston: Birkhauser, 1985.
Polya, George (1887-1985)
There are many questions which fools can ask that wise men cannot answer.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
Polya, George (1887-1985)
When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
The American Mathematical Monthly, v. 100, no. 3.