Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.

Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.

Time Enough for Love.

[Criticized for using formal mathematical manipulations without understanding how they worked:]

Should I refuse a good dinner simply because I do not understand the process of digestion?

Oliver Heaviside

[The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.

A History of Greek Mathematics. 1921.

God not only plays dice. He also sometimes throws the dice where they cannot be seen.

The real danger is not that computers will begin to think like men, but that men will begin to think like computers.

In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.

R. Langlands, "Harish-Chandra," Biographical Memoirs of Fellows of the Royal Society 31 (1985) 197 - 225.

[H]e seemed to approach the grave as an hyperbolic curve approaches a line, less directly as he got nearer, till it was doubtful if he would ever reach it at all.

Far from the Madding
Crowd.

The fact is that there are few more "popular" subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

A Mathematician's Apology, London, Cambridge University Press, 1941.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

A Mathematician's
Apology, London,
Cambridge University
Press, 1941.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

A Mathematician's Apology, London, Cambridge University Press, 1941.