Mathematicians have long since regarded it as demeaning to work on problems related to elementary geometry in two or three dimensions, in spite of the fact that it is precisely this sort of mathematics which is of practical value.

Mathematicians have long since regarded it as demeaning to work on problems related to elementary geometry in two or three dimensions, in spite of the fact that it is precisely this sort of mathematics which is of practical value.

It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, `Yes, it is true, but you won't be able to understand the proof.'

John Horgan,
*Scientific
American* 269:4
(October 1993),
92-103.

This is not mathematics; it is theology.

[On being exposed to Hilbert's work in invariant theory.]

Quoted in P. Davis
and R. Hersh, The
Mathematical
Experience, Boston:
Birkhauser, 1981.

There are no deep theorems -- only theorems that we have not understood very well.

The Mathematical Intelligencer, vol. 5, no. 3, 1983.

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 1754.

It has been said that figures rule the world. Maybe. But I am sure that figures show us whether it is being ruled well or badly.

In J. P. Eckermann, Conversations with Goethe.

I don't believe in natural science.

[Said to physicist John Bahcall.]

Ed Regis, Who Got Einstein's Office? Addison Wesley, 1987.

And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 548.

The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not.

In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

Mathematics is a language.