[His motto:] Few but ripe. (

Pauca sed matura.)

[His motto:] Few but ripe. (

Pauca sed matura.)

C F Gauss

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

In G. Simmons Calculus Gems, New York: McGraw Hill inc., 1992.

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

Letter to Bessel, 1830.

God does arithmetic.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

In G. Simmons Calculus Gems, New York: McGraw Hill inc., 1992.

There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956. p. 314.

If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956. p. 326.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

[A reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem.] In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956. p. 312.

Mathematics is not only real, but it is the only reality. [The] entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of? They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.

Gardner on Gardner:
JPBM Communications
Award Presentation.
Focus: The
Newsletter of the
Mathematical
Association of
America, v. 14, no.
6, December 1994.

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals -- the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

In G. Simmons,
Calculus Gems, New
York: McGraw Hill,
1992.