It is easier to square the circle than to get round a mathematician.

It is easier to square the circle than to get round a mathematician.

In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.

[When asked about his age.] I was x years old in the year x^2.

In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.

Mathematics is the only instructional material that can be presented in an entirely undogmatic way.

In The Mathematical Intelligencer, v. 5, no. 2, 1983.

One began to hear it said that World War I was the chemists' war, World War II was the physicists' war, World War III (may it never come) will be the mathematicians' war.

The Mathematical Experience, Boston: Birkhauser, 1981.

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

Number, Scientific American, 211, (Sept. 1964), 51 - 59.

Mathematics seems to endow one with something like a new sense.

In N. Rose (ed.),
Mathematical Maxims
and Minims, Raleigh
NC: Rome Press Inc.,
1988.

The numbers are a catalyst that can help turn raving madmen into polite humans.

In N. Rose (ed.) Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.

Every new body of discovery is mathematical in form, because there is no other guidance we can have.

In N. Rose (ed.) Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.

Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics.

How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.