705 Quotes About Mathematics

If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither ‘number’ nor ‘size,’ but always form.

The person who wishes to attain human perfection should study logic first, next mathematics, then physics, and, lastly, metaphysics.

Abel has left mathematicians enough to keep them busy for five hundred years.

Obscenity is a function of culture - a function in the mathematical sense, I mean, its value changing with that of the variables on which it depends.

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

There must be a trick to the train of thought, a recursive formula. A group of neurons starts working automatically, sometimes without external impulse. It is a kind of iterative process with a growing pattern. It wanders about in the brain, and the way it happens must depend on the memory of similar patterns.

It so happens that one of the greatest mathematical discoveries of all times was guided by physical intuition.

The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.