Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that b….

It is impossible to discuss realism in logic without drawing in the empirical sciences... A truly realistic mathematics should be conceived, in line ….

God exists because arithmetic is consistent - the Devil exists because we can't prove it!.

In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry..

Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functio….

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong..

Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the univers….

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold..

... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simp….

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind..

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number..

No mathematician of equal stature has risen from our generation... Hilbert was singularly free from national and racial prejudices; in all public que….

The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence….

A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and alm….

But it seems an irony of creation that man's mind knows how to handle things the better the farther removed they are from the center of his existence….

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, wh….

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of con….

We must learn a new modesty. We have stormed the heavens, but succeeded only in building fog upon fog, a mist which will not support anybody who earn….

Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, bea….

The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its fi….

One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sha….