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

One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.

You can not apply mathematics as long as words still becloud reality.

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 final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.

No mathematician of equal stature has risen from our generation... Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom.