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

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.

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

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

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.

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

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 universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.