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

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

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

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.

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.

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

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