It is far better to foresee even without certainty than not to foresee at all.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

There are no solved problems; there are only problems that are more or less solved.

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.

Hypotheses are what we lack the least.

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

All of mathematics is a tale about groups.