When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

All of mathematics is a tale about groups.

But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.