It is not order only, but unexpected order, that has value.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

All of mathematics is a tale about groups.

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

It is by logic we prove. It is by intuition we discover.

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.

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.