It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

. . . 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.

Every good mathematician should also be a good chess player and vice versa.

If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.

Mathematics is the art of giving the same name to different things.

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

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.