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

. . . 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.

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.

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose.

One does not ask whether a scientific theory is true, but only whether it is convenient.

Mathematical discoveries, small or great are never born of spontaneous generation.

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