A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

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

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.

If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws.

Applying logic to potentially illogical behaviour is to construct a house on shifting foundations. The structure will inevitably collapse.

Geometry is not true, it is advantageous.