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.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

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.

Analyse data just so far as to obtain simplicity and no further.

Geometry is not true, it is advantageous.