Henri Poincaré

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 laws.

The search for truth should be the goal of our activities; it is the sole end worthy of them.

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

Just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science.

The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.

The problem of three bodies is of such importance, and has so occupied the attention of mathematicians, that it would be superfluous to dwell upon it here.

Sociology is the science with the greatest number of methods and the least results.

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.

The feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true aesthetic feeling that all real mathematicians know.

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen that there are people who do not understand mathematics?

It is by the scientific method that we prove, but by the intuitive method that we discover.

The scientist must set in order. 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.

To invent is to choose.

The true philosopher does not worship his ideas because they are his, but because he believes them to be true.

Geometry is the art of reasoning well from badly drawn figures.

The most interesting facts are those which can be used several times, those which have a chance of recurring.