HENRI POINCARE

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.

How is an error possible in mathematics?

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.

Science is built up of 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.

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

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

Just as houses are made of stones, so is science made of facts.

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.

No more than these machines need the mathematician know what he does.

Science is facts.

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

It has adopted the geometry most advantageous to the species or, in other words, the most convenient.

Thought is only a flash between two long nights, but this flash is everything.

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

To invent is to discern, to choose.

Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.

If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.

In the old days when people invented a new function they had something useful in mind.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

Hypotheses are what we lack the least.

Facts do not speak.

A small error in the former will produce an enormous error in the latter.

Need we add that mathematicians themselves are not infallible?