Quotes from Henri Poincare

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

Mathematicians are born, not made.

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.

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

Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of giving different names to the same thing].

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.

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

How is an error possible in mathematics?

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

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

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

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

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

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

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

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.

Chance ... must be something more than the name we give to our ignorance.

Deviner avant de démontrer! Ai-je besoin de rappeler que c'est ainsi que se sont faites toutes les découvertes importantes.

A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.

Science is built of facts the way a house is built of bricks but an accumulation of facts is no more science than a pile of bricks is a house.