Quotes from Henri Poincare

To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.

Facts do not speak.

Thus, they are free to replace some objects by others so long as the relations remain unchanged.

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

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.

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.

Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

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

[G]eometry is not true, it is advantageous.

It is through science that we prove, but through intuition that we discover.

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 built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.

The mind uses its faculty for creativity only when experience forces it to do so.

Science is facts.

Science is facts; 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.

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

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

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

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

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.

Geometry is the art of correct reasoning from incorrectly drawn figures.

Mathematicians do not study objects, but relations between objects.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know