Quotes By Henri Poincare

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

Point set topology is a disease from which the human race will soon recover.

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

Facts do not speak.

Hypotheses are what we lack the least.

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.

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.

Need we add that mathematicians themselves are not infallible?

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

Science is facts.

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

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

Geometry is not true, it is advantageous.

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

Mathematicians are born, not made.

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

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.

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

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

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.

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

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

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

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

Mathematicians do not study objects, but relations between objects.

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

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.

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

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

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