Quotes By Henri Poincare

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

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.

How is an error possible in mathematics?

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.

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

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

Facts do not speak.

Hypotheses are what we lack the least.

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.

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 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 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.

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.

Geometry is not true, it is advantageous.

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

Mathematicians are born, not made.

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.

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.

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

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.

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

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

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.

Mathematicians do not study objects, but relations between objects.