A scientist worthy of his name, about all a mathematician, experiences in his work is the same impression as an artist; his pleasure is as great and of the same nature.

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

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.

Mathematicians are born, not made.

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

Science is facts.

Hypotheses are what we lack the least.

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.

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.

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...

But even if it were the case that the natural laws had nolonger any secret for us, we could still know the situation approximately.

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

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

Facts do not speak.

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

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

Geometry is not true, it is advantageous.

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

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...

Mathematicians do not study objects, but relations between objects.

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

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

Need we add that mathematicians themselves are not infallible?

How is an error possible in mathematics?

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

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

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.

To invent is to discern, to choose.

Now, they invent them deliberately just to invalidate our ancestors’ reasoning, and that is all they are ever going to get out of them.

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.

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

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...

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