Hypotheses are what we lack the least.
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
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.
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.
Thought is only a flash between two long nights, but this flash is everything.
Point set topology is a disease from which the human race will soon recover.
Mathematical discoveries, small or great are never born of spontaneous generation.
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.
Just as houses are made of stones, so is science made of facts.
Science is facts.
In the old days when people invented a new function they had something useful in mind.
How is an error possible in mathematics?
Need we add that mathematicians themselves are not infallible?
No more than these machines need the mathematician know what he does.
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
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.
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.
Facts do not speak.
A small error in the former will produce an enormous error in the latter.
