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.
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 is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
It is through science that we prove, but through intuition that we discover.
If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.
One geometry cannot be more true than another; it can only be more convenient.
The mind uses its faculty for creativity only when experience forces it to do so.
Mathematical discoveries, small or great are never born of spontaneous generation.
A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
There are no solved problems; there are only problems that are more or less solved.
Mathematicians are born, not made.
How is error possible in mathematics?
In the old days when people invented a new function they had something useful in mind.
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.
When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.