A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance..

A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment..

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

Every good mathematician should also be a good chess player and vice versa..

All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As fo….

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..

All of mathematics is a tale about groups..

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

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

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relatio….

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..

In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ance….

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,….

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the ….

It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment ….

How is error possible in mathematics?.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations ….

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..

Often when works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, long or short, and sits down anew to th….

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection..

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous..