If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

Thought is only a flash between two long nights, but this flash is everything

How is it that there are so many minds that are incapable of understanding mathematics? … the skeleton of our understanding, … and actually they are the majority. … We have here a problem that...

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

En un mot, pour tirer la loi de l’expérience, if faut généraliser; c’est une nécessité qui s’impose à l’observateur le plus circonspect.In one word, to draw the rule from experience, one must generalize; this is...

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

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. To invent is to discern, to choose.

La pensée n’est qu’un écliar au milieu d’une longue nuit. Mais c’est cet éclair qui est tout.Thought is only a flash in the middle of a long night. But this flash means everything.

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.

Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a...

Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to...

Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n’est pas plus une science qu’un tas de pierres n’est une...

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were...

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

Mathematics is the art of giving the same name to different things.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means . . . .