Henri Poincare

It is by logic we prove. It is by intuition we discover.

— Henri Poincare

How is an error possible in mathematics?

— Henri Poincare

It is not order only, but unexpected order, that has value.

— Henri Poincare

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

— Henri Poincare

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

— Henri Poincare

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know…

— Henri Poincare

There are no solved problems; there are only problems that are more or less solved.

— Henri Poincare

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

— Henri Poincare

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

— Henri Poincare

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

— Henri Poincare

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

— Henri Poincare

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling,…

— Henri Poincare

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it…

— Henri Poincare

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external…

— Henri Poincare

If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the…

— Henri Poincare

“ 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…

— Henri Poincaré

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order,…

— Henri Poincare

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

— Henri Poincare

Einstein does not remain attached to the classical principles, and when presented with a problem in physics he quickly envisages all of…

— Henri Poincare

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature…

— Henri Poincare

When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be…

— Henri Poincare

I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion…

— Henri Poincare

“ Derrière la série de Fourier , d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par…

— Henri Poincaré

“ Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une…

— Henri Poincare

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to…

— Henri Poincare

Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms…

— Henri Poincare

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give…

— Henri Poincare

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

— Henri Poincare

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

— Henri Poincare

It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances…

— Henri Poincare

But for harmony beautiful to contemplate, science would not be worth following.

— Henri Poincare

“To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.”

— Henri Poincaré

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?

— Henri Poincare

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science…

— Henri Poincare

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

— Henri Poincare

Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

— Henri Poincare

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

— Henri Poincare

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

— Henri Poincare

Sociology is the science with the greatest number of methods and the least results.

— Henri Poincare

But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

— Henri Poincare