Henri Poincare Quotes

Point set topology is a disease from which the human race will soon recover.

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.

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

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.

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

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

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

One geometry cannot be more true than another; it can only be more convenient.

Geometry is the art of correct reasoning from incorrectly drawn figures.

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

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

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

Analyse data just so far as to obtain simplicity and no further.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Intuition is more important to discovery than logic.

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

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

Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of giving different names to the same thing].

The mind uses its faculty for creativity only when experience forces it to do so.

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

Mathematicians are born, not made.

Mathematicians do not study objects, but the relations between objects.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

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

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

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.

All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

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

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

Geometry is not true, it is advantageous.

One does not ask whether a scientific theory is true, but only whether it is convenient.

How is error possible in mathematics?

All of mathematics is a tale about groups.

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

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

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

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

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

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

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

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

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

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.

Experiment is the sole source of truth.

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

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

The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.

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

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.