Top 125 Quotes & Sayings by Henri Poincare

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

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

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

To invent is to discern, to choose.

Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.

If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws.

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

Geometry is not true, it is advantageous.

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

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

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.

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

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.

Mathematicians do not study objects, but relations between objects.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.

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

Hypotheses are what we lack the least.

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

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 has adopted the geometry most advantageous to the species or, in other words, the most convenient.

Mathematicians are born, not made.

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

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

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

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

Need we add that mathematicians themselves are not infallible?

A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.

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

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.

Facts do not speak.

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, it is impossible not to be struck by the analogies existing.

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.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

Science is facts.

How is an error possible in mathematics?

A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.

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

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 not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.

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

Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.

Intuition is more important to discovery than logic.

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

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

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

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

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

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 is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

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

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

It is with logic that one proves; it is with intuition that one invents.

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

Science is built up with 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.

Chance ... must be something more than the name we give to our ignorance.

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 may happen that small differences in the initial conditions produce very great ones in the final phenomena.

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