Henri Poincare Quotes - Page 3

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

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

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

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 ancestors' reasoning, and that is all they are ever going to get out of them.

Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

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

Astronomy is useful because it raises us above ourselves; it is useful because it is grand; .... It shows us how small is man's body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.

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

How is error possible in mathematics?

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

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

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.

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.

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.

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

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

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

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

Experiment is the sole source of truth.

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

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

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

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 ask for an eclipse by prayer.

Deviner avant de démontrer! Ai-je besoin de rappeler que c'est ainsi que se sont faites toutes les découvertes importantes.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.