Henri Poincaré, fully Jules Henri Poincaré

Henri
Poincaré, fully Jules Henri Poincaré
1854
1912

French Mathematician, Theoretical Physicist, Engineer and Philosopher of Science

Author Quotes

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.

Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from th at moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile or vain.

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.

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 that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. 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 laws. But it is not always so; 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 latter. Prediction becomes impossible, and we have the fortuitous phenomenon.

Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.

The chief aim of mathematics teaching is to develop certain faculties of the mind, and among these intuition is by no means the least valuable.

Zero is the number of objects that satisfy a condition that is never satisfied. But as never means "in no case", I do not see that any progress has been made.

If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it cannot conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, cannot be happy through science but today he can much less be happy without it.

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

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.

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

Mathematicians are born, not made.

The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.

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.

Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

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

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

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.

The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious.

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

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

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.

It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.

Need we add that mathematicians themselves are not infallible?

Author Picture
First Name
Henri
Last Name
Poincaré, fully Jules Henri Poincaré
Birth Date
1854
Death Date
1912
Bio

French Mathematician, Theoretical Physicist, Engineer and Philosopher of Science