Henri Poincaré quotes - page 4

But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something. (Henri Poincaré)
Science is facts just as houses are made of stones, so is science made of facts but a pile of stones is not a house And a collection of facts is not necessarily science. View quote
Henri Poincaré
Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? ...If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism. View quote
Henri Poincaré
The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. View quote
Henri Poincaré
All that is not thought is pure nothingness. View quote
Henri Poincaré
Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. View quote
Henri Poincaré
The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. View quote
Henri Poincaré
When we say force is the cause of motion, we talk metaphysics. View quote
Henri Poincaré
The very possibility of the science of mathematics seems an insoluble contradiction. View quote
Henri Poincaré
For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion. View quote
Henri Poincaré
What has taught us to know the true profound analogies, those the eyes do not see but reason divines? It is the mathematical spirit, which disdains matter to cling only to pure form. (Henri Poincaré)
It is only through science and art that civilization is of value. View quote
Henri Poincaré
In this domain of arithmetic,.. the mathematical infinite already plays a preponderant rôle, and without it there would be no science, because there would be nothing general. View quote
Henri Poincaré
When shall we say two forces are equal? View quote
Henri Poincaré
The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms. View quote
Henri Poincaré
We must, for example, use language, and our language is necessarily steeped in preconceived ideas. View quote
Henri Poincaré
Every definition implies an axiom, since it asserts the existence of the object defined. View quote
Henri Poincaré
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. View quote
Henri Poincaré
No more than these machines need the mathematician know what he does. View quote
Henri Poincaré
Thus, they are free to replace some objects by others so long as the relations remain unchanged. View quote
Henri Poincaré
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. (Henri Poincaré)
The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide. View quote
Henri Poincaré
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. View quote
Henri Poincaré
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means . . . . View quote
Henri Poincaré
A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. ...we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it. View quote
Henri Poincaré