Words matter. These are the best Henri Poincare Quotes, and they’re great for sharing with your friends.
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.
In the old days when people invented a new function they had something useful in mind.
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.
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.
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
A small error in the former will produce an enormous error in the latter.
Mathematicians do not study objects, but relations between objects.
It is through science that we prove, but through intuition that we discover.
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 nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Thought is only a flash between two long nights, but this flash is everything.
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.
Need we add that mathematicians themselves are not infallible?
Just as houses are made of stones, so is science made of facts.
Thus, they are free to replace some objects by others so long as the relations remain unchanged.
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.
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
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.
In the old days when people invented a new function they had something useful in mind.
Mathematical discoveries, small or great are never born of spontaneous generation.
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.
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.
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
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.
Science is facts.
Point set topology is a disease from which the human race will soon recover.
Mathematics is the art of giving the same name to different things.
It is far better to foresee even without certainty than not to foresee at all.
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.
Facts do not speak.
Geometry is not true, it is advantageous.
Point set topology is a disease from which the human race will soon recover.
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.
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
The mind uses its faculty for creativity only when experience forces it to do so.
Mathematics is the art of giving the same name to different things.
Facts do not speak.
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.
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.
How is an error possible in mathematics?
Mathematicians are born, not made.
It is through science that we prove, but through intuition that we discover.
Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
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.
To invent is to discern, to choose.
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.
Geometry is not true, it is advantageous.
To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.
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.
No more than these machines need the mathematician know what he does.
If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Science is facts.
Mathematicians do not study objects, but relations between objects.
