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