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Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
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More quotes by Henri Poincare

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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.
Henri Poincare
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Thought is only a flash between two long nights, but this flash is everything.
Henri Poincare
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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
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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. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
Henri Poincare
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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.
Henri Poincare
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Science is built up with 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
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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
Henri Poincare
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Mathematicians do not study objects, but relations among objects they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
Henri Poincare
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It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
Henri Poincare
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Mathematicians do not study objects, but the relations between objects.
Henri Poincare
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All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.
Henri Poincare
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A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
Henri Poincare
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
Henri Poincare
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...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
Henri Poincare
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When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole it is to intuition that we must look for it.
Henri Poincare
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In the old days when people invented a new function they had something useful in mind.
Henri Poincare
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Analyse data just so far as to obtain simplicity and no further.
Henri Poincare
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Point set topology is a disease from which the human race will soon recover.
Henri Poincare
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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.
Henri Poincare
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It is far better to foresee even without certainty than not to foresee at all.
Henri Poincare