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Henri Poincare Inspirational Quotes (65)

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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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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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Every good mathematician should also be a good chess player and vice versa.
Henri Poincare
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It is far better to foresee even without certainty than not to foresee at all.
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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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
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Pure logic could never lead us to anything but tautologies it can create nothing new not from it alone can any science issue.
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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...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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A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
Henri Poincare
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The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
Henri Poincare
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Mathematicians do not study objects, but the relations between objects.
Henri Poincare
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Mathematicians are born, not made.
Henri Poincare
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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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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I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.
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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In the old days when people invented a new function they had something useful in mind.
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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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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