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If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

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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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
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Analyse data just so far as to obtain simplicity and no further.
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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.
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It is far better to foresee even without certainty than not to foresee at all.
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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.
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All of mathematics is a tale about groups.
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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.
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Thought is only a flash between two long nights, but this flash is everything.
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But for harmony beautiful to contemplate, science would not be worth following.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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
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It is the simple hypotheses of which one must be most wary because these are the ones that have the most chances of passing unnoticed.
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How is error possible in mathematics?
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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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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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For a long time the objects that mathematicians dealt with were mostly ill-defined one believed one knew them, but one represented them with the senses and imagination but one had but a rough picture and not a precise idea on which reasoning could take hold.
Henri Poincare
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Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.
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.
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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
Henri Poincare
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Mathematics is the art of giving the same name to different things.
Henri Poincare