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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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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
Engineer
Mathematician
Philosopher
Philosopher Of Science
Physicist
Researcher
Topologist
University Teacher
Le Cateau
Jules Henri Poincaré
Poincaré
Henri Poincare
Jules Henri Poincare
Poincare
Imagination
Believed
Dealt
Idea
Defined
Represented
Science
Senses
Mathematician
Ideas
Mathematics
Precise
Take
Picture
Reasoning
Long
Objects
Rough
Time
Hold
Ill
Knew
Mostly
Mathematicians

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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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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Geometry is the art of correct reasoning from incorrectly drawn figures.
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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.
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Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.
Henri Poincare
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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.
Henri Poincare
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Mathematicians do not study objects, but the relations between objects.
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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...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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Geometry is not true, it is advantageous.
Henri Poincare
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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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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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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Les faits ne parlent pas. Facts do not speak.
Henri Poincare
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When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
Henri Poincare
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
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.
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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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Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
Henri Poincare