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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
Knew
Mostly
Mathematicians
Imagination
Believed
Dealt
Idea
Defined
Represented
Science
Senses
Mathematician
Ideas
Mathematics
Precise
Take
Picture
Reasoning
Long
Objects
Rough
Time
Hold
Ill

More quotes by Henri Poincare

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Mathematical discoveries, small or great are never born of spontaneous generation.
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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.
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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.
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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
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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.
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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.
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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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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.
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. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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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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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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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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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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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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But for harmony beautiful to contemplate, science would not be worth following.
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The mind uses its faculty for creativity only when experience forces it to do so.
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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.
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