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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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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
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Mathematician
Philosopher
Philosopher Of Science
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Jules Henri Poincaré
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Henri Poincare
Jules Henri Poincare
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More quotes by Henri Poincare
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
One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.
Henri Poincare
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
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
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
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
Mathematicians do not study objects, but the relations between objects.
Henri Poincare
...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
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
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
Henri Poincare
It is through science that we prove, but through intuition that we discover.
Henri Poincare
Geometry is the art of correct reasoning from incorrectly drawn figures.
Henri Poincare
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
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
Mathematics is the art of giving the same name to different things.
Henri Poincare
Just as houses are made of stones, so is science made of facts.
Henri Poincare
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
Intuition is more important to discovery than logic.
Henri Poincare
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
Henri Poincare
Geometry is not true, it is advantageous.
Henri Poincare
