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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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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
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Henri Poincare
Jules Henri Poincare
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More quotes by Henri Poincare
Mathematics is the art of giving the same name to different things.
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
Thought is only a flash between two long nights, but this flash is everything.
Henri Poincare
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
Henri Poincare
Intuition is more important to discovery than logic.
Henri Poincare
In the old days when people invented a new function they had something useful in mind.
Henri Poincare
How is error possible in mathematics?
Henri Poincare
Every good mathematician should also be a good chess player and vice versa.
Henri Poincare
In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.
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
Mathematicians do not deal in objects, but in relations between objects thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.
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
. . . 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.
Henri Poincare
Point set topology is a disease from which the human race will soon recover.
Henri Poincare
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
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
Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
Henri Poincare
Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
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
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
