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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.

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
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Mathematicians
Study
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Interest
Indifferent
Others
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Form
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Change
Relation
Pedagogy
Matter
Objects
Replacement
Important
Among
Replacements

More quotes by Henri Poincare

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It is through science that we prove, but through intuition that we discover.
Henri Poincare
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It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry the founders are hampered in their general grasp by third and fourth decimal places.
Henri Poincare
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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.
Henri Poincare
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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
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Analyse data just so far as to obtain simplicity and no further.
Henri Poincare
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If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living
Henri Poincare
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How is error possible in mathematics?
Henri Poincare
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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.
Henri Poincare
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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 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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A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
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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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.
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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
Henri Poincare
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Geometry is the art of correct reasoning from incorrectly drawn figures.
Henri Poincare
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Thought is only a flash between two long nights, but this flash is everything.
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation.
Henri Poincare
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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
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Intuition is more important to discovery than logic.
Henri Poincare