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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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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
Interested
Replace
Objects
Mathematician
Deal
Irrelevant
Deals
Relations
Free
Content
Others
Thus
Form
Relation
Unchanged
Long
Remain
Mathematicians

More quotes by Henri Poincare

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It is far better to foresee even without certainty than not to foresee at all.
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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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Analyse data just so far as to obtain simplicity and no further.
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How is error possible in mathematics?
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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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Mathematicians are born, not made.
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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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Mathematics is the art of giving the same name to different things.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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.
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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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. . . 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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One geometry cannot be more true than another it can only be more convenient.
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Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
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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.
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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.
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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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All of mathematics is a tale about groups.
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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