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One geometry cannot be more true than another it can only be more convenient.

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
Cannot
Theorems
Geometry
Convenient
Mathematics
Another
True

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Point set topology is a disease from which the human race will soon recover.
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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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It is far better to foresee even without certainty than not to foresee at all.
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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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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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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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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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Geometry is not true, it is advantageous.
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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?
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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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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
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In the old days when people invented a new function they had something useful in mind.
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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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Mathematicians do not study objects, but the relations between objects.
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Intuition is more important to discovery than logic.
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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.
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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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. . . 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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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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