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" Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence. "
Henri Poincare
Earth
Mark
Space
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" The mind uses its faculty for creativity only when experience forces it to do so. "
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" Point set topology is a disease from which the human race will soon recover. "
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" To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection. "
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" Science is facts. "
Henri Poincare
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" Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. "
Henri Poincare
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" No more than these machines need the mathematician know what he does. "
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" How is an error possible in mathematics? "
Henri Poincare
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" Geometry is not true, it is advantageous. "
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" In the old days when people invented a new function they had something useful in mind. "
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Days
Mind
" The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. "
Henri Poincare
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Nature
He
" A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. "
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Fail
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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. "
Henri Poincare
Capable
Knowledge
Worthy
" If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing. "
Henri Poincare
Go
Problems
Physics
" Science is built up of 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. "
Henri Poincare
Science
Stones
Up
" A small error in the former will produce an enormous error in the latter. "
Henri Poincare
Error
Will
Produce
" It is through science that we prove, but through intuition that we discover. "
Henri Poincare
Prove
Through
Science
" It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. "
Henri Poincare
Unity
Happy
Balance
" Need we add that mathematicians themselves are not infallible? "
Henri Poincare
Infallible
Mathematicians
Need
" Mathematicians are born, not made. "
Henri Poincare
Made
Mathematicians
Born
" Mathematical discoveries, small or great are never born of spontaneous generation. "
Henri Poincare
Great
Never
Born
" Hypotheses are what we lack the least. "
Henri Poincare
Least
Hypotheses
Lack
" It has adopted the geometry most advantageous to the species or, in other words, the most convenient. "
Henri Poincare
Geometry
Words
Most
" If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment. "
Henri Poincare
Nature
Universe
Moment
" Thus, they are free to replace some objects by others so long as the relations remain unchanged. "
Henri Poincare
Replace
Long
Free
" To invent is to discern, to choose. "
Henri Poincare
Discern
Choose
Invent
" Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination. "
Henri Poincare
Rose
Pairs
Ideas
" It is far better to foresee even without certainty than not to foresee at all. "
Henri Poincare
Better
Certainty
Far
" A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations. "
Henri Poincare
Sane
Logical
Guilty
" What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? "
Henri Poincare
Elegance
Solution
Indeed
" 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
Science
Nature
Mathematics