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" 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
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" Thus, they are free to replace some objects by others so long as the relations remain unchanged. "
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" 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. "
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" Need we add that mathematicians themselves are not infallible? "
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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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" What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? "
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" 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. "
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" Point set topology is a disease from which the human race will soon recover. "
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Disease
Race
Soon
" 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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Work
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" 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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" 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. "
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Go
Problems
Physics
" Mathematicians do not study objects, but relations between objects. "
Henri Poincare
Objects
Study
Mathematicians
" Mathematical discoveries, small or great are never born of spontaneous generation. "
Henri Poincare
Great
Never
Born
" It is far better to foresee even without certainty than not to foresee at all. "
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Better
Certainty
Far
" 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. "
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Beautiful
Nature
He
" Science is facts. "
Henri Poincare
Facts
Science
" It is through science that we prove, but through intuition that we discover. "
Henri Poincare
Prove
Through
Science
" No more than these machines need the mathematician know what he does. "
Henri Poincare
Machines
More
Need
" It has adopted the geometry most advantageous to the species or, in other words, the most convenient. "
Henri Poincare
Geometry
Words
Most
" Just as houses are made of stones, so is science made of facts. "
Henri Poincare
Houses
Science
Stones
" 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
" To invent is to discern, to choose. "
Henri Poincare
Discern
Choose
Invent
" A small error in the former will produce an enormous error in the latter. "
Henri Poincare
Error
Will
Produce
" In the old days when people invented a new function they had something useful in mind. "
Henri Poincare
Old Days
Days
Mind
" How is an error possible in mathematics? "
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Error
Possible
Mathematics
" 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
" Geometry is not true, it is advantageous. "
Henri Poincare
True
Geometry
" Mathematics is the art of giving the same name to different things. "
Henri Poincare
Same
Name
Mathematics
" 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
" Hypotheses are what we lack the least. "
Henri Poincare
Least
Hypotheses
Lack
" 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