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" 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
Related Quotes:
" If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws. "
Henri Poincare
Predict
Same
Laws
" 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
" 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
Artist
Work
Same
" 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
" It has adopted the geometry most advantageous to the species or, in other words, the most convenient. "
Henri Poincare
Geometry
Words
Most
" A small error in the former will produce an enormous error in the latter. "
Henri Poincare
Error
Will
Produce
" 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
" Science is facts. "
Henri Poincare
Facts
Science
" 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
" 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
" 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
" Thought is only a flash between two long nights, but this flash is everything. "
Henri Poincare
Long
Only
Thought
" It is through science that we prove, but through intuition that we discover. "
Henri Poincare
Prove
Through
Science
" 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
" Thus, they are free to replace some objects by others so long as the relations remain unchanged. "
Henri Poincare
Replace
Long
Free
" How is an error possible in mathematics? "
Henri Poincare
Error
Possible
Mathematics
" Point set topology is a disease from which the human race will soon recover. "
Henri Poincare
Disease
Race
Soon
" Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. "
Henri Poincare
Useless
Minority
Infinite
" Facts do not speak. "
Henri Poincare
Facts
Speak
" 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
Worth
Life
Beautiful
" Mathematicians are born, not made. "
Henri Poincare
Made
Mathematicians
Born
" Mathematicians do not study objects, but relations between objects. "
Henri Poincare
Objects
Study
Mathematicians
" Hypotheses are what we lack the least. "
Henri Poincare
Least
Hypotheses
Lack
" In the old days when people invented a new function they had something useful in mind. "
Henri Poincare
Old Days
Days
Mind
" Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination. "
Henri Poincare
Rose
Pairs
Ideas
" No more than these machines need the mathematician know what he does. "
Henri Poincare
Machines
More
Need
" To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection. "
Henri Poincare
Reflection
Believe
Doubt
" It is far better to foresee even without certainty than not to foresee at all. "
Henri Poincare
Better
Certainty
Far
" Need we add that mathematicians themselves are not infallible? "
Henri Poincare
Infallible
Mathematicians
Need
" Mathematics is the art of giving the same name to different things. "
Henri Poincare
Same
Name
Mathematics