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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

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
Ones
Initial
Differences
Initials
Happen
Phenomena
Small
Final
Science
Finals
Happens
Chaos
May
Produce
Great
Conditions
Fortuitous

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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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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.
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But for harmony beautiful to contemplate, science would not be worth following.
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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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Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
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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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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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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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If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.
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How is error possible in mathematics?
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
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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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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
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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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One geometry cannot be more true than another it can only be more convenient.
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Mathematicians do not study objects, but the relations between objects.
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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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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
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