Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of mathematics. He’s often called a polymath, also in mathematics as”The Last Universalist”, because he excelled in all areas of the discipline as it existed throughout his life. As a mathematician and physicist, he made many first fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics.
In his research about the three-body difficulty, Poincaré became the very first person to find a disorderly deterministic system that laid the foundations of modern chaos theory. He is also considered to be among the founders of the field of topology.
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Author: Henri Poincare | Find on Amazon: Link |
Nationality: France | Find on Amazon India: Link |
Born: 29 April 1854, Nancy, France | |
Died: 17 July 1912, Paris, France |
Henri Poincare Quotes
The Scientist must set in order. 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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“It is by logic that we prove, but by intuition that we discover.”
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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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“To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.”
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“Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer?”
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In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.”
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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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Thought is only a flash in the middle of a long night. But this flash means everything.”
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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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“It is through science that we prove, but through intuition that we discover.”
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After the Fourier series, other series have entered the domain of analysis; they entered by the same door; they have been imagined in view of applications.”
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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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“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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Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
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Thought is only a flash between two long nights, but this flash is everything.
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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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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.
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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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Science is facts.
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Hypotheses are what we lack the least.
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It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
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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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Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.
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A small error in the former will produce an enormous error in the latter.
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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.
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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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In the old days when people invented a new function they had something useful in mind.
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Point set topology is a disease from which the human race will soon recover.
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Just as houses are made of stones, so is science made of facts.
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It is far better to foresee even without certainty than not to foresee at all.
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Geometry is not true, it is advantageous.
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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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It is through science that we prove, but through intuition that we discover.
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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.
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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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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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To invent is to discern, to choose.
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If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
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“Facts do not speak.”
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“The mind uses its faculty for creativity only when experience forces it to do so.”
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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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Henri Poincare Mathematics Quotes
“Mathematics is the art of giving the same name to different things.”
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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.
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No more than these machines need the mathematician know what he does.
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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.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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Need we add that mathematicians themselves are not infallible?
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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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How is an error possible in mathematics?
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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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Mathematics is the art of giving the same name to different things.
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Mathematicians are born, not made.
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“Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.”
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“Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.”
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“The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way.”
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“Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable.”
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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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“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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