Jules Henri Poincaré (1854–1912) was a leading French mathematician. He introduced the field of modern combinatorial topology and made lasting contributions to mathematical analysis, celestial mechanics, differential equations, electromagnetism, and the philosophy of science and mathematics.
Born in Nancy, Poincaré studied at the École Polytechnique and the École des Mines. After teaching at the University of Caen, he became a professor of mathematics in Paris in 1881.
Poincaré was extraordinary for the range of his mathematical interests and the pace of his work. He published over 500 papers and 30 books and advanced many branches of mathematics. In mathematics, he created the concept of automorphic functions, which combined new ideas in group theory, non-Euclidean geometry, and complex functions. With this, he demonstrated the significance of topology in differential equations.
Numerous concepts in modern topology, such as triangulation, homology, the Euler-Poincare formula, and the fundamental group, can be attributed to Poincaré. Besides, he delivered influential lectures on issues such as thermodynamics, optics, magnetism, and electricity. In 1906, independently of Albert Einstein, Poincaré achieved some of the results of the special theory of relativity.
In his last years, Poincaré published several articles (later collected as books) on the philosophy of science and scientific method, including La Science et I’hypothèse (1903; Science and Hypothesis) and Science et methode (1909; Science and Method, 1915.) His papers were published as Œeuvres de Henri Poincaré (11 vols., 1916–54.)
In 2006, the Russian mathematician Grigory Perelman solved the Poincaré Conjecture, a topological problem advanced by Poincaré in 1904.
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It is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it.
—Henri Poincare
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.
—Henri Poincare
Topics: Science
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.
—Henri Poincare
Topics: Science
A scientist worthy of the name, above 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
To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.
—Henri Poincare
Topics: Doubt
The task of the educator is to make the child’s spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them.
—Henri Poincare
Experience guides us in this choice without forcing it upon us; it tells us not which is the truest geometry, but which is the most convenient.
—Henri Poincare
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