Henri Poincare (29 April 1854 - 17 Jul 1912) was a French mathematician and philosopher, who made vast contributions in the area in applied and pure mathematics, and in the area of Philosophy of Science. He is best known for the Poincare Conjecture
By john.hauk37
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Dissertation on functions and celestial mechanics leads to the rise of algebraic topology https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9
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Poincare is made Chair of Mathematical Physics at the University of Paris https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9
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Publishes Analysis situs, the early systematic treatment of topology. https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9
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Poincare publishes a three volume work entitled " Les Methods nouvelle de la mechanique celeste" where he tries to describe all the motions of the solar system http://www.resonancepub.com/mathematics.htm
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Poincare was known for his conventionalist philosophy. Overall philosophy of math was that intuition provides a foundation for all mathematics. Poincare wanted conventionalism for the sciences, and made arguments for Continuity and Indefinitite Repetition. https://www.iep.utm.edu/poi-math/#H3
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Publishes Science and Hypothesis; argues that absolute truth in science is unattainable, focuses on priority than apriority. Argues that the continuum is mathematics, rather than it is given by a priori intuition. https://en.wikipedia.org/wiki/Science_and_Hypothesis
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Publishes The Value of Science; starts to move towards the apriorist view, discusses "primitvely amorphous" continuum. https://en.wikipedia.org/wiki/The_Value_of_Science (https://www.youtube.com/watch?v=28NXF1MyEgg)
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Science and Method; Poincare"s last publication, defines the basic methodology and psychology of scientific discovery
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" The true method of foreseeing the future of Mathematics is to study its history and its actual state" Henri Poincare
https://www.youtube.com/watch?v=DCMb9o8URdQ