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Henri Poincaré
Jules Henri Poincaré, (born in Nancy, France and died Paris). He's a French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics. Reference:
Gray, J. John (2022, April 25). Henri Poincaré. Encyclopedia Britannica. https://www.britannica.com/biography/Henri-Poincare -
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Henri Poincare
began work on curves defined by a particular type of differential equation, in which he was the first to consider the global nature of the solution curves and their possible singular points (points where the differential equation is not properly defined). Do the solutions spiral into or away from a point? Reference:
Gray, J. John (2022, April 25). Henri Poincaré. Encyclopedia Britannica. https://www.britannica.com/biography/Henri-Poincare -
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Space
Require showing that equations of motion for the planets could be solved & the orbits of the planets shown to be curves that stay in a bounded region of space for all time. Soon realized couldn't make any headway unless he concentrated on a simpler, in which 2 massive bodies orbit 1 another in circles around their common centre of gravity while a minute 3rd body orbits. Gray, J. John (2022, April 25). Henri Poincaré. Encyclopedia Britannica. https://www.britannica.com/biography/Henri-Poincare -
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Henri Poincare
Poincaré intended this preliminary work to lead to the study of the more complicated differential equations that describe the motion of the solar system. In 1885 an added inducement to take the next step presented itself when King Oscar II of Sweden offered a prize for anyone who could establish the stability of the solar system. Reference:
Gray, J. John (2022, April 25). Henri Poincaré. Encyclopedia Britannica. https://www.britannica.com/biography/Henri-Poincare -
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Henri Poincare
Poincaré took up the task and looked for ways in which such manifolds could be distinguished, thus opening up the whole subject of topology, then known as analysis situs. Riemann had shown that in two dimensions surfaces can be distinguished by their genus (the number of holes in the surface), and Enrico Betti in Italy and Walther von Dyck in Germany had extended this work to three dimensions, but much remained to be done.