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Les Méthodes nouvelles de la mécanique céleste (The New Methods of Celestial Mechanics)
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Analysis Situs
This mathematical paper, along with its author, became known as the father of algebraic topology. Poincare produced five subsequent supplements to the original paper, including the famous Poincare Conjecture in the fifth.
Here is a link a video about the Poincare Conjecture (one of the things Poincare "knew was right" but did not prove). https://www.youtube.com/watch?v=GItmC9lxeco -
La Valeur de la science (The Value of Science)
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Science et méthode (Science and Method)
In this book Poincare offers another philosophical view of the scientific method. The book is mostly a normative description of science in which Poincare deals with such concepts as the selection of facts and the relativity of space. He compares Euclidean and non-Euclidean geometry, and he says when faced with the choice "we have chosen the most convenient space" or rather history has shown our infatuation with Euclidean geometry (Poincare 115).