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Born
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Poincaré’s Analysis Situs (1895)
He is often called the father of algebraic topology due to a mathematics paper he published in 1895 named Analysis Situs. This helped lead to the Poincaré Conjecture as well as his Philosophy of Mathematics and Science. -
Published his book Science and Hypothesis (La Science et L’hypothese) in 1902
Poincaré argued that scientific theories come from experience, but are neither verifiable nor falsifiable based on the experience alone. Imagine plotting points on a graph and then connecting those points with a curved line. Which curve is chosen is based on both experience and desired smoothness. This curve is not an exact replication of the experience because it corrects itself and does not falsify the law. A scientific theory is not directly falsifiable by the experience. -
Science and Hypothesis Cont.
Poincaré said each theory has its own language that is chosen based on which best fits the situation. He argued for a conventionalist view of mathematics. He said the aim of science is prediction, but to make predictions, science must use generalizations that go beyond experience. Poincaré’s view of scientific theories is that even if a theory is proven wrong, it's still useful to scientists because it gives the possibility to see something we would not have seen if the theory had not failed. -
Euclidean or non-Euclidean Geometry
Poincare argued that the reason we chose Euclidean geometry in regards to explaining space was due to it being the easiest for us to use. Imagine, however, beings that are infinitely flat and turned into a spherical shape, they will not doubt create a geometry much different than Euclidean, and will choose that geometry because it is the easiest to them, as Poincare explains in "Science and Hypothesis". -
Period: to
Published numerous papers
Published La Science et l’hypothèse (1903; Science and Hypothesis), La Valeur de la science (1905; The Value of Science), and Science et méthode (1908; Science and Method). These helped distinguish him as a philosopher of science and mathematics. -
Poincaré Conjecture
Perhaps his most famous contribution to science was the Poincare Conjecture, which took over a century for someone to solve. Is it possible to determine the shape of the universe without stepping outside of it.
https://www.youtube.com/watch?v=GItmC9lxeco -
Death
