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During his doctoral dissertation of 1879, Henri Poincare marked himself as the first person to study the general geometric functions of differential equations.
Poincare's initiative to dive into untouched territory opened the door not only for algebraic topology, but also for the clarification of the stability of the solar system. Poincare was a pioneer in the research conducted to find if the planetary orbits were regular or chaotic. -
1904 unsolved mystery of spherical topology
One off Henri Poincare's most famous accomplishments was his conjecture of an unsolved mystery of science; spherical topology. His legacy would be further carried by Grigori Perelman; a Russian mathematician who was able to successfully demonstrate this theory almost a century later. -
Chapter 12 of "Science and Hypothesis"
In 1905, Poincare released a work of literature that could've very well had changed the way empirical science was conducted. He expressed that it was necessary to have the mathematics in place before continuing forward. He said, "The purpose of mathematical theories is not to reveal the true nature of things. Such a claim would be unreasonable. Their only goal is to coordinate the physical laws that experiment reveals to us, but that we could not even state without the help of mathematics."