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Developed Qualitative Theory of Differential Equations
Based largely upon his work for his doctoral thesis, Poincare publishes his "Mémoire sur les courbes définiés par une équation différentielle" (Memoirs on the curves defined by a differential equation), on differential equations. Poincare demonstrates how to qualitatively define many unsolvable differential equations, thus producing the new field of mathematics. -
The Poincare Conjecture
Henri Poincare presents the "Poincare Homology Sphere", a counterexample to his own contributions in the field of Homology (a form of Algebraic Topology). This conjecture was so seemingly impossible to prove that it became one of the seven "Millenium Problems". As of 2019, it is the only Millenium Problem to have been solved, having been proved in 2003 by Grigori Perelman.
Poincare Conjecture -
Discovers relationships between energy and mass
In a lecture delivered in St. Louis, Poincare discussed his discovery, from around four years prior, that the force of an electromagnetic field expressed the same characteristics matter for a gravitational field. He showed an electromagnetic field could be described as a liquid with a density of M=E/C2, just like real matter. Though he recognized a paradox that his equations would allow perpetual motion, Einstein's work on equivalence solved this paradox. (The Foundations of Science, 1913) -
First Proposed Gravitational Waves
Although the prediction of gravitational waves is generally attributed to Albert Einstein, Poincare proposed this more than 11 years earlier that, as a general rule of "space-time geometry", gravity must travel in waves propagating at light-speed. This was published in his academic "Sur la dynamique de l'électron" (On Electron Dynamics), in the French publication "Académie des Sciences". -
Poincare's last non-posthumous nomination
By his death, Poincare had received 51 nominations for the Nobel Prize in Physics since 1904,with 34 of them in 1910 alone (of 58 total that year). Many of these came from well known scientists including Marie Curie and Hendrik Lorentz. These individuals pointed out the bias of the committee that prefers experimentation of theorization, though Poincare singlehandedly contributed to almost every field of math and science in his lifetime. (Gray, Jeremy (2013). "The Campaign for Poincaré")
