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Publishes First Paper
In 1874, Poincaré published his first paper, Démonstration nouvelle des propriétés de l'indicatrice d'une surface (1884), meaning 'new indicator of the properties of a surface'. Already we see his work on a field within mathematics that will make him famous today. Poincaré. "Démonstration nouvelle des propriétés de l'indicatrice d'une surface." Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale 13 (1874): 449-456. http://eudml.org/doc/98873. -
Graduates from University of Paris
In 1879 he wrote his doctoral dissertation, describing new ways of analyzing the properties of functions defined by differential equations. He specifically studied their geometric properties and applied this thinking to the motion of multiple free bodies in the solar system. With this achievement, he earned his Doctorate of Science in Mathematics. -
Beginning Two Careers
In 1881 he began working as an engineer for the Ministry of Public Services, and was given responsibility for railway development. He also began his lifelong teaching career at the University of Paris (the Sorbonne). -
Science and Hypothesis
In this major work of the philosophy of science, he described his philosophical understanding of mathematics as a synthetic science, yet also an a priori one. He describes math as heavily intuitive rather than rigidly logical.
He further ruminates in this book on how his mind functions while thinking, and describes a process where random combinations are generated in his subconscious, that he then consciously selects and validates. Poincaré, Henri. Science and Hypothesis. Science Press, 1905. -
Conjecture
Poincare formulated a conjecture that wasn't solved until 1904 by Grigori Perlman. In its standard form, the conjecture is, "Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere." This was famous for the fact that it was the first major conjecture in the field of topology.
For an attempt at explaining this to the layman, see https://www.youtube.com/watch?v=GItmC9lxeco. Poincaré, H. "Cinquième complément à l'analysis situs." Rend. Circ. Mat. Palermo 18, 45-110, 1904. -
Predicts Gravitational Waves
At least as early as 1905, Poincare predicted the existence of gravitational waves, a concept that was experimentally verified over a century later. His idea was a generalization of the concept that the speed of light is the maximum speed of any physical object or force, and so the force of gravity must propagate in a wave travelling the speed of light.
Poincare, Henri. “On Electron Dynamics.” Académie Des Sciences, 5 June 1905.
