Editing Henri Poincaré (section)

===First scientific achievements===
After receiving his degree, Poincaré began teaching as junior [[lecturer]] in mathematics at the [[Caen University|University of Caen]] in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of [[automorphic function]]s.

There, in [[Caen]], he met his future wife, Louise Poulain d'Andecy (1857–1934), granddaughter of [[Isidore Geoffroy Saint-Hilaire]] and great-granddaughter of [[Étienne Geoffroy Saint-Hilaire]] and on 20 April 1881, they married.<ref>{{Cite journal |last=Rollet |first=Laurent |date=2012-11-15 |title=Jeanne Louise Poulain d'Andecy, épouse Poincaré (1857–1934) |url=https://journals.openedition.org/sabix/1131 |journal=Bulletin de la Sabix. Société des amis de la Bibliothèque et de l'Histoire de l'École polytechnique |language=Fr |issue=51 |pages=18–27 |doi=10.4000/sabix.1131 |s2cid=190028919 |issn=0989-3059}}</ref> Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).

Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the [[University of Paris]]; he accepted the invitation. During the years 1883 to 1897, he taught [[mathematical analysis]] in the [[École Polytechnique]].

In 1881–1882, Poincaré created a new branch of mathematics: [[qualitative theory of differential equations]]. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in [[celestial mechanics]] and [[mathematical physics]].