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Automorphic Functions
Poincaré was writing his doctoral thesis when he made the discovery of automorphic functions. This was one of his first discoveries which made him widely known amongst mathematicians. Using Poincaré's definition, an automorphic function is a function where which is analytic under its domain and which is invariant under a denumerable infinite group of linear fractional transformations; they are the generalizations of trigonometric functions and elliptic functions. -
Famous Work
Henri Poincaré, "Mémoire sur les courbes définies par une équation différentielle", Journal de Mathématiques Pures et Appliquées (1881, in French) -
Qualitative Theory of Differential Equations
In 1881 Poincare found that you can find useful information from insoluble differential equations by using analysis and topology. He thought that you could solve these equations qualitatively. -
The Three Body Problem and the Effect on Chaos Theory
Poincaré went on to give a partial solution to the three body problem and won an award from the King of Sweden. Poincaré actually made a mistake in this solution. None of the judges of the competition noticed this mistake, but Poincaré did when reviewing his work. He found that little changes to the way a process begins, can make drastic changes to the way the problem ends. This became the basis of Chaos Theory. -
Topology
Topology, also known as bendy geometry, was talked about in a paper entitled Analysis situs, where Poincaré founded algebraic topology. The Poincaré Conjecture, which was a problem in topology, and was one of the greatest unsolved problems in mathematics was later solved in 2002. -
Science and Hypothesis
Book by Poincare -
Theoretical Physics
Poincaré's symmetrical presentation of the Lorentz transformations was an influential part in the formulation of Einstein’s theory of special relativity. -
The Value of Science
Book by Poincare