Editing Henri Poincaré (section)

===Summary===
Poincaré made many contributions to different fields of pure and applied mathematics such as: [[celestial mechanics]], [[fluid mechanics]], [[optics]], [[electricity]], [[telegraphy]], [[capillarity]], [[Elasticity (physics)|elasticity]], [[thermodynamics]], [[potential theory]], [[Quantum mechanics]], [[theory of relativity]] and [[physical cosmology]].

Among the specific topics he contributed to are the following:
*[[algebraic topology]] (a field that Poincaré virtually invented)
*the theory of analytic functions of [[several complex variables]]
*[[abelian variety|the theory of abelian functions]]
*[[algebraic geometry]]
*the [[Poincaré conjecture]], proven in 2003 by [[Grigori Perelman]].
*[[Poincaré recurrence theorem]]
*[[hyperbolic geometry]]
*[[number theory]]
*the [[three-body problem]]
*the theory of [[diophantine equation]]s
*[[electromagnetism]]
*[[special relativity]]
*the [[fundamental group]]
*In the field of [[differential equations]] Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the [[Poincaré homology sphere|Poincaré sphere]] and the [[Poincaré map]].
*Poincaré on "everybody's belief" in the [[q:Henri Poincaré|''Normal Law of Errors'']] (see [[normal distribution]] for an account of that "law")
*Published an influential paper providing a novel mathematical argument in support of [[quantum mechanics]].<ref name=McCormmach>{{Citation | last = McCormmach | first = Russell | title = Henri Poincaré and the Quantum Theory | journal = Isis | volume = 58 | issue = 1 | pages = 37–55 | date =Spring 1967 | doi =10.1086/350182| s2cid = 120934561 }}</ref><ref name=Irons>{{Citation | last = Irons | first = F. E. | title = Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms | journal = American Journal of Physics | volume = 69 | issue = 8 | pages = 879–884 | date = August 2001 | doi =10.1119/1.1356056 |bibcode = 2001AmJPh..69..879I }}</ref>