Editing Émile Picard (section)

==Life==

He was born in [[Paris]] on 24 July 1856 and educated there at the [[Lycée Henri-IV]]. He then studied mathematics at the [[École normale supérieure (Paris)|École Normale Supérieure]].<ref>{{cite book|title=Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002|date=July 2006|publisher=The Royal Society of Edinburgh|isbn=0-902-198-84-X| url=https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf |archive-date=2022-10-09 |url-status=live}}</ref>

Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. [[Picard's little theorem]] states that every nonconstant [[entire function]] takes every value in the [[complex plane]], with perhaps one exception. [[Picard's great theorem]] states that an [[analytic function]] with an [[essential singularity]] takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He made important contributions in the theory of [[differential equation]]s, including work on [[Picard–Vessiot theory]], [[Painlevé transcendents]] and his introduction of a kind of [[symmetry group]] for a [[linear differential equation]]. He also introduced the [[Picard group]] in the theory of [[algebraic surface]]s, which describes the classes of [[algebraic curve]]s on the surface modulo linear equivalence. In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of [[algebraic topology]]. In addition to his theoretical work, Picard made contributions to [[applied mathematics]], including the theories of [[telegraphy]] and [[Elasticity (physics)|elasticity]]. His collected papers run to four volumes.

[[Louis Couturat]] studied [[integral calculus]] with Picard in 1891-1892, taking detailed notes of the lectures. These notes were preserved and now are available in three cahiers from [[Internet Archive]].<ref>[[Louis Couturat]] notes (1891,2) [https://archive.org/details/ENS01_Ms0124_01/page/n1 Cours de Calcul Integral par M. Picard, cahier 1], [https://archive.org/details/ENS01_Ms0124_02/page/n2 cahier 2], [https://archive.org/details/ENS01_Ms0124_03/page/n2 cahier 3]</ref>

Like his contemporary, [[Henri Poincaré]], Picard was much concerned with the training of mathematics, physics, and engineering students.
He wrote a classic textbook on [[Mathematical analysis|analysis]] and one of the first textbooks on the [[theory of relativity]]. Picard's popular writings include biographies of many leading French mathematicians, including his father in law, [[Charles Hermite]].

Picard was an International Honorary Member of the [[American Academy of Arts and Sciences]],<ref>{{Cite web |date=2023-02-09 |title=Charles Emile Picard |url=https://www.amacad.org/person/charles-emile-picard |access-date=2023-12-07 |website=American Academy of Arts & Sciences |language=en}}</ref> an International Member of the United States [[National Academy of Sciences]],<ref>{{Cite web |title=Emile Picard |url=https://www.nasonline.org/member-directory/deceased-members/20001877.html |access-date=2023-12-07 |website=www.nasonline.org}}</ref> and an International Member of the [[American Philosophical Society]].<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=C.+Emile+Picard&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2023-12-07 |website=search.amphilsoc.org}}</ref>