Editing John Horton Conway (section)

===Group theory===
He was the primary author of the ''[[ATLAS of Finite Groups]]'' giving properties of many [[finite simple group]]s. Working with his colleagues Robert Curtis and [[Simon P. Norton]] he constructed the first concrete representations of some of the [[sporadic group]]s. More specifically, he discovered three sporadic groups based on the symmetry of the [[Leech lattice]], which have been designated the [[Conway groups]].<ref>{{cite journal |last=Harris |first=Michael |author-link=Michael Harris (mathematician) |date=2015 |title=Mathematics: The mercurial mathematician |journal=Nature |volume=523 |pages=406–7 |doi=10.1038/523406a |others=Review of ''Genius At Play: The Curious Mind of John Horton Conway''
|issue=7561 |bibcode=2015Natur.523..406H |doi-access=free }}</ref> This work made him a key player in the successful [[classification of the finite simple groups]].

Based on a 1978 observation by mathematician [[John McKay (mathematician)|John McKay]], Conway and Norton formulated the complex of conjectures known as [[monstrous moonshine]]. This subject, named by Conway, relates the [[monster group]] with [[elliptic modular function]]s, thus bridging two previously distinct areas of mathematics—[[finite group]]s and [[complex function theory]]. Monstrous moonshine theory has now been revealed to also have deep connections to [[string theory]].<ref>{{Cite web |last=Darling |first=David |title=Monstrous Moonshine conjecture |url=https://www.daviddarling.info/encyclopedia/M/Monstrous_Moonshine_conjecture.html |access-date=2024-11-05 |website=www.daviddarling.info}}</ref>

Conway introduced the [[Mathieu groupoid]], an extension of the [[Mathieu group M12|Mathieu group M<sub>12</sub>]] to 13 points.