Editing Greg Egan (section)

===Mathematics===
In 2002, Egan co-authored two papers about Riemannian 10j symbols, [[spin network]]s appearing in Riemannian [[quantum gravity]], together with [[John C. Baez|John Baez]] and Dan Christensen. Spin networks also play a central role in his novel ''[[Schild's Ladder]]'' released the same year.

In 2014, Egan conjectured a generalization of the [[Grace–Danielsson inequality]] about the relation of the [[Radius|radii]] of two [[sphere]]s and the distance of their respective centres to fit a [[simplex]] between them to also hold in higher [[dimension]]s, which later became known as the [[Egan conjecture]]. A proof of the inequality being sufficient was published by him in 2014 under a blog post of [[John C. Baez|John Baez]]. They were lost due to a rearrangement of the website, but the central parts were copied into the original blog post. Further comments by Greg Egan on 16 April 2018 concern the search for a generalized conjecture involving [[ellipsoid]]s.<ref name=":18">{{cite web|access-date=2023-11-22|author=John Baez|date=2014-07-01|language=en|title=Grace–Danielsson Inequality|url=https://blogs.ams.org/visualinsight/2014/06/01/grace-danielsson-inequality/}}<!-- auto-translated by Module:CS1 translator --></ref> A proof of the inequality also being necessary was published by Sergei Drozdov on 16 October 2023 on [[ArXiv]].<ref name=":19">{{cite arXiv|author=Sergei Drozdov|language=en|title=Egan conjecture holds|date=2023 |class=math.MG |eprint=2310.10816 }}<!-- auto-translated by Module:CS1 translator --></ref>

In 2018, Egan described a construction of [[superpermutation]]s, thus giving an upper bound to their minimum length. On 27 February 2019, using ideas developed by Robin Houston and others, Egan produced a superpermutation of seven symbols of length 5906, breaking previous records.<ref>{{cite web |last1=Egan |first1=Greg |title=Superpermutations |url=https://www.gregegan.net/SCIENCE/Superpermutations/Superpermutations.html |access-date=2 February 2019}}</ref><ref>{{cite web |last1=Klarreich |first1=Erica |title=Mystery Math Whiz and Novelist Advance Permutation Problem |url=https://www.quantamagazine.org/sci-fi-writer-greg-egan-and-anonymous-math-whiz-advance-permutation-problem-20181105/ |website=[[Quanta Magazine]] |date=5 November 2018 |access-date=13 May 2019}}</ref>