Editing Racks and quandles (section)

==History==
In 1942, {{ill|Mituhisa Takasaki|ja|高崎光久}} introduced an algebraic structure which he called a {{Transliteration|ja|kei}} ({{wikt-lang|ja|圭}}),<ref name="takasaki">{{cite journal|first=Mituhisa |last=Takasaki| title=Abstractions of symmetric functions|year=1943|journal=[[Tohoku Mathematical Journal]]|volume=49|pages=143&ndash;207}}</ref><ref name="elhamdadi">{{citation|last=Elhamdadi|first=Mohamed|year=2020|title=A Survey of Racks and Quandles: Some Recent Developments|doi=10.1142/S1005386720000425|arxiv=1910.07400}}</ref> which would later come to be known as an involutive quandle.<ref name="kamada">{{citation|last=Kamada|first=Seiichi|title=Knot invariants derived from quandles and racks|year=2002|volume=4|pages=103–117|doi=10.2140/gtm.2002.4.103|journal=Geometry & Topology Monographs|arxiv=math/0211096}}</ref> His motivation was to find a nonassociative algebraic structure to capture the notion of a [[reflection (mathematics)|reflection]] in the context of [[finite geometry]].<ref name="elhamdadi" /><ref name="kamada" /> The idea was rediscovered and generalized in an unpublished 1959 correspondence between [[John Horton Conway|John Conway]] and [[Gavin Wraith]], who at the time were undergraduate students at the [[University of Cambridge]]. It is here that the modern definitions of quandles and of racks first appear. Wraith had become interested in these structures (which he initially dubbed '''sequentials''') while at school.<ref name="wraith">{{cite web|first=Gavin|last=Wraith|title=A Personal Story about Knots|url=http://www.wra1th.plus.com/gcw/rants/math/Rack.html|url-status=dead|archiveurl=https://web.archive.org/web/20060313115547/http://www.wra1th.plus.com/gcw/rants/math/Rack.html|archivedate=2006-03-13}}</ref>  Conway renamed them '''wracks''', partly as a pun on his colleague's name, and partly because they arise as the remnants (or 'wrack and ruin') of a [[group (mathematics)|group]] when one discards the multiplicative structure and considers only the [[inner automorphism|conjugation]] structure.  The spelling 'rack' has now become prevalent.

These constructs surfaced again in the 1980s:  in a 1982 paper by [[David E. Joyce (mathematician)|David Joyce]]<ref name="joyce">{{cite journal|first=David|last=Joyce|title=''A classifying invariant of knots: the knot quandle''|journal=[[Journal of Pure and Applied Algebra]]|volume=23|year=1982|pages=37&ndash;65|doi=10.1016/0022-4049(82)90077-9|doi-access=free}}</ref> (where the term '''quandle''', an arbitrary nonsense word, was coined),<ref>{{cite web|last1=Baez|first1=John|title=The Origin of the word 'Quandle'|url=https://golem.ph.utexas.edu/category/2015/05/the_origin_of_the_word_quandle.html|website=The n-Category Cafe|accessdate=5 June 2015}}</ref> in a 1982 paper by [[:ru:Сергей Матвеев|Sergei Matveev]] (under the name '''[[distributive property|distributive]] [[groupoids]]''')<ref name="matveev">{{cite journal|first=Sergei|last=Matveev|title=''Distributive groupoids in knot theory''|journal=[[Math. USSR Sbornik]]|volume=47|year=1984|issue=1 |pages=73&ndash;83|doi=10.1070/SM1984v047n01ABEH002630|bibcode=1984SbMat..47...73M }}</ref> and in a 1986 conference paper by [[Egbert Brieskorn]] (where they were called '''[[automorphism|automorphic]] [[set(mathematics)|sets]]''').<ref name="brieskorn">{{cite book|first=Egbert|last=Brieskorn|title=Braids |chapter=Automorphic sets and braids and singularities |series=Contemporary Mathematics |volume=78|year=1988|pages=45&ndash;115|doi=10.1090/conm/078/975077|isbn=9780821850886 }}</ref>  A detailed overview of racks and their applications in knot theory may be found in the paper by [[Colin Rourke]] and [[Roger Fenn]].<ref name="fr">{{cite journal|first2=Roger|last2=Fenn|first1=Colin|last1=Rourke|journal=[[Journal of Knot Theory and Its Ramifications]]|title=''Racks and links in codimension 2''|volume=1|year=1992|pages=343&ndash;406|doi=10.1142/S0218216592000203|issue=4}}</ref>