DITH PRAN/NYT/REDUX/EYEVINE J professor of at Princeton mathematics other diversions,someof hisown creation. in New Jersey playing backgammon, and Go Cambridge, UK,andPrinceton University in the common rooms of the University of lover of games of allkinds.Hespenthours complications related toCOVID-19, wasa his livingplaying cards, andlater worked as a born inLiverpool, UK,in1937. Hisfathermade University before his retirement in2013, was ning Conway’s Gameof Lifeastheirscreensaver. of the world’sone-quarter computers were run Gardner. Bythe mid-1970s, it wasestimated that Scientific American by 1970 accessibility of this game was popularized in its nearest neighbours.Thesimplicity and and ‘death’ of each cell, based on the status of evolves according toasetof rulesforthe‘birth’ gridlive ordeadcells inatwo-dimensional a cellular automaton in which the pattern of also ledConway todevelop theGameof Life, and Richard Guy.Thisfascinationwithgames of games, writtenwithElwyn Berlekamp theory (1982), a compendium of information on the Winning Ways foryourMathematicalPlays from the influentialresearch project andbook of newnumbersinbetween. ones, andallsorts infinitely large numbers, infinitesimally small real numbersthatweallknow, butalsonew It contained not onlythepositive andnegative community.which stunned the mathematics a truly gigantic system, the surreal numbers, between numbersandgames thatledhimto est discovery wasasurprisingcorrespondence games andtheirstrategies. Perhaps hisgreat- tions were madewhilehewasthinkingabout Several of Conway’s most celebrated contribu captured thepublic’s imagination. knots, rainbows, tilings, free will and more His lectures aboutnumbers,games, magic, among mathematiciansandamateursalike. attention andapopicon everywhere hewent, all whowouldlistenmadehimthecentre of withany and ability totalkaboutmathematics personality, quirky senseof humourand deep yetaccessible work,larger-than-life algebra and combinatorial His game theory. Playful masterof games whotransformed mathematics. (1937–2020) ConwayJohn Horton Obituary Conway, whowastheJohnvon Neumann Conway’s work on surreal numbers emerged Conway, whodiedatthe age of 82 from topology, number theory, geometry, numbertheory, topology, analysis,tributions togroup theory, whomadeinfluentialcon past century, most versatilemathematiciansof the Conwayohn Horton wasoneof the columnist Martin columnist Martin - - - “His lectures about numbers, aboutnumbers, lectures “His symmetries of theLeech lattice —aremark determining all8,315,553,613,086,720,000 he moved toPrinceton. turer, andbecameprofessor in1983. In1987, was subsequentlyhired atCambridge asalec- under theadvisership of Harold Davenport, PhD from theUniversityof Cambridge in1964 mathematician at Cambridge. He received his byematics; the age of 11, he wanted to be a avid reader. He showed early interests in math Conway,McCartney. like his mother, was an school attendedby George HarrisonandPaul technician laboratory at a local high chemistry with hisATLAS knowledge of symmetriesledhim topropose, ATLAS FiniteGroups of (1985). His deep book and assemblingtheiconic symmetry mathematics. of twentieth-century groups —oneof thecapstoneachievements mental in the classification of finite simple Conway simplegroups, whichwere funda Leech in1967. Thisledtohisdiscovery of the 24-dimensional space discovered by John ably regular arrangement of points in games, magic, knots, games, magic,knots, the public’s imagination.” rainbows andmore captured Conway had a primary roleConway inresearching had aprimary Conway firstattainedfamein1968 for ©

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A l l r i g h t s r e s e r v e d . - - - philosophy. Hiscontributions toculture, and etymology games, aswell history, speaker, andthemany tricksheperformed with hislong-time collaborator NeilSloane. system ofimportant numbers, the icosians, tilings asdeveloped by Roger Penrose. tilings, includingproperties of quasi-periodic tries, sphere packings, lattices, polyhedra and made key discoveries in the study of symme topic of research Ingeometry,he intopology. Conway polynomial became an important — usedtotelldifferent —calledthe knotsapart algebra, analysis, physicsandbeyond. wave suchdiscoveries of further connecting —inspiringa of blackholesinstringtheory —includingintheunderstandingin physics the Moonshineconjectures play akey part crete mathstonon-discrete maths.Today, groups toanalysis—andthusdis symmetry for thefirsttime,seriouslyconnected finite Monstrous Moonshineconjectures. These, e-mail: [email protected] H. Conway at Princeton. graduate advisee, and later colleague, of John University, New Jersey, USA. He was a first-year professor of mathematics at Princeton Manjul Bhargava is the R. Brandon Fradd with others—hewillbesorely missed. and generous way in which he shared these his mathematicaldiscoveries —andtheplayful ing impact. For theremarkable profundity of through hisworkandoutreach, willhave alast- one syllable. tures word inwhichevery hesaidhadonly onhischin,anddeliveringentireobjects lec his tongue into a variety of shapes, balancing penny balanced onitsinsideedge, contorting twirlingahangerany witha dateinhistory, stating immediatelytheday of theweekfor to illustrate mathematicalconcepts included: bers (forexample, 21isthesumof 16, 4, 1and0). whole numberisthesumof foursquare num Louis Lagrange, positive whichstatesthatevery mathematicianJoseph- by eighteenth-century izations of thefour-squares theorem, proved the 290-conjecture; thesewere vastgeneral (with his studentWilliamSchneeberger) and powers. He also developed the 15-theorem whole numberisthesumof atmost 37 fifth Conway showed In numbertheory, that every He loved and totalkaboutmathematics Conway wasamemorable teacherand In algebra, Conway discovered another Conway’s discovery of anewknotinvariant Nature |Vol 582 |4 June 2020 |27 - - - - -