I do hisdoctorate attheUniversityof Geneva, university, hewasawarded ascholarshipto athislocal After studyingmathsandphysics algebras. work Jones contributed important systems of operators known as Von Neumann towards a complete classification of particular sions. By the 1970s, Connes had made strides ofspectrum anelement’s fluorescent emis of experimental measurements, suchasthe of operators encode allthe possible results wheretum physics, thegeometric properties are central tomany areas of mathsandtoquan being thesimplerotations of 3Dspace. They with any numberof dimensions — anexample Connes, thepre-eminent expert inthefield. of operators, which led him to work with theory Switzerland. There hebecameinterested inthe the great jewelsof theunity of mathematics”. de France inParis, calledthediscovery “one of Connes, aFields Medal winner at the Collège puting. Jones’s informaldoctoral adviser, Alain emerging fieldof topologicalquantumcom ideas thatphysicists laterdeveloped intothe as theJonespolynomial,seededsomeof the of knots.Hisinvention, whichbecameknown algebras, provided apowerful toolinthestudy their discipline.Jones’s speciality, operator reveal linksbetweendistantbranches of of anearinfection. on 6September, aged 67, from complications and friend.Bornin1952, Jonesdiedsuddenly Nashville, Tennessee, along-time collaborator tician Dietmar Bisch at Vanderbilt University in humble,”same timehewasvery says mathema “He waslarger thanlifeinmany ways, butatthe jersey of New Zealand’s national rugby team. attended thesolemnceremony wearingthe maths thatstudiesknotsandothershapes.He thebranchlutionized thefieldof of topology, the Fields Medal — for an invention that revo became thefirstNewZealander tobeawarded experimenting withsmoke rings. In1990, he physicists field launchedby nineteenth-century academia. Hecared aboutthestudyof knots,a Berkeley, I almost lost my job.” Ididthisin “When the assembledacademics, Mathematician whose invention connectedknotstoquantumphysics. (1952–2020) Vaughan Jones Obituary Operators are transformations of a space Jones grew upinAuckland, NewZealand. Mathematicians treasure discoveries that Jones had little time for the stuffy halls of rings. Withamischievous grin,hetold Corsini, litacigar andbegan toblow smoke national academy inRome’s Palazzo walked on stage to address the Italian n 1994, mathematician Vaughan Jones - - - - - “Jones was a laid-back “Jones wasalaid-back of Pennsylvania inPhiladelphia,Jonescame that appearinthestudyof braids. Mathemati- satisfied. Thesewere reminiscent of formulas across some formulas that his nested algebras matic numericalratios. their relative sizes conform to precise but enig these algebras are nestedwithinoneanother, the Jonesindex theorem, showed thatwhen towards thatgoal. Oneresult, now known as apart. Inparticular,apart. itcould distinguish most poly­ realized withastonishment thatthe‘Jones was indeedthecase.Birmanrecalls how she knot’s properties. expression — apolynomial — thatencoded a Jones’s formulascould beusedtogenerate an knot. Bothresearchers began that tosuspect a braid canbe‘closed up’ endtoend,forma University inNewYork City.Sheexplained that on braids, topologistJoan BirmanatColumbia other. Intrigued, Jones talked to the authority linestwistedaroundsisting of each curved cians studybraids asgeometric con objects, mathematicians.” even personality by the standards of by thestandards of In 1984, whileworkingattheUniversity A weeklater, Jonesshowed Birmanthatthis ©

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A l l r i g h t s r e s e r v e d . - - to otherfields.Heintroduced anewtech Neumann algebras andtheirconnections as a feature of the quantum physics of a uni showed that the polynomial can be interpreted for Advanced StudyinPrinceton, NewJersey, retical physicist Edward WittenattheInstitute aged properties of large numbersof particles. thestudyofwith statisticalmechanics, aver and physics. Jones investigated connections plethora of betweenknottheory connections smoke-ring pioneer. Researchers alsofounda by Peternineteenth century GuthrieTait — the some of whichhadbeenformulatedinthelate ments helped to solve long-standing problems, the poly­ decades. Soon, of toolthattopologistshadbeenseekingfor knots from theirmirror images. Itwasthekind sciences reportersciences at Davide Castelvecchi is a senior physical- south, runningasummerschool. he spent the first months year of down every inhisnativeNewZealand,mathematics and join BischatVanderbilt. Hewas keen tofoster Berkeley, where hehadtaught since 1985, to ing. In2011, heleft theUniversityof California, where participants could alsogo skiingorhik quently organized smallconferences inplaces an avid windsurferandkitesurfer, andfre Loyola University in Chicago, Illinois. He was his former doctoral student Emily Peters at Hemisphere scorn forsocialhierarchies,” says fident inhisown powers andhadaSouthern the standards of mathematicians. “Hewas con wise elusivemathematicalrelationships. enabled Jonesandotherstodiscover other 2D graphical arrangement. Thisplanaralgebra algebra — symbolsarranged linearly — witha nique, replacing theexpressions of ordinary calculating Jonespolynomials. could runquantum algorithms essentiallyby for building future quantum computers. They phases’ are now seenas apossible platform space-time. Anyons and similar ‘topological around eachother, asifthey formedbraids in Anyons can‘remember’ how they have moved quantum statescalledanyons.form collective ultracoldone layer incertain devices, they can 2D universes.Whenelectrons are confined to then foundapossible applicationforWitten’s two dimensions of space. Other theoreticians verse withsimplifiedlaws of nature andjust The most surprisinglinkcamein1989. Theo Jones was a laid-back personality even by Jones’s mainfocus continued tobeVon Nature |Vol 586 |8 October 2020 |195 Nature. nomial and itsrefine ------

GEORGE M. BERGMAN/MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH