Celebratio Mathematica

Vaughan F. R. Jones

Professor Sir John Meurig Thomas
presenting Professor Vaughan F. R. Jones
for admission to the honorary degree of Doctor of Science

by John Meurig Thomas

Jones (right) is shown here in a 2017 photo with Sir John Meurig Thomas (left) and David Evans (center). They are standing before the portrait of physicist Peter Guthrie Tait (1831–1901) that hangs at Peterhouse, Cambridge.
Photo: Martha Jones.

In 1926, an eld­erly wid­ow named Mary But­ler, moth­er of el­ev­en chil­dren, liv­ing in Gwendraeth Val­ley bade farewell to two of her daugh­ters. One left for Canada; the oth­er, Bessie, took her son Jimmy and his broth­er and sis­ter to join their fath­er Fred­die Jones, who had left Burry Port a few years earli­er to seek a bet­ter life in New Zea­l­and. Mary But­ler nev­er saw her daugh­ters again. The forty year old grand­son of Bessie and Fred­die Jones stands be­fore you today, a former un­der­gradu­ate and now hon­or­ary gradu­ate of the Uni­versity of Auck­land, Pro­fess­or of Math­em­at­ics at the Uni­versity of Cali­for­nia at Berke­ley since 1985, the first re­cip­i­ent of the Ruther­ford Gold Medal awar­ded by the New Zea­l­and Gov­ern­ment, Fel­low of the Roy­al So­ci­ety, Hon­or­ary Fel­low of the Amer­ic­an Academy of Arts and Sci­ences and, most sig­ni­fic­ant of all, win­ner in 1990 of the Fields Medal, awar­ded every four years, the math­em­at­ic­al equi­val­ent of the No­bel Prize — an in­tel­lec­tu­al as well as a phys­ic­al gi­ant.

What is it that has made this man one of the greatest math­em­aticians of the age? The an­swer ne­ces­sar­ily has to be a little labyrinth­ine. It was Ein­stein who said that “The most in­com­pre­hens­ible fact of Nature is the fact that Nature is com­pre­hens­ible”. When Ga­lileo de­clared over four cen­tur­ies ago that “every ob­ject con­tin­ues in its state of rest or uni­form mo­tion in a straight line” he ef­fect­ively paved the way for New­ton and his laws of mo­tion which, in turn, per­mit us to pre­dict the ebb and flow of tides, to com­pute the paths of comets and plan­ets and the mo­tion of man-made satel­lites, to build bridges, to con­struct sky­scrapers. From deep math­em­atico-phys­ic­al ana­lys­is one of­ten gains un­ima­gin­able and un­fore­see­able in­sight in­to the work­ings of the ex­tern­al world: from the soul of those who search more closely in­to the nature of things, pro­found truths emerge about the mys­ter­ies of Nature, and in a strange and ex­hil­ar­at­ing fash­ion new ways are found to har­ness its forces.

It was while Vaughan Jones presen­ted a sem­in­ar in the Uni­versity of Geneva in 1984 in a some­what ar­cane area of math­em­at­ics deal­ing with knot­ted­ness of knots — how to de­scribe and in­ter­pret the prop­er­ties and dis­tin­guishab­il­ity of knots — that he ar­rived at what has since be­come known, and will forever re­main, as the Jones poly­no­mi­al and the Jones in­vari­ant. This bril­liant in­sight was ex­traordin­ary, for it was soon to re­vo­lu­tion­ize many seem­ingly dif­fer­ent branches of phys­ics and math­em­at­ics and lat­terly bio­logy. The Jones poly­no­mi­al is the pivot around which many of the ad­vanced branches of twen­ti­eth cen­tury phys­ics turn. Thus to­po­logy, which is con­cerned with the con­nec­ted­ness of vis­ible ob­jects (like knots in a string), was shown by Vaughan Jones to be linked to stat­ist­ic­al mech­an­ics and spe­cial­ised branches of al­gebra in a breath­tak­ingly un­ex­pec­ted way. Moreover, quantum field the­ory, re­lativ­ity and gen­er­al elec­tro­mag­net­ism, all ma­jor areas in mod­ern phys­ics and cos­mo­logy, have since been shown to be in­ter­re­lated via the Jones poly­no­mi­al. And to cap it all, Jones’ work in knot the­ory has already been of use in mo­lecu­lar bio­logy since it deep­ens our un­der­stand­ing of the be­ha­viour of the double helices of DNA, the most im­port­ant mo­lecule of all liv­ing things.

Your Roy­al High­ness, there is a sense of time­less kin­ship between the people of Wales and mem­bers of the Welsh di­a­spora. I feel that in hon­our­ing Vaughan Jones — y gŵr llachar ac an­rhy­ded­dus hwn o Se­land Newydd — we are also hon­our­ing his Welsh grand­par­ents, who nearly sev­enty years ago set out on the long and tor­tu­ous jour­ney to an un­cer­tain fu­ture on the oth­er side of the world. Vaughan Jones has brought great glory to the land of his fath­ers. Y mae yn gwbl deil­wng o’r radd Doe­th­ur mewn Gwyddo­ni­aeth, er an­rhy­dedd. He is a worthy re­cip­i­ent of the hon­or­ary de­gree of Doc­tor of Sci­ence.