Sir Vaughan Frederick Randal Jones (31 December 19526 September 2020) was a New Zealand mathematician known for his work on

von Neumann algebra In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann algeb ...

s and

knot polynomial In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. History The first knot polynomial, the Alexander polynomial, was introdu ...

s. He was awarded a

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

in 1990.

Early life

Jones was born in Gisborne,

New Zealand New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island count ...

, on 31 December 1952. He was brought up in

Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

, New Zealand, where he attended St Peter's School. He subsequently transferred to

Auckland Grammar School Auckland (pronounced ) ( mi, Tāmaki Makaurau) is a large metropolitan city in the North Island of New Zealand. The most populous urban area in the country and the fifth largest city in Oceania, Auckland has an urban population of about I ...

after winning the Gillies Scholarship, and graduated in 1969 from Auckland Grammar. He went on to complete his undergraduate studies at the

University of Auckland , mottoeng = By natural ability and hard work , established = 1883; years ago , endowment = NZD $293 million (31 December 2021) , budget = NZD $1.281 billion (31 December 2021) , chancellor = Cecilia Tarrant , vice_chancellor = Dawn F ...

, obtaining a BSc in 1972 and an MSc in 1973. For his graduate studies, he went to

Switzerland ). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...

, where he completed his PhD at the

University of Geneva The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centu ...

in 1979. His thesis, titled ''Actions of finite groups on the hyperfinite II₁ factor'', was written under the supervision of

André Haefliger André Haefliger (born 22 May 1929 in Nyon, Switzerland) is a Swiss mathematician who works primarily on topology. Education and career Haefliger went to school in Nyon and then attended his final years at Collège Calvin in Geneva. He studied ...

, and won him the Vacheron Constantin Prize.

Career

Jones moved to the United States in 1980. There, he taught at the

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

(1980–1981), and the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

(1981–1985), before being appointed as professor of mathematics at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. His work on

s, with the discovery of what is now called the

Jones polynomial In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynom ...

, was from an unexpected direction with origins in the theory of

von Neumann algebras In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann alge ...

, an area of

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

already much developed by

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vande ...

. It led to the solution of a number of classical problems of

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

, to increased interest in

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot th ...

, and the development of

quantum topology Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology. Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associa ...

. Jones taught at

Vanderbilt University Vanderbilt University (informally Vandy or VU) is a private research university in Nashville, Tennessee. Founded in 1873, it was named in honor of shipping and rail magnate Cornelius Vanderbilt, who provided the school its initial $1-million ...

as Stevenson Distinguished Professor of mathematics from 2011 until his death. He remained Professor Emeritus at University of California, Berkeley, where he had been on the faculty from 1985 to 2011 and was a Distinguished Alumni Professor at the

. Jones was made an honorary vice-president for life of the

International Guild of Knot Tyers The International Guild of Knot Tyers (or IGKT) is a worldwide association for people with an interest in knots and knot tying. Formation and beginning Officially established in 1982, the founding members were initially drawn together by the ...

in 1992. The Jones Medal, created by the

Royal Society of New Zealand Royal may refer to: People * Royal (name), a list of people with either the surname or given name * A member of a royal family Places United States * Royal, Arkansas, an unincorporated community * Royal, Illinois, a village * Royal, Iowa, a cit ...

in 2010, is named after him.

Personal life

Jones met his wife, Martha Myers, during a ski camp for foreign students while they were studying in Switzerland. She was there as a

Fulbright scholar The Fulbright Program, including the Fulbright–Hays Program, is one of several United States Cultural Exchange Programs with the goal of improving intercultural relations, cultural diplomacy, and intercultural competence between the people of ...

, and subsequently became an associate professor of medicine, health and society. Together, they have three children. Jones died on 6 September 2020 at age 67 from health complications resulting from a severe

ear infection Otitis is a general term for inflammation or infection, inner ear infection, middle ear infection of the ear, in both humans and other animals. When infection is present, it may be viral or bacterial. When inflammation is present due to fluid buil ...

Honours and awards

* 1990awarded the

* 1990elected

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

* 1991awarded the Rutherford Medal by the

* 1991awarded the degree of

Doctor of Science Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...

by the

* 1992elected to the

Australian Academy of Science The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The academy is modelled after the Royal Soci ...

as a Corresponding Fellow * 1992awarded a

Miller A miller is a person who operates a Gristmill, mill, a machine to grind a grain (for example corn or wheat) to make flour. Mill (grinding), Milling is among the oldest of human occupations. "Miller", "Milne" and other variants are common surname ...

Professorship at the University of California Berkeley * 2002appointed

Distinguished Companion of the New Zealand Order of Merit The New Zealand Order of Merit is an order of merit in the New Zealand royal honours system. It was established by royal warrant on 30 May 1996 by Elizabeth II, Queen of New Zealand, "for those persons who in any field of endeavour, have rend ...

(DCNZM) in the 2002 Queen's Birthday and Golden Jubilee Honours, for services to mathematics * 2009his DCNZM redesignated to a

Knight Companion of the New Zealand Order of Merit The New Zealand Order of Merit is an order of merit in the New Zealand royal honours system. It was established by royal warrant on 30 May 1996 by Elizabeth II, Queen of New Zealand, "for those persons who in any field of endeavour, have ren ...

in the 2009 Special Honours * 2012elected a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Publications

* * * * * * *

References

External links

* *
Jones' home page

* Joan S. Birman: ''The Work of Vaughan F. R. Jones'' in

Ichirō Satake (25 December 1927 – 10 October 2014) was a Japanese mathematician working on algebraic groups who introduced the Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of linear algebraic groups and symmetri ...

(ed.): ''Proceedings of the International Congress of Mathematicians, 21–29 August 1990, Kyoto, Japan'', Springer, 1991 (Laudatio for Fields-Medal 1990
online
{{DEFAULTSORT:Jones, Vaughan 1952 births 2020 deaths People from Gisborne, New Zealand People from Waikato People educated at Auckland Grammar School University of Auckland alumni Fields Medalists 20th-century New Zealand mathematicians 21st-century New Zealand mathematicians New Zealand expatriates in Switzerland University of Geneva alumni University of California, Los Angeles faculty University of Pennsylvania faculty University of California, Berkeley College of Letters and Science faculty Vanderbilt University faculty Knights Companion of the New Zealand Order of Merit Fellows of the American Mathematical Society Fellows of the Royal Society of New Zealand New Zealand Fellows of the Royal Society Members of the United States National Academy of Sciences Recipients of the Rutherford Medal Fellows of the Australian Academy of Science