# Vaughan Frederick Randal Jones

### Quick Info

Gisborne, New Zealand

**Vaughan Jones**is a New Zealand mathematician who won a Fields Medal for his work on Knot theory.

### Biography

**Vaughan Jones**attended St Peter's School in Cambridge, New Zealand from the age of eight years until he was 12. In 1966 he began his secondary schooling at Auckland Grammar School in Auckland. He left school having been awarded a University Entrance Scholarship and a Gilles Scholarship to assist him to study at the University of Auckland. He also received a Phillips Industries Bursary.

In 1970 Jones entered the University of Auckland graduating with a B.Sc. in 1972 and an M.Sc. with First Class Honours in 1973. He was awarded a Swiss Government Scholarship in 1973 to enable him to undertake research in Switzerland. He also won a F W W Rhodes Memorial Scholarship.

After teaching for a while as an assistant lecturer at Auckland, he entered the École de Physique in Geneva in 1974, moving in 1976 to the Écoles Mathématiques. In Geneva his research was supervised by A Haefliger and he also taught as an assistant. In 1979 Jones was awarded his Docteur es Sciences (Mathématiques), and the following year he was awarded the Vacheron Constantin Prize for his doctoral thesis.

In 1980 Jones moved to the United States spending the academic year 1980-81 as E R Hedrick Assistant Professor of Mathematics at the University of California at Los Angeles. In 1981 he moved to the University of Pennsylvania where he was assistant professor until 1984 when he was promoted to associate professor. In 1985 he was appointed as Professor of Mathematics at the University of California at Berkeley.

Jones worked on the Index Theorem for von Neumann algebras, continuing work begun by Connes and others. His most remarkable contribution, however, was that in the course of this work he discovered a new polynomial invariant for knots which led to surprising connections between apparently quite different areas of mathematics.

Jones was awarded a Fields Medal at the 1990 International Congress in Kyoto, Japan for his remarkable and beautiful mathematical achievements. Jones gave a lecture to the 1990 Congress dressed in a rather unusual way for a mathematics lecture. He was wearing the "All Blacks" rugby strip! Joan Birman lectured on Jones's work at the ICM-90 and introduced his work as follows [4]:-

In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space. His invariant had been missed completely by topologists, in spite of intense activity in closely related areas during the preceding 60 years, and it was a complete surprise. As time went on, it became clear that his discovery had to do in a bewildering variety of ways with widely separated areas of mathematics and physics .... These included (in addition to knots and links) that part of statistical mechanics having to do with exactly solvable models, the very new area of quantum groups, and also Dynkin diagrams and the representation theory of simple Lie algebras. The central connecting link in all this mathematics was a tower of nested algebras which Jones had discovered some years earlier in the course of proving a theorem which is known as the "Index Theorem".Birman also talked of the way Jones freely exchanged his ideas with other mathematicians [4]:-

His style of working is informal, and one which encourages the free and open interchange of ideas. During the past few years Jones wrote letters to various people which described his important new discoveries at an early stage, when he did not yet feel ready to submit them for journal publication because he had much more work to do. He nevertheless asked that his letters be shared, and so they were widely circulated. It was not surprising that they then served as a rich source of ideas for the work of others. As it turned out, there has been more than enough credit to go round. His openness and generosity in this regard have been in the best tradition and spirit of mathematics.Jones has received many honours for his work in addition to the Fields Medal. He was awarded a Guggenheim Fellowship in 1986 and elected a Fellow of the Royal Society in 1990. In 1991 he was awarded the New Zealand Government Science Medal and given an honorary D.Sc. from the University of Auckland in 1992. In 1993 he was awarded a second honorary D.Sc. this time from the University of Wales. Also in 1993 he was elected to the American Academy of Arts and Science.

He was elected to the United States National Academy of Sciences (1999), and the Norwegian Royal Society of Letters and Sciences (2001). In 2000 he was presented with the Onsager medal of Trondheim University and in 2002 he was awarded Distinguished Companionship of the New Zealand Order of Merit. Also in 2002 he was elected as an honorary Member of the London Mathematical Society and awarded an honorary degree by the Universite du Littoral, Cote d'Opale. He was further honoured by being elected Vice-President of the American Mathematical Society in 2004 and awarded the Prix Mondial Nessim Habif in 2007.

Jones has made many other contributions to the mathematical community, particularly in his editorial work as editor or associate editor for many journals: the

*Transactions of the American Mathematical Society*, the

*Pacific Mathematics Journal*, the

*Annals of Mathematics*, the

*New Zealand Journal of Mathematics*,

*Advances in Mathematics*, the

*Journal of Operator Theory*,

*Reviews in Mathematical Physics*, the

*Russian Journal of Mathematical Physics*, the

*Journal of Mathematical Chemistry*,

*Geometry and Topology*, and

*L'Enseignement Mathematique*. He has served on the Scientific Advisory Boards of the Fields Institute of Mathematics, the Erwin Schrödinger Institute, the Mathematical Sciences Research Institute at Berkeley, the Center for Communications Research (United States), the Institut Henri Poincaré, and the Miller Institute for Basic Research in Sciences. He served on the Nominating committee and the Steele Prize committee of the American Mathematical Society, and on the Programme Committee for the International Congress of Mathematicians held at Madrid in 2006.

### References (show)

- Biography in
*Encyclopaedia Britannica.*http://www.britannica.com/biography/Vaughan-Jones - F Araki and S Iitaka, Profiles of the ICM-90 Fields Medal prizewinner (Japanese),
*Sugaku***42**(4) (1990), 361-366. - J S Birman, On the work of Vaughan F R Jones,
*Addresses on the works of Fields medalists and Rolf Nevanlinna Prize winner*(Tokyo, 1990). - J S Birman, The work of Vaughan F R Jones,
*Proceedings of the International Congress of Mathematicians, Kyoto, 1990***I**(Tokyo, 1991), 9-18. - Eulogy of Vaughan Jones,
*New Zealand Math. Soc. Newslett. No.***55**(1992), 9-10. - ICM-90 Kyoto, Japan,
*Notices Amer. Math. Soc.***37**(9) (1990), 1209-1216. - Y Kawahigashi, Vaughan F R Jones' achievements I (Japanese),
*Sugaku***43**(1) (1991), 29-34. - C C King, Vaughan Jones and knot theory : a New Zealand mathematician unravels a new invariant which links diverse sciences in an unforeseen thread,
*New Zealand Math. Soc. Newslett. No.***37**(1986), 28-32. - J Murakami, V F R Jones' achievements II (Japanese),
*Sugaku***43**(1) (1991), 35-40. - G Skandalis, Médaille Fields de Vaughan Jones,
*Gaz. Math. No.***47**(1991), 17-19. - R Schmid, Strings, knots, and quantum groups: a glimpse at three 1990 Fields medalists,
*SIAM Rev.***34**(3) (1992), 406-425.

### Additional Resources (show)

Other websites about Vaughan Jones:

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Written by J J O'Connor and E F Robertson

Last Update September 2009

Last Update September 2009