- 1990 Fields Medal

### Intro

1990 Fields Medal

New Zealand mathematician. Professor Emeritus in UC Berkeley and Professor of Mathematics in Vanderbilt University. He was awarded a Fields Medal in 1990 for his work on von Neumann algebras and knot polynomials.

### Education and Work Experience

1979, Ph.D. in Mathematics, University of Geneva

1985-2012, Professor of Mathematics, UC Berkeley

2013-Present, Professor emeritus, UC Berkeley

2011-Present, Professor of Mathematics, Vanderbilt University

### Honors and Awards

1986, Guggenheim Fellowship

1990, Fields Medal

1991, Rutherford Medal

1999, Member of the United States National Academy of Sciences

### Major Academic Achievements

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".