Skip to content


Fellows Directory

Vaughan Jones

Vaughan Jones

Sir Vaughan Jones FRS


Elected: 1990


Vaughan Jones’s first work was a complete classification of the action of finite groups on von Neumann algebras of type II. He went on to define an ‘index’ for a subfactor of a II1 factor, and found its possible values, most strikingly the unsuspected discrete series 4 cos2(pi/n). This work has profoundly changed the perspective of its whole field. It also produced a completely new family of representations of the braid groups, and Vaughan showed how these gave a new polynomial invariant for knots. On one side this transformed knot theory, while in another direction it opened up a new field embracing statistical mechanics, conformal quantum field theory, and the quantisation of Lie groups. Vaughan’s most recent work concerns planar algebra and representations of Richard Thompson’s groups F and T.

Sir Vaughan Jones KNZM FRS died on 6 September 2020.

Interest and expertise

Subject groups

  • Mathematics
    • Pure mathematics
  • Astronomy and physics
    • Mathematical and theoretical physics


Analysis, Algebra, Topology, von Neumann algebras, Knot theory, Mathematical physics


  • Fields Medal

    For his discovery of an unexpected link between the mathematical study of knots – a field that dates back to the 19th century – and statistical mechanics, a form of mathematics used to study complex systems with large numbers of components.

Was this page useful?
Thank you for your feedback
Thank you for your feedback. Please help us improve this page by taking our short survey.