Sir Vaughan Jones, who died last year, is remembered and honoured by former friends and colleagues in this memorial tribute produced by the American Mathematical Society.

Sir Vaughan Frederick Randal Jones, who died at age 67 on September 6, 2020, was one of the most influential and inspirational mathematicians of the last four decades. His original and penetrating analysis of inclusions of von Neumann algebras led to the creation of new fields of research, while reinvigorating old ones, thereby setting off an extraordinary interplay between disparate areas of mathematics, from analysis of operator algebras, to low-dimensional topology, statistical mechanics, quantum computing, and quantum field theory.

Memories of Vaughan Jones: American Mathematical Society

Mathematics was revolutionised by Sir Vaughan in the early 1980s when he found deep connections between subfactors, analytic objects in the theory of operator algebras and topological objects, knots and links in three-dimensional space.

His remarkable and unexpected discovery of the Jones polynomial associated to knots and links resolved, amongst other things, problems left open since the 19th century on the Tait conjectures. This rapidly opened up vast new areas of research in wide areas of mathematics in analysis, algebra, geometry and topology. Subsequent developments have found applications and connections with statistical mechanics and random matrices, quantum field theory in physics and the topology of DNA strands and protein folding.

For these breakthroughs he received the Fields Medal, the mathematical equivalent of the Nobel Prize, and also received the Rutherford Medal and the Onsager Medal. He was a Fellow of the Royal Society of New Zealand Te Apārangi and of the Royal Society, a Member of the US National Academy of Sciences, and a Foreign Member of several other national learned societies.

Sir Vaughan was the Distinguished Professor and Stevenson Professor at Vanderbilt University, and Director of the New Zealand Mathematics Research Institute.

Further reading

• Colleagues and friends remember distinguished Vanderbilt mathematician Vaughan Jones
• Sir Vaughan Jones memorial, University of Aukland (YouTube)

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