Spotlight

Vaughan Jones -- Mathematician in Knots

By Cathryn Crane, NZSM

The burly, bearded mathematician strides up and down in front of the blackboard, chalking arcane equations which bring nods and the occasional laugh from his audience. Dr Vaughan Jones is in his element talking in algebra.

A few months ago, Jones achieved fame in the mathematics world when he became the first mathematician from the southern hemisphere to win the Fields Medal. The medal is the equivalent of the Nobel Prize in mathematics -- Alfred Nobel is said to have disliked mathematicians and ignored their field in his academic awards.

The solid gold medal carries the legend "to transcend oneself and master the universe". It's a phrase which Vaughan Jones can relate to. Unlike the Nobel Prize, the Fields Medal tends to be seen as an encouragement to further research, rather than as a reward for work already done. As such, it's traditionally awarded to mathematicians under the age of 40. Jones has been delighted by the recognition, but a little disappointed that the signal honour is only really appreciated by the mathematics community.

Jones got his grounding in mathematics with a secondary education at Auckland Grammar and an undergraduate degree from Auckland University. While tagged as the first southern recipient of the medal, Jones has not worked in the southern hemisphere for quite some time. He left New Zealand to do his doctorate in Switzerland and since then has spent the bulk of his working life in the United States.

"I wanted to go on in mathematics, but it was impossible in New Zealand, " he says. "No-one was working on what interested me."

The small size of the academic community in New Zealand makes research in such a rarefied discipline difficult. Not only are there few colleagues to bounce ideas off, there is little in the way of funding for a discipline which goes over the head of most people.

"One of the PR problems with maths is it's a very abstract field and the layman can't grasp many of the topics, " Jones admits.

At the heart of Jones's work is knot theory, a complex algebra covering the behaviour of things as diverse as superstrings, said to govern the structure of the universe, and the genetic code in every living cell. Jones's discovery, now called the Jones Polynomial, concerns the mathematical description of how complex objects twist and turn themselves into knots.

Molecular biologists have grasped the Jones Polynomial with glee. It has provided them with a useful insight into the linkages in DNA, enabling them to develop a quick means of approximating the complex configurations of genetic material. The biologists may not understand the mathematics involved, but they see its practical benefits.

No-one was more surprised than Jones to find his work had practical applications.

"In the space of six months I went from abstract pie in the sky von Neumann algebra to talking to molecular biologists in their labs, " he says.

Cathryn Crane is a freelance journalist with an interest in environmental issues.