Wed 10 Nov 2010. A new medal for excellence in mathematics was awarded by the Royal Society of New Zealand at their annual research honours celebration in Christchurch on Wednesday night.

The Jones Medal was presented to Professor Emeritus John Butcher FRSNZ of The University of Auckland and recognises his lifetime achievement in mathematics.

It was presented by the scientist it is named after Professor Sir Vaughan Jones, a world-renowned New Zealand mathematician now living in the USA.  The medal was designed by Marian Fountain, a New Zealand sculptor living in France.

Dr Garth Carnaby, president of the Royal Society of New Zealand, said Professor Butcher’s exceptional work on numerical methods for solving differential equations is regarded as some of the best work ever done in this area.

“This work has remained at the forefront of international research for more than 45 years. John Butcher has also been a tremendous leader for developing mathematical sciences in New Zealand.”

“Over the past half century, he has established himself, not only as one of the most internationally acclaimed New Zealand mathematicians, but also as one of the most important leaders of mathematics within New Zealand.”

Professor Sir Vaughan Jones, after whom the medal is named, also presented Professor Butcher with $5000 in prize money and praised him for his work, saying he owed a ‘personal mathematical debt’ to Butcher.

“I believe we are living in a Golden Age for New Zealand mathematics. There is ample evidence for this. Our disproportionate representation at the International Congress of Mathematics, and a remarkable performance at the Mathematics Olympiad are but two instances. I believe this Golden Age was ushered in by John Butcher.”

Professor Butcher’s research has earned him a wide range of top international prizes, including the prestigious Fellowship of the Society for Industrial and Applied Mathematics (the only New Zealander holding this fellowship); the Hector Medal in 1996 from the Royal Society of New Zealand; and the New Zealand Mathematical Society’s Research Award when it was offered for the first time in 1991.

Professor Butcher is regarded as the founder of the modern theory of Runge-Kutta methods, one of the principal classes of numerical methods for solving ordinary differential equations. His methods are used in computer simulations that have become a fundamental scientific tool in computational physics, chemistry, biology and engineering.

In February 2011 he will be presented with the Van Wijngaarden Prize for mathematics. The prize is awarded every five years by the Centrum Wiskunde & Informatica in the Netherlands and is named after the late Adriaan van Wijngaarden, a pioneer in numerical analysis and computer science.

He was the first supervisor of a full time PhD student in mathematics at The University of Auckland and has subsequently supervised many other PhD students, many of whom hold prestigious positions worldwide.

Professor Butcher was a founding member of the New Zealand Mathematical Society, and its second president, and was the first editor of the ‘Mathematical Chronicle’, the journal which later became the ‘NZ Journal of Mathematics’. He was elected as a Fellow of the Royal Society of New Zealand in 1980.

Symbolism of the Jones Medal design

The Jones Medal was specially designed by the renowned New Zealand sculptor medalist Marian Fountain who lives in Paris. She specialises in medals.

Mathematical elements are incorporated into the design as well as a human element with the clasped hands. Marian Fountain says these hands represent the measure of thought, direction, patience and clarity required to arrive at a solution.

The knot design reflects the work on knot polynomials for which Jones won the 1990 Fields medal, with the discovery of what is now called the Jones polynomial.  The design is a knot with two different strings intertwined. Jones’  work on knots has been of interest in many areas besides its home, topology: including statistical mechanics, quantum field theory, functional analysis, group theory, abstract algebra, category theory and, surprisingly, molecular biology where it has been used to investigate the knotting of DNA molecules.

The three strings of zeros and ones are the binary expansions of the three mathematically fundamental numbers – ‘e’, ‘pi’ and the ‘golden ratio’. The golden ratio played a big part in Jones’ work on subfactors which led to the knot theory discovery.

The nautilus shell is a natural object which fits the golden ratio, a special number in mathematics. For the designer it also “represents all living things in terms of growth, like the fern frond, and in terms of change, like the cusp of a wave”.

The circles in the design represent hyperbolic geometry.

The Pea Pod is a bronze sculpture which exists in 3 sizes:

127 x 45 x 25cm,  83 x 30 x 15cm and the small one at 25cm high

For the Christchurch Earthquake Appeal. Exhibition in collaboration with Douglas Mac Diarmid, painter.

No. 140 in catalogue

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