15 August 2013
Victoria researcher solves 40 year-old math problem
A Victoria University of Wellington mathematician has experienced his own eureka moment, solving a 40 year-old
Professor Geoff Whittle, from Victoria’s School of Mathematics, Statistics and Operations Research, has been working
with colleagues Professor Jim Geelen (Canada) and Professor Bert Gerards (Netherlands) to solve a problem posed by the
famous mathematician and philosopher Gian-Carlo Rota in 1970.
Earlier this year the trio realised that, after more than 15 years of work, they had achieved all the essential
ingredients to prove Rota’s Conjecture.
Geoff visited the United Kingdom last month to break news of the discovery to mathematics colleagues at a conference
where he was a guest speaker.
Rota’s Conjecture relates to a specialised area of mathematics known as matroid theory, a modern form of geometry, which
Geoff specialises in.
Rather than focusing on distance and angles, matroid theory investigates properties of structures which don’t change
under projection—for example, whether or not three points are always on a line, or four points are on a plane.
The theory investigates geometric structures that can be completely different from those in our world, and Rota’s
Conjecture is a way of using mathematics to recognise these alternative structures.
“I like to compare it to Kafka’s Metamorphosis story, where a man wakes up and realises he has transformed into an
insect—the way he views the world changes entirely,” says Geoff.
“Matroid theory is all about visualising a world of new geometrical structures and developing ways of describing the
big, overarching structures which would emerge.”
Although he has been working on proving Rota’s Conjecture for a long period of time, Geoff says the hard work will
really begin now, as the team starts writing up the results of its work.
“Resolving Rota’s Conjecture is really special, and the product of many, many years of collaborative work.
“Now, we have a lot of writing to do, which I expect to take several more years—as well as many hundreds of pages of
“It’s a little bit like discovering a new mountain—we’ve crossed many hurdles to reach a new destination and we have
returned scratched, bloodied and bruised from the arduous journey—we now need to create a pathway so others can reach
Head of School Dr Peter Donelan is also excited about the news, which he believes will attract international
“This will be regarded as one of the outstanding mathematical achievements in recent years,” he says.
Geoff has been based at Victoria University since 1992, when he joined the School of Mathematics, Statistics and
Operations Research as a lecturer. He was promoted to Reader in 1997 and to Professor in 2001.
Geoff is recognised as a world leader in the field of discrete mathematics. He has spent time as a visiting research
fellow at Merton College, Oxford and is a Fellow of the Royal Society of New Zealand. In 1996, his achievements were
recognised with the New Zealand Mathematical Society’s Research Award.
Watch a video of Geoff talking about his career and research here: www.youtube.com/watch?v=Lw8D15amE_4