40 year-old math problem solved

A mathematician in New Zealand has experienced his own eureka moment, solving a 40 year-old mathematical problem after 15 years of work.
Professor Geoff Whittle, from Victoria University of Wellington has been working with colleagues Professor Jim Geelen from Canada and Dutch Professor Bert Gerards 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 UK 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," said 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," said Geoff.
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.