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Rota’s Conjecture: Researcher solves 40-year-old math problem

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Posted August 16, 2013

A Victoria University mathematician has experienced his own eureka moment, solving a 40 year-old mathematical problem.

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.

 

Read more at: Phys.org

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