BBC News Online: Education

Making mad, passionate maths

In the University town of Cambridge, the mid-week shoppers and the tourists milling through the market square are probably blissfully unaware of concepts like vertex algebra, Banach spaces and Monster Moonshine.

But a short distance away, in the department of pure mathematics, these are the ideas being put to the test at the cutting edge of modern maths.

Professor Richard Borcherds is one of the mathematicians who last month, with the approval of an international panel of his peers, won the coveted Fields medal, the maths world's equivalent of the Nobel Prize.

He says: "It's a bit like maybe trying to solve a crossword puzzle, except that instead of spending 10 minutes on it, you're spending 10 years on it.

"My work's mostly about studying symmetry groups in very high dimensional spaces. If you want the number of people who understand it - very few really. Maybe one or two others in Cambridge and several others around the world.

"I mean if I'd wanted to be famous and so on I guess I'd have gone in for a slightly different career."

Monstrous maths

Professor Borcherds' work is concerned with a purely mathematical and unimaginable object that lives in 196,883 dimensions.

It's called the Monster. His fellow Fields medal winner, Professor Timothy Gowers, works in symmetry, investigating what are known as Banach spaces.

Both men admit that a practical use for their work is not obvious - rather they are solving complex mathematical puzzles that have baffled academics for decades.

But Professor Gowers believes that despite the abstract nature of their work, mathematicians can reveal some fundamental truths about the world around us.

He says: "It's almost true by definition that if you want to explain the physical world you need mathematics, because you don't want to take into account every last feature of the physical world.

"You want to abstract somehow the essential ones, and what you get is a mathematical model.

"The thing that is mysterious is that these models turn out often to be governed by one or two very simple principles, like Newton's law of gravitation and things like that. And I don't know whether there is an adequate explanation for that."

Buzz

Having two winners of the prestigious Fields medal has only added to a buzz that exists in the world of maths at the moment.

For Peter Goddard, Professor of Theoretical Physics at Cambridge University, these are exciting times.

"The mathematics that comes up in different areas, say in solid state physics or studying the cosmos, can itself be very closely related," says Professor Goddard.

"So I think the theme of the second part of the century, these last few decades, has been realising the deep connections between different areas of mathematics and different areas where mathematics is applied."

He adds: "Now I think that is related to the public perception of mathematics, as coming up everywhere, and of exciting things happening."

Artistic interpretations

Some of those exciting things include the starring role of maths in the Hollywood movie Good Will Hunting, while two further maths films have been shown at this year's Edinburgh festival.

The story behind the solving of a centuries old problem called Fermat's Last Theorem has been turned into a best selling book, while a biography of mathematician Paul Erdos is also doing well.

But many people have immense difficulty in trying to relate their normal understanding of maths, two plus two equals four, to the sort of work that wins a Fields medal.

Dr Marcus du Sautoy, a research fellow at the Department of Pure Mathematics in Cambridge, explains it like this: "Mathematics you learn at school is rather like the scales you learn in music, I mean they're not really the real music, but you need to learn them in order to actually play proper music.

"And in some senses you're learning the language and grammar of mathematics at school, but you don't actually ever get the chance to hear some real mathematics."

So as the mathematical stars of today make sweet music with their complex calculations, the rest of us can only look on in bemused wonder.

Maths may be on the up, but for the majority the world of hyperplane problems, number theory and elliptic curves will long remain a thing of mystery.

Links to other Education stories