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Last Updated: Friday, 17 October, 2003, 10:48 GMT 11:48 UK
Two and two is four... discuss
By Jonathan Duffy
BBC News Online

Maths circles, the numeric equivalent of reading groups, have taken off in Boston, US. Now, the couple who started the craze want to count Britain in as well.

Ellen and Bob Kaplan
Maths missionaries: Ellen and Bob Kaplan
It doesn't sound like the most riveting evening's entertainment. Probably the last time you went out to enjoy yourself and thought about maths was at a showing of A Beautiful Mind, the award-winning biopic about troubled genius John Nash.

Literature, maybe. Reading groups have, after all, taken off remarkably in the past few years.

However, the idea of getting together with friends to discuss a complex mathematical equation doesn't have the same ring about it.

Yet it's what Bob and Ellen Kaplan would like to see. They've already done it in the United States, where they set up the first maths circle nine years ago. The idea took off, and today five such groups meet regularly in and around Boston.

Now Britain, the Kaplans' adopted home for six months of every year, is in their sights.

They set the ball rolling on Thursday night with an inaugural maths circle lecture in central London.

Bob and Ellen are not 'natural' mathematicians - he studied languages and philosophy, she classics and archaeology
The pair have written a book about infinity, called The Art of the Infinite (above)
A pair of sprightly septuagenarians, Bob and Ellen positively fizz with enthusiasm for mathematics. They are self-confessed proselytisers, maths missionaries infused with the belief that numbers are good for the soul.

But the gospel they preach is not the one you probably heard at school. They are not so much interested in solving maths problems, they say, as debating them, rather as you might debate a work of art.

After all, says Bob, a lecturer at Harvard University, "Maths is an art".

It sounds like a hard-sell too far. Surely maths is black and white; right or wrong. The fact that 2 + 2 = 4 is not up for discussion.

But maths offers many variables, says Bob. "If I say to you, are there different sizes of infinity, do you have the answer? We have to find a way of discussing it."

Music metaphor

He constantly equates maths with music, calling it the "sister art of music". If you consider that every piece of music can be broken down and notated on a mathematical grid - a stave - it starts to sound plausible.

Now that's cheating
"Everyone has the capacity to enjoy maths and to do maths if they are led into it the way people are led into music," says Ellen.

Yet too often children are introduced to maths at primary school age by teachers who are "afraid" of it, "probably because they don't understand it themselves".

According to Bob, maths is our "birthright". None of us is born better at it than others, it's how we develop, he says.

As someone who only scraped through his maths O-level (second time around) I am heartened by this charitable reading of my potential. School maths started to run away from me when teachers began slotting letters - principally x and y - into sums.

It immediately punctured the reassuring distinction I'd always held that numbers are for arithmetic, letters are for English. By the time I got to logarithms, sine and cosine, I was languishing in a metaphorical rut at the bottom of the square-root symbol.

Patio brainteaser

These days even the principles of long division have deserted me. So could the Kaplans work their maths magic on me?

Bob is confident - by the end of this evening, you'll have given up journalism for a career in arithmetic, he jests.

It was encouraging - I thought the puzzle couldn't be solved, but we got there
Arthur Goodhart, aged 8, on the inaugural lecture
A few minutes later the pair step into the spotlight of the London lecture hall, where a capacity audience of 130 await.

The diverse age range - children to pensioners - reflects that of the maths circles in America.

After a brief introduction, the Kaplans pose a simple teaser to all assembled. Could you, they ask, pave a rectangular patio with squares, each of a different size?

The audience quickly warms to the subject, chipping in ideas that are visually translated by Ellen on an overhead projector. It looks like one of those brain teasers that sits next to the chess column in the back of a broadsheet newspaper.

As ideas are mooted, tried and rejected, scepticism kicks in. Can it be done? The audience is asked to give a show of hands. A clear majority think not.

Back to Mr Barker's

Yet they keep on trying new ideas. Start with the biggest square then continue halving the size of the rectangular space that remains. But then it would go on forever, for infinity. You would always have a space left to fill.

What if the first square sat in the middle, not touching the sides of the rectangle? And so on.

This is the point: the Kaplans have fostered a debate about a simple conundrum that appears to engage everyone present.

Before the hour is up, and with a little steering from our instructors, we come to an answer. Unfortunately, those arithmetical ogres "x" and "y" have a role to play in the solution, leaving me mentally languishing back in Mr Barker's classroom circa 1984, with my familiar old arithmetical insecurities.

So I can't relay to you the solution, save to say it involves a "propeller effect". But, it's not the answer so much as the debate that is important, says Bob.

He may be right, but I couldn't see that going down too well on my O-level re-take paper.

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