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Last Updated: Tuesday, 23 August 2005, 11:54 GMT 12:54 UK
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Numbers game
 Bringing text book maths to life
Stash your calculator, limber up your brain - a new radio series sets out to show maths can be interesting, and prove that the number 1,729 is special.

Imagine if school league tables reflected the popularity of individual subjects among pupils. It's a fair bet maths would not rank highly.

Numbers have a reputation for being dull - a belief that is "officially" sanctioned by a new slice of academic research which claims to prove that number crunching accountants are, well, boring.

Increasingly, children are opting for so-called "soft" subjects at school. Only last week, it was revealed that physics has been overtaken by media studies in A-level popularity.

One of those trying to reverse this tide is author and broadcaster Simon Singh, who is on a mission to shed a more positive light on maths.

Tax returns

Numbers, says Singh, are inherently interesting. Right now the numbers "one", "two", "six", "1,729" and "6.6742" are particularly occupying his mind.

 Maths ambassador Simon Singh
Take number one for starters. In the endless order of figures from zero to infinity, it perhaps doesn't sound the most promising launch pad.

One, after all, has a reputation for being a lonesome number - a singleton in a world otherwise populated by multiples. In fact, he says, this couldn't be further from the truth.

The root of all counting, one is the most popular number - a fact proved by something called Benford's Law. It states simply that in any large, randomly produced set of natural numbers, such as tables of logarithms or corporate sales statistics, 30% of them will start with a one (instead of the 10% one might expect if all digits were equally likely).

Anyone can give it a go. Grab a newspaper and have a quick glance at the various figures - dates, prices, racing programmes. However, when anyone is asked to think up a random section of figures, those starting with one are far less common.

The theory has been adopted by US tax collectors, says Singh, as a sifting device, revealing those more likely to have made up their numbers.

"The idea is to make people realise that maths is all around them," says Singh.

Yak herder

 Futurama robot Bender - no coincidence he's serial no 1729
So what about "six"? For Singh this is special because of the small world phenomenon that everyone in the world is linked through no more than six degrees of separation. It was a principle proved by the maverick psychologist Stanley Milgram.

"The connectedness is astonishing. You can race around the world and suddenly you are related to a Mongolian yak herder."

"Two" meanwhile allows him to look at the "surprising powers of doubling" and "6.6742" - well that's a key figure in determining the value of gravity. Were the number slightly higher or lower, the world as we know it would not exist, and nor indeed would we.

Of all the numbers Singh throws a spotlight on, "1,729" is perhaps the most inauspicious. But to Singh it is very proof that every number is special.

He relates an anecdote in which the number is cited as boring until a mathematician points out that in fact it is the sum of nine-cubed plus 10-cubed, and 12-cubed plus one-cubed."

So what? So, says Singh, "it is the smallest number that is the sum of two cubes in two different ways".

Interesting, as far as it goes, but not exactly practical. When most people want to tot up their weekly outgoings they probably reach for a calculator, rather the divine the gravitational constant. Isn't that enough for the majority of us?

"Of course not. Just because everyone can use a calculator dosn't mean we should give up on maths. That's like saying because we've got spell check, we needn't bother with English literature."

A Further Five Numbers is broadcast on Tuesday mornings on BBC Radio 4 starting on 23 August. See Internet links, above right, to listen to the programmes online after they have been broadcast.

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