Marcus du Sautoy is Britain's second most famous mathematician. And since, as she'd be the first to admit, Carol Vorderman is really famous for her skills as an arithmetician, she doesn't really count. Yet it is significant – and somewhat abject, really – that these two very different exponents of the numbers game have recently been recruited to a broadly similar cause.

Vorderman has signed up to assist the Conservative Party, as it attempts to unravel the mysteries of Britain's lacklustre maths teaching. Du Sautoy, rather more elevatedly, has been appointed as the second ever Simonyi Professor of the Public Understanding of Science, replacing the geneticist Richard Dawkins, who held the chair created for him for 13 years.

Dawkins had latterly become more focused on rebutting religion than promoting science, and gave up the post, in part, so that he could pursue that passion further. Du Sautoy is also an atheist (though his wife is Jewish and his son attends a Jewish school). But he says that while the debate between science and religion is "interesting", he wants to "leave that to others". He admits, with an apologetic cringe, that "judging by the e-mails" a lot of people are somewhat cheered at this change of focus.

Du Sautoy sees the reinvigoration of mathematics in schools as a central, and urgent, aspect of his remit. "When I see the numbers going into the sciences going down, and departments closing, that depresses me. If we miss out a generation of scientists we're going to be stuffed," he says with emphasis. "It's hard to recover from that."

Du Sautoy's is a clever appointment. He is the sort of man for whom the phrase "boyish enthusiasm" might have been coined. The neat silver hair only serves to emphasise the 43-year-old's youthful good looks, just as the shiny red leather sofa he is sitting on simply points up the exuberance of his baggy pink linen shirt.

Du Sautoy's media-friendly affability, and skill as a communicator, have already gained him a lot of work in television and radio. He's also published a couple of well-received popular science books, which manage to be readable without sacrificing too much in the way of complexity. In his new job he's hoping to push that aspect of his career much further. But for him, all that exposure is a means to an end. It's the thrill of maths, far more than the buzz of public exposure, that gets him out of bed in the morning.

Here, in the family room of the north-London home he shares with his wife and three children (the couple's young identical twins are adopted), he is describing his experience of great "Eureka!" moments, and it does sound like a blast. "You remember them exactly, because when they happen, it's like a drug, it's such an adrenalin rush. That's why I keep on doing maths, because I keep wanting to have another one of those.

"I remember one very clear one, when I discovered a new symmetrical object which had never been seen before. Mathematicians talk about that flash they get, and it was almost electrical. You could probably look at the neuroscience of it and see that there actually was some sort of electrical surge. In that moment, a new thing was created. Which was mine. Nobody has ever thought of it before and it made a connection between two totally different areas of mathematics. It took my subject in a completely new direction."

Du Sautoy's discovery exists in nine-dimensional space and connected the world of symmetry with the (until then) entirely unrelated area of elliptic curves. He apologises because he can't actually show the shape to me, but I accept that the fault is mine. I'm conceptually imprisoned in three dimensions, like nearly everyone on the planet. Only about a dozen other group theorists in the entire world completely get what Du Sautoy is on about, and he describes his far-flung colleagues and collaborators as "like a nomadic tribe". Anyway, Du Sautoy himself retreats to just the three dimensions as he explains how much the unearthing of his formula means to him, which is comforting.

"That discovery is what I want carved on my gravestone. I can write it down in ... well, it's got quite a lot of characters and apparently you have to pay by the character ... so on your gravestone ... Well, it might cost my family a bit much.

"But that's something very special about mathematics, that this thing is going to exist for ever. There's something very attractive about that sense of immortality you can get in mathematics. I think there are probably very few other subjects where something will stand the test of time like that."

It might, of course, be some years before Du Sautoy's formula finds a practical use. It was three-and-a-half centuries, he points out, before some of Pierre de Fermat's ground-breaking work with prime numbers proved to be just the thing for encrypting credit-card details on the internet. Conversely, people are only catching on now to the fact that the crucial early developments that earnt the French lawyer and number theorist a place in history as one of the fathers of calculus, had been familiar to the intellectual elite of 14th-century Kerala, long before Isaac Newton or Gottfried Leibniz hit paydirt.

Du Sautoy passionately believes that one of the problems with maths teaching is that it often fails to place mathematical discovery in the real world. Some children, he says, are turned on to maths when they understand more about its cultural background, historical story, or practical applications. Others get there when they see that it can be fun. Du Sautoy finds it strange that so many of us believe that we never "use" maths, when every time we pick up a sudoku puzzle, or a pool cue, we're really indulging in a bit of maths for pure enjoyment.

"A lot of people, especially in England, they say, 'Oh I hated maths, I don't have a maths brain'. And I think they think some people are born with an innate ability to do maths, and actually I think that's totally false. In this year when we're celebrating 200 years since Darwin's birth, I think Darwin can be put to good use to show that everybody has a maths brain, because to survive in the jungle we had to develop mathematical skills.

"Just judging distances, being able to do geometry. If you want to attack something, you need to know about distances, relative distances : 'Now is the moment that I can pounce.' Projectile motion is solving quadratic equations. So actually when people at school say: 'Why do I have to solve a quadratic equation?' Well, we all intuitively know how to do it, because we know either to avoid an incoming trajectory or catch it.

"As a footballer, you're trying to get in line with an incoming free kick. Wayne Rooney is subconsciously solving a quadratic equation every time he works out where to stand in the box. That doesn't mean he can do it on paper and I'm sure he's probably forgotten how to do it. But the point is that our brains are evolutionarily programmed to be able to do it.

"It's my belief that you can take everyone down a logical path if you take them slowly enough, and the trouble is that mathematical brains can get scrambled a little bit on the way. You get a bad teacher, it messes you up for the rest of the journey."

A lot of the trouble with maths and schools is simply a vicious circle of supply and demand. There's a shortage of maths teachers, of course, which rations the good teaching that we need to turn out mathematicians. But the huge demand for mathematicians throughout the economy means that maths graduates can pick and choose other careers. Du Sautoy, even though he is a natural optimist, cannot help but exhibit a little frustration with the negative-feedback loop that Britain has got itself into.

"I'm working at the moment to try to develop an internet maths school, where people can just play games and learn maths through doing it. But the developers are saying we don't have enough people who know the maths to be able to programme these games in England. We're having to take it overseas.

"All the games that these kids play – look at my son's shelf up there, it's full of PlayStation games and things. And it's all maths. It's maths that's hiding behind there. We don't have the skilled mathematicians here to programme these games. This needs fantastic maths and a great imagination.

"The point is with good maths skills you have just wonderful opportunities and if you don't have good maths skills, there are just so many things that you won't be able to do. Architecture, for example. Zaha Hadid. Norman Foster. Ove Arup. Mathematicians. Zaha Hadid was a mathematician in Iraq. She trained as a mathematician and now she's one of the world's top architects.

"Then there's mobile-phone technology. The best mobile phone had the best mathematician. They know how to fit a huge amount of data into a small amount of space. How to do things efficiently, how to do them cleverly. We're just missing telling people all that exciting stuff.

"Hedge funds are full of mathematicians, like mini maths departments. It wasn't the mathematics that went wrong in the credit crunch, it was the incentivisation to take risks that went wrong. The mathematicians realised that the big bonuses that were being offered to them meant that they were being offered incentives to take huge risks that wouldn't impact on them."

Du Sautoy is pleased that one consequence of the credit crunch has been a revival of interest in maths teaching, of course. But the phenomenon suggests that people still have the idea that finance or teaching is all you can do with a maths degree. Instead, as technology drives a need for ever more complex encrypted information, an in-depth knowledge of maths is a guaranteed passport to all kinds of powerful corridors. Yet despite the sterling efforts of Carol Vorderman, maths is still not viewed as the acme of glamour – even though, as Du Sautoy admits, about half of the people he teaches now end up working in national security, at GCHQ.

This rather amuses Du Sautoy, because before he got into maths as a teenager, he fervently wished to become a spy when he grew up. He believed that his mother had been a spy before she had him, because she had worked at the Foreign Office before she married, and had travelled abroad quite a bit for her work. She did not, he says, disabuse him of the notion, and instead used to tease him that her little black gun was hidden somewhere in the house, just in case she was recalled for some secret assignment overseas. "I thought she was 007," he says, looking blissful at the memory.

In pursuit of his ambition, Du Sautoy tried to learn all the languages that he could. He was annoyed, though, by the lack of logic that so many languages displayed.

When Du Sautoy was about 12, his maths teacher, Mr Bailson, took him behind the bike sheds – where he went at break-time to smoke a cigar – and told his pupil that he would probably find it beneficial if he acquainted himself with "what mathematics was really about". To this end, the teacher recommended a couple of books.

"One of the books he recommended was Frank Land's The Language of Mathematics. And there was my bridge. I thought: 'What an amazing language.' It's quite an unusual language. It's got lots of strange twists and turns, but everything makes total logical sense. And also this book explained how maths is the language of nature. Fibonacci numbers – [which relate to] how the petals on a flower know where to grow, spirals, all that stuff. And I thought: 'This is just wonderful.'

"But I was into arty-type things too – I was learning to play the trumpet, went a lot to the theatre. So I quite liked creative things. The other book he recommended was A Mathematician's Apology by GH Hardy, a Cambridge mathematician from the beginning of the 20th century. This book just celebrated maths as a creative art. Obviously it's a useful science. But the reason why we do maths is because it's like poetry. It's about patterns, and that really turned me on. It made me feel that maths was in tune with the other things I liked doing. It's the 50th anniversary this year of CP Snow's 'Two Cultures' lecture, which sort of said: 'You either do science or you do humanities, and it's a tragedy that we don't seem to mix the two.' Today those boundaries are breaking down."

Du Sautoy is still a serious theatregoer, and takes pleasure in the fact that some of our greatest contemporary playwrights meet him half-way, by writing plays about science. He praises Tom Stoppard, especially for his maths-and-gardening play Arcadia, and rates Michael Frayn's Copenhagen as the play that did maths more brilliantly than any other he has seen. Du Sautoy also leapt at the chance to work with one of Britain's most consistently inventive theatre companies, Complicite, when they adapted A Mathematician's Apology for the theatre (under the title A Disappearing Number, voted Best New Play at last year's Laurence Olivier Awards).

It was Du Sautoy's mum, the superannuated spy, who had fostered her son's creative side. She played theatre games with him when he was little, and also started learning the flute, to keep him company when he took up the trumpet. But it was his dad, who had gone straight into the computer industry from school, who bought for him the books that Mr Bailson had recommended. He also took his son to one of the Royal Institution's 1978 series of Christmas Lectures, which by happy coincidence were focusing on mathematics for the first time since they had been founded in the 1820s. "It was so extraordinary that I came away thinking: 'Wow!' The guy who did it was Christopher Zeeman and I thought: 'I want to be him when I grow up. He looks like he's having so much fun.'"

The lectures have turned to the subject of maths only twice since, and on one of those occasions, two years ago, it was Du Sautoy himself who was delivering the lectures. In Zeeman's day, the lectures were broadcast on the BBC, and were a big televisual deal. It's a miserable sign of the lack of backbone in much of today's public-service broadcasting that they are now screened by Channel Five. Still, Du Sautoy is not complaining too much. At least someone is still putting the lectures on the telly, and doing it like they mean it.

"It's great giving a lecture to 200 children. But to talk to a million people – we hit a million towards the end of the lectures – that is fantastic. Channel Five does a great job. Prime time – 7pm – on Christmas Day. Up against Doctor Who. Dr Maths or Dr Who? On the day, half a million people actually turned on to Dr Maths."

Ultimately, though, Du Sautoy believes that only a wider cultural shift will change British attitudes to mathematics. He cites the huge surge of activity in 19th-century Germany, from which non-Euclidian geometry emerged. "In Germany then, the humanist movement came in, and education started being valued for its own sake and not only as a servant to society. That freed up people to think about ideas in a more abstract way. So I think that you can understand that new direction that mathematics took, as the consequence of a change in the education system in Germany."

Another nail, one fervently hopes, in the coffin of league-table schooling.

*'The Num8er My5teries: A Mathematical Odyssey Through Everyday Life', Marcus du Sautoy's book based on his Royal Institution lectures, will be published later in the year*

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