Marcus du Sautoy is answering the phone and making tea while his laptop does the math.
It's arduous math: hours of long division, testing massive numbers for "primeness," or indivisibility by other numbers. It's also high-stakes math: the first person to find a 10 million digit prime number -- hugely valuable to defense and commercial security systems -- will win a US$100,000 prize.
Professors of math like du Sautoy are not the only runners in this race. Business teams, talented amateurs, lone individuals, even groups of Chinese schoolchildren (who regularly e-mail him to report their progress) are all chasing prime numbers.
Thanks to a freeware Web site that gives out the testing formulae in return for an eventual share of the prize, anyone with time, commitment and a computer can now have a stab at a problem that has obsessed and eluded professional mathematicians for centuries.
What is unusual about du Sautoy is that he hopes that anyone will.
Du Sautoy is a walking oxymoron: the popular mathematician. He has a bestselling book, newspaper columns, radio series, a TV show, schools and public lecture tours and now the landmark TV scientist slot -- this year's Royal Institution Christmas Lectures. With the title The Num8er My5teries, and subjects ranging from codes, magic tricks, insect evolution and the shape of the universe, he hopes to turn a generation of young teenagers on to math, just as he was.
At primary school, he wasn't particularly good at sums, he says; his parents were told not to bother entering him for selective secondaries because he couldn't spell and didn't know his multiplication tables. But a sharp-eyed secondary school teacher spotted his interest in mathematical patterns and suggested he read the math column in Scientific American.
Then, in Christmas 1978, when he was 13, his father took him to the RI lectures. For the first time since 1820, they were given by a mathematician, Sir Christopher Zeeman. Du Sautoy was entranced.
"They were totally inspiring. Zeeman really pushed people; he did stuff like catastrophe theory. I came away saying: `I don't understand that language, but I want to learn it,'" du Sautoy said.
It's a message he continues to push. Mathematics is not just sums, he tells children and adults -- particularly math teachers -- and it need not necessarily be taught hierarchically. You don't always have to get step A right before lifting the veil on step B.
"We don't say to children learning music `You're only allowed to play scales until you've got them all right,'" he said. "Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there."
Nevertheless, he hesitated before joining that world full-time himself. He won a coveted place as a fellow of All Souls College at Oxford University immediately after his first degree, then gave it up to go and work on a kibbutz in Israel. He thought about becoming an actor. He considered the US.
Then the Royal Society offered him a 10-year fellowship based in Oxford -- initially All Souls, and now at Wadham College, where he was an undergraduate -- in which he could split his time between his own research, investigating theoretical symmetry in infinite dimensions, and "selling" mathematics. He took it.
A mathematician's lifestyle, as he shows in his 2003 book The Music of the Primes -- popular in the UK, but a bestseller in Italy, where Umberto Eco made it his book of the year -- is not quite like anyone else's.
Quoting Julia Robinson, a Berkeley professor who dedicated her life to finding equations to predict prime numbers, he describes the typical mathematician's week: "Monday, tried to prove theorem; Tuesday, tried to prove theorem; Wednesday, tried to prove theorem; Thursday, tried to prove theorem; Friday, theorem false."
Some mathematicians are better at posing questions, others at finding answers, he said.
"The answer gives you the real adrenaline rush. In my own work I've forged connections that weren't there before, but I couldn't just ask questions," he said.
Answers can appear anywhere, at any time.
"If I'm flying to China, I can sit and think about a problem. Other scientists have to go to the lab. I'm always thinking about math, even when I'm doing other things. A lot of the time you're going up blind alleys and it's very frustrating, but then you have a sudden rush of ideas. You can live off that for quite some time," he said.
Returning from Israel and re-establishing himself at All Souls, he lived off his own ideas rather well. He published papers and won a prestigious international mathematics prize. In 1994, at an All Souls dinner, he sat next to a senior journalist from the Times.
"Over a drunken dessert he asked what I did. I gave my spiel; he said `That sounds so sexy, write me an article,' and gave me his card. I woke up next morning, couldn't remember what I'd said, wasn't confident enough to phone him, and did nothing," du Sautoy said.
"Three years later, I sat next to him at the same dinner, and he said, `You never wrote that article.' I was more confident then, and said, `My job is to prove theorems; you'll never understand it'. He said `Bloody hell, you're funded with public money.' I woke up next morning thinking `What am I doing if I can't communicate it?' So I wrote something. It was the hardest thing I ever did," du Sautoy said.
Nevertheless, it became a habit. Andrew Wiles had just proved Fermat's Last Theorem in a flurry of publicity; the films Good Will Hunting and A Beautiful Mind were heading for production.
"It felt almost sexy to be a mathematician," du Sautoy explained.
As he became more ambitious, the math he communicated became harder, culminating in his book on prime numbers, which centers on an almost incomprehensible hypothesis by a 19th-century mathematician called Bernhard Riemann about whether primes occur at random or in a detection-resisting pattern.
"Other mathematicians said to me `You're going to try and explain the Riemann hypothesis?' and laughed. But I don't think there's any mathematics which is too hard for people to understand," he said. "The wonderful thing about math is it's a totally logical subject, and a pathway has been marked out. I think a lot of these things can be crystallized in something quite essential, that people can get. If I can't explain it, I realize that's probably because I don't completely understand it myself."
Explaining it has taken him to the home of the prime minister in Downing Street and Buckingham Palace, as well as most recently into three days of workshops with the radical theatre company Complicite, creating a new play around the Indian mathematician Ramanujan, who appears in Du Sautoy's book. He was brought from India to Cambridge by the English mathematician GH Hardy in 1914, only to freeze socially and physically to death.
Few mathematicians would be as comfortable with actors as du Sautoy is.
"We sat around jamming till I came up with fun things to show them. Like why certain infinities are bigger than other infinities," he said. "You can do that with people pretending to be cicadas and predators."
And some mathematicians would certainly not approve.
"It was Hardy who said only second-rate mathematicians need to talk about their work -- that the real job of a mathematician is to prove theorems," du Sautoy said.
"It's important to me that no one can say I'm not pumping out high-level research," he said.
"Next summer I've been invited to present my work to the International Congress of Mathematicians. I think 15 years ago it would have been much harder to do what I do and still convince people you were a serious mathematician.
But now everyone realizes that we need ambassadors for science; we need to find ways to stop mathematics departments closing down and to build a new generation of mathematicians," he said.
"Now people say to me, `I couldn't do what you're doing, but thank God somebody's doing it,'" he said.
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