If any numbers genius can prove a centuries-old theorem, Faber the publisher, promises to pay $1m. Report by Anjana Ahuja.
It is not the easiest way to win a million dollars but it must be one of the coolest. Crack a notoriously difficult mathematical enigma within two years and the money's yours. This is the challenge from Faber, which is hoping to garner appropriate publicity for its latest fictional offering, Uncle Petros and Goldbach's Conjecture, by the Greek author Apostolos Doxiadis. There are estimated to be about 20 people in the world who could do it and a victory, Faber hopes, will help it to cash in on one of the hippest happenings in publishing since Bridget Jones.
The eponymous conjecture is a seemingly straightforward mathematical puzzle put forward by the Prussian historian and mathematician Christian Goldbach, who scribbled it in a letter to the famous mathematician Leonhard Euler in 1742. It states that every even number greater than two can be expressed as the sum of two primes (a prime is a number that is only divisible by itself and by 1, such as 7 and 13). For example, 18 equals 7 plus 11, and both 7 and 11 are primes. In general terms, N equals P1 plus P2. The conjecture is believed to be true but - and this is the crucial bit - nobody has come up with an absolute proof that it is true for all numbers. As Goldbach wrote: "That every even number is a sum of two primes, I consider an entirely certain theorem in spite of that I am not able to demonstrate it."
Supercomputers can check the conjecture's veracity, but only up to a point. The last computing milestone was in 1998, when the conjecture was found to hold true for every even number up to 400,000,000,000,000. But no amount of computing power could confirm it for every candidate number up to infinity. The key to that is an abstract proof, a mathematical sleight-of-hand that shows irrefutably that Goldbach, a mathematics professor in St Petersburg who went to Moscow as tutor to the family of Tsar Peter II, got it right.
Faber has stipulated that the proof must be submitted to a respectable mathematical journal within two years of the book's publication next week, and published within four years. A panel of world-renowned mathematicians will be appointed to decide whether the proof is valid (Faber is refusing to disclose the panel's names, for fear that they will be flooded with letters from amateurs). The publishing house will not have to fork out - it has spent a five-figure sum to insure itself. "Now that we are insured, I'd love it if someone won," says Toby Faber, who insists that the challenge is more than a stunt.
So who could scoop the loot? While the conjecture sounds simple enough, it is virtually impossible that anyone other than a top mathematician will be able to do it. And there are estimated to be only a handful of men (there are shockingly few women at the loftiest echelons in mathematics) who could navigate the appropriate intellectual waters. These are the number theorists, the few brilliant thinkers who are at home in the invisible, intangible and downright baffling world of numbers. One name that crops up repeatedly is that of Alan Baker, a Cambridge University professor and Fields medallist. Fields medals, the highest honour a mathematician can receive, are awarded every four years to outstanding mathematicians under 40 (there is no Nobel prize for mathematics). So, is he the man for the job?
"You can never tell what will happen," Baker says, when I tell him that he is a favourite contender. He is in two minds about whether the proof is possible within the forseeable future, let alone within two years - the relevant mathematical techniques seem too primitive to present a way forward. But he doesn't rule it out. He points out that Chen, a Chinese mathematician, made some headway in 1966.
Chen proved that every even number is the sum of one prime, plus a number that is the product of two primes. So, for example, 18 is equal to 3 plus (3 X 5). That is like saying that N equals P1 plus (P2 X P3). It seems close to Goldbach's conjecture (N equals P1 plus P2), but nobody has managed to bridge the gulf during the intervening three decades. Baker sums up: "That is the best result so far, and it is unlikely that we will get any further without a big breakthrough. Unfortunately there is no such big idea on the horizon. But if we get that big idea, then we have something to build on."
Perhaps the money will jolly things along a bit? Baker shows himself to be a true man of numbers: "I don't think the money makes much difference. If people do it, they will do it for the challenge."
Ian Stewart, a mathematics professor at Warwick University and Britain's best-known popular writer on mathematics, disagrees. "I think some mathematicians will be dazzled by a million dollars," he says. It just might tilt the balance." While Stewart is pessimistic that the prize will be claimed, he notes that the pure mathematics of number theory is populated by solitary geniuses who can sometimes stun the Establishment. "It could well be a loner who gets this," he says.
The reason that nobody wants to say never is Fermat's Last Theorem, which stood for 350 years before crumbling in the face of a determined effort by Andrew Wiles, a shy, gifted Briton who now resides at Princeton University (sadly, he was too old to qualify for a Fields medal). So, perhaps Goldbach will give up its secrets too. More importantly, the story of Wiles's seven-year quest to provide the proof for the theorem, originally scribbled in the margins of a page, captivated the book-buying public. Simon Singh's sensitive account became a bestseller, continuing a trend started by Stephen Hawking's A Brief History of Time and Dava Sobel's Longitude. Since then, publishers have been chasing permutations of the same dead-cert formula - take one man, preferably an eccentric genius, add an obscure problem, a sprinkling of science or maths, and watch the money roll in. Even mathematicians considered lost in the mists of time have been resurrected for the cause - biographies of Paul Erdös (The Man Who Loved Only Numbers, by Paul Hoffman) and John Nash (A Beautiful Mind, by Sylvia Nasar) are early, readable examples. Now my shelves are groaning with stories about Charles Darwin, Charles Babbage (who invented computing), Ada Lovelace (Byron's daughter and Babbage's muse), Gregor Mendel (the father of genetics), Dmitri Mendeleyev (who thought up the periodic table), Galileo's daughter. The protagonist need not even be a person - there have been several "biographies" of pi and of zero. Even Hollywood has fallen in love with numbers - Good Will Hunting featured Matt Damon as a janitor-turned-genius.
Doxiados, 46, who graduated with a maths degree from Columbia University at 18 and now writes novels and plays in Greece, is simply continuing the lucrative tradition. He admits that his agent was "staggered" by Faber's advance to an unknown, foreign author; Uncle Petros and Goldbach's Conjecture, which centres on a man who devotes his life to searching for a proof, has already been translated into 15 languages.
The glamour of numbers extends beyond publishing. Carol Vorderman may not have been top of her maths class at Oxford but her head for figures has made her Britain's highest-paid woman television presenter. Stewart says that she has helped to overhaul the image of mathematicians: "Here is a woman who feels comfortable with mathematics, and an attractive one at that.
"I have noticed how things have changed at dinner parties. Twenty years ago, if people found out I was a mathematician, they would say, 'Ooh, I was never any good at maths at school'. Now start talking to me about fractals.
"People have got used to the occasional bit of maths cropping up here and there. It amused me to see in the newspaper a formula for dunking biscuits, because it was on a news page and not on the science page. People realise that mathematics is actually quite a respectable human activity." In fact, Stewart is in so much demand as a public speaker that Warwick University has released him from his undergraduate teaching commitments to continue his media work.
Numbers are not just proving popular for bedtime readers. The number of teenagers opting to read mathematics at university is also rising. Professor Chris Budd, who deals with undergraduate admissions to Bath University, says: "A lot of them say they have been inspired by reading books such as Fermat's Last Theorem. I think we are moving into a golden age."
That is making the few at the top of the profession extremely covetable. Some months ago, rumours were circulating in the mathematical community about Professor Simon Donaldson, revered for a stunning piece of mathematics that he produced at the age of 25 (a Fields medal followed four years later). He had been signed up, it was whispered, for a six-figure salary by Imperial College London. That would make him the highest-paid university mathematician in the country.
Donaldson will not disclose his salary but says it is "not astronomical".
Observers note that securing a top-flight professor such as Donaldson is a move likely to pay for itself because he will attract better researchers, who will earn a higher research rating (Imperial's mathematics department earned a rating of 5 but is still beaten by Oxford and Cambrige, which have earned 5* ratings). And moving one rung up the research ratings ladder could bring in up to £500,000 extra a year. In that light, doubling a professor's salary seems like sound business sense.
As for the prize, Doxiadis holds out some hope that the million dollars
will be claimed: "Yes, I know that Andrew Wiles took seven years to do
his proof of Fermat's last theorem. But if you had laid a bet even one
day before Wiles announced his proof, and said you thought it would be
solved within a few years, you would have been called crazy. Sometimes
things just come out of the blue."