Although I, for one, would be reluctant to wager real money on whether a unified theory of physics will be discovered before the decade is out, or on whether the mind-body problem will be dispatched by the end of the century, others are more daring. A member of the Lloyd’s of London insurance syndicate, for example, has recently bet that a certain mathematical conjecture will not be proved before 15th March 2002.
The proposition-Goldbach’s conjecture-is one of the oldest unsolved problems in mathematics. It was first stated in a letter which Christian Goldbach (1690-1764)-a Prussian maths enthusiast who served as tutor to Peter II, the teenage tsar of Russia-sent in 1742 to the great mathematician Leonhard Euler. Goldbach had noticed that any even number he examined could be written as the sum of two prime numbers. (A number is prime if it has no divisors other than itself and 1.) Thus, for example, the even number 24 can be written as the sum of 11 and 13, which are both primes. Perhaps, Goldbach idly guessed, this is true for all even numbers. Euler responded that it probably was, but he had no idea how to go about proving it.
Although it is not of central importance to mathematics, the conjecture has captured the imagination of many mathematicians, professional and amateur, because of its seeming simplicity. Recently, it caught the eye of Apostolos Doxiadis, a Greek film and theatre director who studied mathematics at Columbia University and the Ecole Pratique des Hautes Etudes. His novel, Uncle Petros and Goldbach’s Conjecture, was published in Greece in 1992-on the occasion of the 250th anniversary of Goldbach’s conjecture. Earlier this year, it was published in Britain by Faber and Faber and in the US by Bloomsbury. To promote the novel, these two publishing houses came up with a good gimmick: they would give a prize of $1m to anyone who could achieve the feat that obsesses the novel’s protagonist-prove Goldbach’s conjecture. They stipulated that the proof must be submitted by March 2002 and published in a “reputable” mathematics journal by March 2004.
But what if someone out there actually succeeded in doing this? To indemnify themselves against that ruinous possibility-$1m is still a lot of money in the book trade-the publishers went to Lloyd’s of London. There they found an underwriter who was willing to take on this contingent liability-for a fee, of…