Book of the week

31st March 2000 at 01:00
Uncle Petros and Goldbach's Conjecture. By Apostolos Doxiadis. Faber pound;9.99

It is no longer fashionable to boast of innumeracy. Soon mathematicians will be courted at A-list gatherings and encouraged to stun the assembled celebs with their exquisite little problems. This slim novel from a writer previously unknown outside Greece (now translated into 15 languages) offers the non-mathematician of any age a gap in the clouds through which to gape at the intellectual Mount Olympus of the number theorist, and could appeal to a mathematically inclined teenager who is usually unwilling to read fiction.

It has the pace of a cloak-and-dagger thriller with its red herrings, crushing setbacks and cunning stings, but also contains a witty, touching analysis of family dynamics and speculation on the nature of genius.

Petros Papachristos, whose life is blighted by his pursuit of a seemingly unattainable breakthrough (the proof of Goldbach's Conjecture), his "most favoured of nephews" (the narrator) and the other family members are fictional characters. Uncle Petros's obsession is real, as are the other great early 20th-century mathematicians that he encounters (among them G H Hardy, J E Littlewood and Srinivasa Ramanujuan at Cambridge, and Kurt Godel, the Austrian whose Incompleteness Theorem brings about Petros's professional and emotional collapse).

Goldbach's Conjecture is a puzzle scribbled in a letter in 1742 from a historian and mathematician, Christian Goldbach, to a more famous mathematician, Leonard Euler. 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 1: such as 2, 3, 5, 7 and so on). Goldbach's Conjecture has never been proved up to infinity (only to 400,000 billion, by computer) and Faber is now offering a million dollars to a mathematician who can do it within two years of publication of Uncle Petros.

The crucial point of Doxiadis's tale is not whether Uncle Petros got there or not, but whether he could show that he did. Scholarship does not count without peer validation, and the process of validation means overcoming natural feelings of envy and mistrust.

Uncle Petros's labours on the foothills of Olympus, and his small successes on the way, remain largely uncredited because terror of being overtaken by collegues means that he clutches his interim findings to his chest instead of publishing them. By the time his young nephew reaches the top of his high school mathematics class, Petros has been burnt out and bitter for around half a century, playing chess and tending his sour grapes on the outskirts of Athens. The uncle-and-nephew relationship eventually becomes an intermittently loving one, but the love has to fight its way through games of deceit, trickery and revenge. The disappointed man counters the boy's naive enthusiasm for his subject with jealous cruelty, setting him the "unsolvable" conjecture as a holiday project and taunting him over his inevitable failure. He makes the nephew pledge to give up further study in mathematics, assuming that this will prevent him finding out that he has been duped. But the sort of friendly fellow student that Petros never had helps the younger man to retaliate, and his uncle gains enough respect for him to tell him his story.

Petros is born at the end of the 19th century into a family that is both dazzled by his abilities and terrified of the despair that they generate. His two younger brothers grow up in his shadow to do well in business and patronise the mad professor. The narrator's father's fury at his son's association with the despised uncle springs from decades of resentment, sorrow at the failure of Petros's grand schemes and fear that his son will be lost to the same cause. "The Secret of Life is always to set yourself attainable goals," he tells the boy. Unlike today's high-flying young mathematician Sarah Flannery, interviewed in Friday magazine last week, Petros and his nephew do not find the family a good source of support or the right kind of mentor.

Petros belongs to a breedof genius that is often caricatured in fiction: isolated, cranky, bad at everyday human relationships. Doxiadis makes the caricature human in showing how the isolation crept in and how it could have been beaten off. The irritable uncle may be simply aproduct of his generation: technology means thattoday's geniuses can communicate with like-minded souls, however lofty the peaks on which they have placed themselves.

GERALDINE BRENNAN Fancy a shot at Faber's million dollars? The Prime Pages website will show you what you're up against: www.utm.eduresearchprimesglossaryGoldbachConjecture.html

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