Apostolos Doxiadis

UNCLE PETROS AND GOLDBACH'S CONJECTURE

It is difficult to bring about a successful blend of mathematics and fiction; indeed, not many people have attempted it. However, Doxiadis, who is himself a mathematician, has brought it off brilliantly here.

The core of the book is the story of the narrator's uncle, the eponymous Petros. He is a reclusive, living just north of Athens (in a district I know well, as it happens, which makes the whole thing all the more vivid for me). Shunned by his brothers as a failure who threw away his position as a professor in Germany, he is in fact a mathematician of near-genius who has been acquainted with some of the most famous figures in twentieth-century mathematics (Hardy, Ramanujan, Gödel). As a young man he became obsessed with the challenge of trying to prove Goldbach's Conjecture. This is one of the great unsolved problems in mathematics and, unlike most others of the kind, it can be stated quite simply: every even number greater than 2 is is the sum of two primes. If he could prove it, Petros would be recognized as one of the greatest mathematicians of all time. However, he failed, and the consequent sense of disappointment destroyed his life.

A complex relationship, sometimes affectionate, sometimes resentful, and evolving over many years, develops between uncle and nephew. Inspired by their conversations, the nephew decides to become a mathematician himself; Petros tries to dissuade him, and finally sets him the notorious Goldbach challenge as a test, though without disclosing that this is what it is. The nephew fails, of course, but goes to the USA to study mathematics anyway, furious with his uncle for the trick he played on him. But in the end he finds he has not the talent or the wish to do original mathematical research and so he returns to Athens and goes into the family business with his father.

Now more mature, the young man resumes his contact with his uncle and persuades him to relate the story of his quest for the proof. This forms a substantial part of the book. Some discrepancies in his uncle's account, however, continue to puzzle the narrator. Just as he thinks he has finally reached an understanding of the whole affair, there occurs an unexpected and dramatic climax, which it would spoil the book for readers to divulge here.

Some readers might be put off by the thought of a novel centred on mathematics, but this would be a pity, for there is never the least suggestion of didacticism in the writing and no need to struggle with mathematical theorems while reading. Ultimately, this is a love story: Uncle Petros is in love with mathematics, which replaces the love of women for him. In a significant detail, while he is trying to prove the Conjecture he has nightmares in which a pair of beautiful girls keeps turning away from him; they symbolize an important pair of numbers. This reflects the nature of the paradox at the heart of Petros's subject. Mathematics, the most profoundly intellectual of all human activities, is pursued by its devotees with a possibly unrivalled intensity of emotion until it becomes an all-consuming obsession.

12 August 2003