This "anti-heroic" novel is centered around a man's changing attitudes toward the passion of his life: the man happens to be a Greek mathematician with a distinguished -- for a while -- career in early twentieth century Germany; and his passion is no other than an unsolved problem that even elementary school kids could understand (but not necessarily comprehend): is every even number the sum of just two odd numbers none of which is the product of smaller odd numbers? The Greek mathematician, Petros Papachristou, is fictional, but the problem, known as Goldbach's Conjecture, is very real and still (June 2000) unsolved, perhaps even unsolvable.
This last word, "unsolvable", is indeed the novel's keystone: to most people it means "something that themselves, and possibly others as well, cannot solve", but to mathematicians it may also mean "something that cannot be solved" or, in more mathematical language, "something that cannot be decided"; more to the point, a mathematical problem is "undecidable" when its solution is elusive not because of the potential solvers' insufficient talent, effort or knowledge, but rather because of its "inner structure". Wonderfully, the first and most famous example of such an "undecidable" statement comes straight out of plane geometry and the world's second most read book, Euclid's "Elements": is it true for every straight line L and every point P not on L that there exists exactly one straight line that is parallel to L and passes through P at the same time? [If you think that the answer is an obvious "yes", imagine our universe as a sphere and then start thinking what "straight lines" and "parallel lines" on that sphere ought to be...]
Papachristou's personal tragedy is precisely that he invested so much of himself on a goal that was not only extraordinarily ambitious, but quite likely profoundly unattainable as well: he worked on a mathematical problem that might have been, or even be, undecidable rather than merely unsolvable. Moreover, he started pursuing his goal at a time that it was not clear to him (or anyone else) how plentiful unattainable goals are: indeed it was only in 1930 that Czech mathematician Kurt Goedel (a real person!) stunned the world by proving that every mathematical system and theory (be it built on numbers or lines or whatever) hides deep inside it undecidable questions; that is, Euclid's undecidable "postulate" was far from an isolated "accident" in our intellectual history...
Shattered by Goedel's discovery, Papachristou the brilliantly successful (but increasingly withdrawn) mathematics professor turns into "Uncle Petros": a social oddity living alone on family inheritance in an Athenian suburb, and visited by disapproving relatives every June 29 (his "name day"). But one of those visiting relatives is an angel (or devil?) of sorts, a young, bright nephew with a developing passion for Mathematics, completely unaware of his uncle's complicated past in the field (which is a sad story for the entire family): Uncle Petros feels obliged to discourage him from pursuing Mathematics by employing Goldbach's Conjecture in a sinister manner, and that's where the story begins to unravel...
Skillfully, Doxiadis, himself withdrawn from a potentially brilliant career in mathematics, builds his novel around the parallel mathematical orbits of uncle and nephew and their encounter with the infamous problem. The emphasis is on human struggle and disillusionment rather than the mathematics itself, which, with the exception of Goedel's "philosophical" theorem, is kept on the story's periphery and on an intentionally, some times even naively so, accessible level. Another mathematical prodigy, a Brooklyn Jew mastering the immensely complicated field of Algebraic Topology in the novel's backstage, is cleverly thrown into the story as an unanticipated link between uncle and nephew.
Those familiar with Doxiadis' first novel, "Parallel Lives" (1985, in Greek), may not be surprised by the novel's ending: Uncle Petros is eventually led back to his life's failed passion by his nephew's unforeseen love of mathematics ... in about the same way a random encounter involving a third person brings back to the "Parallel Lives"' old Christian ascetic his own youth's elusive goal (and very reason for his withdrawing into the Arabian desert) -- a beloved, unfaithful, much repented wife ravaged by old age... One story is centered around mathematical truth, the other one around Christian faith, but one thing Doxiadis seems to warn us about in both is that, long after we have shattered and buried the statues of our youth, the broken marbles may one day resurface to adorn our coffin...
