Although Uncle Petros remained expressionless, I noticed a slight tremor run down his hand. "Who's spoken to you about Goldbach's Conjecture?" he asked quietly.
"My father," I murmured.
:And what did he say, precisely?"
"That you tried to prove it."
"And.... that you didn't succeed."
His hand was steady again. "Nothing else?"
"Hm," he said. "Suppose we make a deal?"
"What sort of deal?"
Intrigued? Then read on.
Uncle Petros and Goldbach's Conjecture is a recent English translation of a 1992 Greek novel. The author -- and I'll say this at the start since, if you're like me, you're very reluctant to read a novel about a mathematician written by an author who knows little about mathematics -- received a bachelors degree in mathematics at Columbia University and a masters degree in applied mathematics at the École Pratique des Hautes Études in Paris. He has directed several computer companies and has written and directed for both the cinema and the stage. Thus, rest assured, not only does he get the math bits correct, he can write fiction as well. Indeed, through the medium of a fictional story, he manages to convey the nature of pure mathematics, the passion that can drive a mathematician to work for years on a seemingly irrelevant problem, and the single-minded dedication it can take to see the project through to its end -- or not, as the case may be. (Of course, for dramatic effect the obsession displayed by Uncle Petros is somewhat greater than is the case with any mathematicians I have met -- and that includes Andrew Wiles -- so, as with the hero in the movie Pi, it is not clear that nonmathematicians who read the book will view mathematics as an attractive pursuit, or mathematicians as completely sane. But most nonmathematicians probably think that already anyway.)
The book is really the story of two generations of obsession, the one a quest for the solution to a mathematical problem, the other a young man's search for the truth about the uncle his family shuns and derides for having thrown away his life.
The story is told in the words of the young nephew, who has just completed his own mathematics degree. He discovers that his Uncle Petros Papachristos, whom he has known hitherto solely as a reclusive gardener his father refuses to talk about, was a child prodigy in mathematics, the youngest ever professor of mathematics at the University of Munich, and at one point a collaborator of Hardy and Littlewood. (Ramanujan, Gödel, and Turing also make cameo appearances in the novel.)
In the spirit of Andrew Wiles' assault on Fermat's Last Theorem (the novel was completed long before Wiles announced his proof, by the way), Uncle Petros locked himself away in seclusion to work on trying to prove Goldbach's Conjecture that every even number is the sum of two primes. (In fact -- and I suspect this will also come as a surprise to many readers of this review -- as I learned from the novel, the problem as originally stated by Goldbach in his famous 1742 letter to Euler is to show that every integer is the sum of three primes. The more familiar -- and obviously equivalent -- version is due to Euler.) In so doing, Petros throws away what had been all set to be a successful career in academic mathematics. But who among us cannot at least appreciate the rationale Uncle Petros provides his nephew: that if you think you have a chance of true greatness as a mathematician, say, in the spirit of Euler, it would be a waste to settle for being simply "good."
But why did Uncle Petros eventually give up altogether, and why did he try to persuade his talented young nephew not to pursue mathematics? Was it, as the nephew surmises, that he developed a technique that might lead to a solution, but lacked the courage to put his entire life's work on the line and follow his idea through to the end? Would the nephew's interest prompt Uncle Petros to having one last try? And if it did, what would be the outcome. The pace picks up exponentially as the novel approaches its climactic end.
It's a fun read. To quote directly from the cover of Nicolaus Copernicus's classic De revolutionibus (see the March edition of Devlin's Angle, elsewhere on this website) my advice is to "buy, read, and enjoy."
As part of their effort to promote this book, Bloomsbury (the American publisher of Uncle Petros and Goldbach's Conjecture) and Faber and Faber (the British publisher) have announced a $1 million prize for the first person to prove Goldbach's Conjecture within the next two years. See the announcement on the Faber and Faber web site.