And, to sum up…
by William Wall

The quest comes in all shapes and sizes. Arthur (and Monty Python) went in search of the Holy Grail. Don Quixote tilted at windmills in his bid to put the world to rights. Mathematicians have their grails too: the great David Hilbert identified 23 in the early part of the last century. One or two of his quests proved fruitful and one or two turned out to be labyrinthine dead ends.

The quest in question follows a well-known genre. Those familiar with The Hobbit and The Lord of The Rings will know, by instinct, that the hero will face seemingly insurmountable problems, great danger and frequently dragons. He will find the friendship of true knights and will be betrayed by false ones. That is the essence of Uncle Petros and Goldbach’s Conjecture; a quest for one of the Holy Grails of science.

The conjecture of the title is a deceptively simple looking problem — every even number greater than 2 is the sum of two primes — but one whose proof has eluded the greatest mathematical minds. However, no mathematical knowledge is required to enjoy this delightful book, the proof of the pudding being that this particular reviewer is a perfect plonker as regards anything more advanced than sums, not to mention the letter x or anything in the Greek line.

The novel can, and should be, enjoyed as the beautifully written story of a man obsessed by numbers. The mathematics has no greater importance than, say, the biology of dragons in Tolkien’s work. However, professionals in the field will be intrigued.
Seen through the eyes of a young man, the “most favoured” of Uncle Petros’ nephews, the narrative opens with the family myth of the old man’s failure. Uncle Petros, it seems, was a good for nothing who let the family down and betrayed his own genius. But when the narrator learns that the catastrophe in question is nothing less than his failure to prove the most difficult of all mathematical problems, he begins to see him as a kind of latter day Don Quixote in search of the impossible dream.

Petros becomes a romantic figure in the boy’s mind and he determines to follow his uncle into the numbers game. Naturally all kinds of obstacles come in the way. There are scientific dragons, temptations, cunningly laid traps, and immense sacrifices to be made.
Delightfully, the plot hinges, not on the sudden appearance of a dragon or a false knight, but on two theorems, of which the second is the so-called Incompleteness Theorem of Kurt Gödel. In this brilliant piece of logic Gödel proved that there are some theories that can never be proved despite the cutest mathematical stroke pulling and thus reiterates the appalling thought that it will never be possible to fill in all the gaps in the number line. This revelation is what finished Uncle Petros. His own quest for personal glory kept him from publishing his earliest work and sees him the brunt of an unfair reputation.

The cold fusion scandal of some years ago was a similar case of overweening ambition. Good reason then to be proud that our country can produce people like Sarah Flannery who published her strong encryption system rather than secretly patenting it. Such idealism is, alas, rare and Uncle Petros And Goldbach’s Conjecture is a cautionary tale for modern science.

William Wall is a novelist and poet. His most recent book is Alice Falling.

April 15, 2000: William Wall – Irish Examiner