# Leonoor Broeder – Volkskrant

Anyone letting slip in literary company that they have never heard of Shakespeare or Mozart, will be regarded rather pityingly and undoubtedly viewed as an uncultured person. Anyone announcing that they know little or nothing about mathematics, physics or chemistry need have no fear for their reputation. More than that: a one-sided interest in arts subjects sometimes actually seems to enhance a person’s image as a culture lover. For some, the fine arts are simply diametrically opposed to the exact sciences.

In addition to this prejudice, one sometimes finds among researchers in the humanities a blind admiration for and a certain fear of the natural sciences. That leads in turn to another opposition: on the one hand snob appeal, which helps popular books in the field of mathematics and physics (whether or not written by charlatans) become bestsellers, and on the other the conviction that the field is completely inaccessible for non-initiates.

Uncle Petros and Goldbach ‘s Conjecture, by the as yet little-known Greek mathematician and writer Apostolos Doxiadis, refutes this complex of opinions and prejudices and is at the same time an unpretentious, gripping and moving novel. Not that the book sets out to refute anything, but the flow of the argument leads automatically to the conclusion that the aesthetics of pure science have more in common with creative art, music and poetry than is often thought. In addition it turns out that a sense of that beauty can be communicated to people with virtually no training in mathematics and unable to grasp the full implications of mathematical problems and solutions.

As the title indicates, the story hinges on one of the greatest mathematical challenges of all time, ‘Goldbach’s Conjecture’, formulated in 1742. The conjecture posits that every even number is the sum of two prime numbers. (A prime number is divisible only by 1 and by itself, and by no other number. The number 64, for example, is the sum of 17 and 47, and 11 and 53.) Uncle Petros is a reclusive old man who lives in a suburb of Athens and fills his days by playing chess and working in his garden. He is sternly lectured by his two younger brothers, successful entrepreneurs who have taken over the family business from their father. They regard him as an abject failure.

A curious nephew discovers that Uncle Petros was a renowned professor of mathematics. Years later he finds out that his uncle devoted his life to the search for a proof of Goldbach’s Conjecture, which for three centuries has defied every attempt to find one. Gradually an ambivalent relationship develops between Petros and his nephew, which is of decisive influence on the career of the young man and the twilight years of the older one.

Petros’ search takes him from the ancient Greek mathematicians to the great mathematicians of the Enlightenment – Fermat, Euler and Gauss – and brings him into personal contact with the mathematical greats of the twentieth century: the theoreticians Littlewood and Hardy from Cambridge, the Indian Ramanujan, Alan Turing and Kurt Gödel. The story of Petros’ lifelong struggle with the mathematical problem and the way in which that struggle becomes bound up with his nephew’s life, is narrated largely in dialogue form and despite the high degree of difficulty has great élan. The open ending, not surprising yet not predictable either, is characteristic of the impressive simplicity of the narrative.

The strength of Uncle Petros lies mainly in the in the concentration and clarity of the dialogues.

In them mathematical problems are presented extensively but never exhaustively, and quite a few contradictions are exposed. Step by step one is inducted into the at once tantalisingly simple and elusively complex world of pure mathematics.

In the first instance this makes one realise that the mind of a mathematician in fact most resembles that of an artist, a composer, a poet. That emerges from the underlying notion that everything in mathematics is regarded as provable. The proof is seen as something that already exists and simply needs finding, like the key that you know has been lost in a particular area and hence can be found there.

Another comparison that looms is that of the sculptor who has only to extract the statue already contained in the stone, or of the composer who writes down music he can already hear. The conviction that brilliant mathematicians are ‘born and not made’ and that there is no such thing as a mediocre mathematician, only great and failed mathematicians, also fits in with this view.

Through the way in which you are carried along on the search you experience, almost physically, the extent to which mathematics is a closed world of its own. It is a non-empirical science that contains its own truth and does not need the real world for explanations and proofs. That makes it a mysterious realm too, separate from reality. The mystical experiences with which virtually all famous mathematicians turn out to be familiar, and a few of which Uncle Petros describes, can only emerge in such a realm. They are most reminiscent of religious experiences or delusions. Seen in this light it is not surprising that many so brilliant mathematicians, including Uncle Petros himself, but also Hardy, Gödel and Turing, should have been not only completely unworldly, but should have finally gone insane or taken their own lives.

Uncle Petros also makes it painfully clear that the world of mathematicians is also a very ordinary one, in which such sentiments as personal ambition, jealousy, pride and revenge are driving forces. For example, Petros decides not to publish a number of important partial discoveries he has made in the course of his monomaniacal research – although he is aware that they may make him world famous – for fear that colleagues might be able to deduce that he is working on the proof of Goldbach’s Conjecture. In searching for pure truth he is also driven by the craving for personal triumph, perhaps even the quest for immortality.

The news of the death of the exceptionally gifted Ramanujan (he died of TB at the age of 32 in a Madras slum) fills Petros with sadness, but also with joyful excitement, because his ‘phenomenal brain was no longer in the arena of number theory’. The motives that lead the uncle to advise his nephew against studying mathematics, certainly also contain elements of revenge. That is no less true of the motive that prompts the nephew to take his uncle back in his old age to the core of the mathematical problem that has both shaped and ruined his life.

Is it stating the obvious to assume that mathematicians will enjoy Uncle Petros and Goldbach ‘s Conjecture more than non-initiates? Perhaps. Mathematicians can follow the complicated calculations and supplement what the novel omits or touches on in passing. But part of the message will probably be more fascinating for those without than for those with a mathematical background.

**Leonoor Broeder – Volkskrant **