Doxiadis, Apostolos;
Uncle Petros and Goldbach's Conjecture [Greek 1992: Theios Petros kai i Eikasia tou GoIbach]
Faber & Faber, 2012, 224 pages
ISBN 057129569X, 9780571295692
topics: | math | fiction |
A story of mathematicians, told from a fictional viewpoint of a mathematician's nephew. The mathematician in question, Uncle Petros, spends his entire life fruitlessly searching for a proof to a three century old problem.
The author is himself an amateur mathematician and filmmaker, who was admitted to Columbia U mathematics after an original paper at the age of 15.
Petros Papachristos is a mathematician who has devoted his life to proving a 250 year old conjecture:.
in a letter [to Euler] written in 1742, the minor mathematician Christian Goldbach brings to the attention of the great Euler a certain arithmetical observation. the Goldbach conjecture states that every even number greater than two is the sum of two primes. The story is narrated from the p.o.v. of Petros's nephew, who has grown up in the knowledge that his uncle has been a failure. But when he discovers that his Uncle had been a well-respected, Cambridge-trained mathematician, the nephew's image of Uncle Petros changes.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean. - GH Hardy, A Mathematician's Apology --- Father [with a scowl]: "Son, do you know the secret of Life?" I: No, I don’t. F: The Secret of Life is always to set yourself attainable goals. They may be easy or difficult, depending on the circumstances and your character and abilities, but they should always be at-tai-na-ble! In fact, I think I’ll hang your Uncle Petros’ portrait in your room, with a caption: EXAMPLE TO BE AVOIDED!" -p.21 What fascinated me was that the kindly, withdrawn and seemingly unassuming uncle of mine was in fact a man who, by his own deliberate choice, had struggled for years on end at the outermost boundaries of human ambition.... While his brothers were studying and getting married, raising children and running the family business, wearing out their lives along with the rest of nameless humanity in the daily routines of subsistence, procreation and killing time, he, Prometheus-like, had striven to cast light into the darkest and most inaccessible corner of knowledge. p.21 At last I understood the meaning of the sign at the entrance of Plato’s Academy : oudeis ageometretos eiseto – ‘ Let no one ignorant of geometry enter’. The moral of my evening emerged with crystal clarity : mathematics was something infinitely more interesting than solving second-degree equations of calculating the volumes of solids, the menial task at which we laboured at school. Its practitioners dwelt in a veritable conceptual heaven, a majestic poetic realm totally inaccessible to the un-mathematical hoi-polloi. p.25
[after UP explains Euclid's proof that there are an infinite number of primes] I: It's so simple. Uncle Petros : ..sometimes things appear simple only in retrospect." UP: Never forget it: Mathematicus nascitur non fit – A mathematician is born, not made. If you don’t carry the special aptitude in your genes, you will labour in vain all your life and one day you will end up a mediocrity. A golden mediocrity, perhaps, but an mediocrity nevertheless. 31 "He who is fated to drown will never die in bed." p.60 Anybody who claims that scientists – even the purest of pure, the most abstract, high-flying mathematicians – are motivated exclusively by the Pursuit of Truth for the Good of Mankind, either has no idea what he’s talking about or is blatantly lying. Although the more spiritually inclined members of the scientific community may indeed be indifferent to material gains, there isn’t a single one among them who isn’t mainly driven by ambition and a strong competitive urge. A mathematician’s declared intention, when embarking on an important research endeavor, may indeed be the discovery of Truth, yet the stuff of his daydreams is Glory. p.77-8 "You know the popular saying that the three conditions impossible to conceal are a cough, wealth and being in love? Well, to me there is a fourth: mathematical gift." 153 Mathematics, Petros had taught me, is a field that acknowledges only its greatest; this particular kind of natural selection offers failures as the only alternative to glory. 164 The amalgam of Truth and Beauty revealed through the understanding of an important theorem cannot be attained through any other human activity, unless it be (I wouldn’t know) that of mystical religion. … Yes, it had made the existence of the Ideal slightly more believable, even tangible. 167
Kurt G\"odel's insanity -- for unquestionably he is in a certain sense insane -- is the price he paid for coming too close to Truth in its absolute form. ... People like him have surpassed the common measure; they've come to know more than is necessary to man, and for this hubris they have to pay. - mathematics student and friend Sammy, p.163 The proverbial 'mad mathematician' was more fact than fancy. I came increasingly to view the great practitioners of the Queen of Sciences as moths drawn towards an inhuman kind of light, brilliant but scorching and harsh. Ramanujam, Hardy, Turing, G\"odel and so many others were too enamoured of the brilliant light: they got too close, scorched their wings, fell and died. - p.166 Seeing [Uncle Petros] helped me keep alive that part of the self that most people lose, or forget about, with adulthood -- call it the Dreamer or the Wonderer or simply the Child Within. 168
from http://www.tau.ac.il/~corry/publications/articles/Narrative/main3.html (review with photos of mathematicians, and much mathematical history): [part 3 of a larger review of narrative in mathematical fiction] the reliability of the story is further supported by the fact that a prominent Greek mathematician, who indeed was professor at the great Berlin school of mathematics, is the advisor of the fictional Petros. There could be no better choice in terms of coherence and internal logic of the story. Nevertheless, a factual problem arises here: Carathéodory arrived in Berlin only in 1918! Does this deviation from strict historical truth matters in any possible sense? Most readers will not even be aware of this rather marginal detail, to begin with, and in any case, this could provide a classical example of poetic license taken by an author that no reader would bother protesting about. Not only it provides no sudden reason for giving up suspense of disbelief, but, as already said, it actually serves very well the plot and plays an actual role in helping put forward a coherently and convincing story. One might perhaps claim that the plot should have been conveniently modified on behalf of historical exactness in this case, but there is no real reason to complain about the poetic license taken by the author. Let us look at a second, interesting place where the plot deviates from the historical record, while providing further support to the plot. In a dialogue between the narrator and his uncle Petros, reference is made to a famous lecture presented by David Hilbert at the occasion of the 1900 Paris International Congress of Mathematicians. This dialogue is meant to provide a glimpse into the way that absolute certainty was expected to pervade mathematics at the turn of the twentieth century, which was also the attitude that guided Petros in his own mathematical activities. Hilbert is presented as the champion of this view, as embodied in two famous sayings quoted by the narrator: "Wir müssen wissen, wir werden wissen" (we must know, we shall know), and "there is no ignorabimus in mathematics". Thus the narrator says: "Thus spake the great David Hilbert in the International Congress of 1900. A proclamation of mathematics as the Heaven of Absolute Truth. The vision of Euclid, the vision of Consistency and Completeness…" Well, there are some problems in this description of what Hilbert said at that opportunity, and the most immediate one concerns the "Wir müssen wissen, wir werden wissen". These words, later engraved in Hilbert's tombstone, were not part of the Paris address, but rather of a talk given in 1930 at a meeting in Königsberg to honour Hilbert on the occasion of being awarded the honorary citizenship of his native town.
Hilbert also broadcasted a speech in the local radio (which was recorded and later made available on a 45 record and recently digitalized). It is in that speech that his famous words appear, as the closing sentence that encapsulates Hilbert's legendary, unbridled feeling of scientific optimism. It is a remarkable coincidence that Hilbert gave this speech during a week in which four mathematical meetings were simultaneously held in Königsberg. In one of those meetings Kurt Gödel presented for the first time his first incompleteness theorem. The results developed by Gödel came to imply a serious blow to the program that Hilbert had been promoting for more than ten years now to prove the consistency of arithmetic by finitary methods. But neither in Königsberg in 1930 nor ever thereafter, Hilbert and Gödel met or listened to each other's talk. "The story is so dramatic that it resembles fiction", has remarked Gregory Chaitin commenting this situation. In Königsberg while Hilbert was declaring "Wir müssen wissen, wir werden wissen", Gödel was speaking about inherent limitations in mathematical knowledge. We tend naturally to consider a situation of this kind more likely to be fiction than historical reality. At any rate, what Hilbert did say in his 1900 speech was not very far away in spirit from what came to be engraved in his tombstone. He thus said: This conviction of the solvability of any mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem, seek its solution. You can found it by pure reason, for in mathematics there is no ignorabimus.
http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/doxiadis.htm-- In the tradition of Fermat's Last Theorem and Einstein's Dreams, a novel about mathematical obsession. Petros Papachristos devotes the early part of his life trying to prove one of the greatest mathematical challenges of all time: Goldbach's Conjecture, the deceptively simple claim that every even number greater than two is the sum of two primes. Against a tableau of famous historical figures--among them G.H. Hardy, the self-taught Indian genius Srinivasa Ramanujan, and a young Kurt Godel--Petros works furiously to prove the notoriously difficult conjecture, but suddenly disappears into a solitary existence playing chess in the Greek countryside. To his nephew, he is known as the solitary, eccentric Uncle Petros, but when the young man finds out that his uncle is an esteemed professor of mathematics, he searches out his uncle's hidden past. Through an adversarial friendship based on chess and mathematics, he drives the retired mathematician back into the hunt to prove Goldbach's Conjecture... but at the cost of the old man's sanity, and perhaps even his life. Uncle Petros and Goldbach's Conjecture is an intellectual adventure, a story of proud genius and the exhilaration of pure mathematics. It is about the search for truth at all costs, and the heavy price of finding it.
http://www.maa.org/publications/maa-reviews/uncle-petros-and-goldbachs-conjecture 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.) 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. --- Apostolos Doxiadis received a Bachelor's Degree in Mathematics from Columbia University and a Master's Degree in Applied Mathematics from the cole Pratique des Hautes Etudes in Paris. He has run a number of successful computer companies, as well as written and directed for screen and stage. The second of his two feature films, Tetriem, won the prize of the International Center for Artistic Cinema at the 1988 Berlin International Film Festival. Doxiadis lives in Athens, Greece. ---blurb Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.
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