Uncle Petros and Goldbach’s Conjecture

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Goldbach’s Conjecture (GC) was first stated in 1742, in a letter written by the minor mathematician Christian Goldbach (tutor to the Czar’s children) to the great Swiss mathematician Leonard Euler. A conjecture in mathematics (as in real life) means a statement that, although suspected to be generally valid, has not been proven. Goldbach, in his letter, pointed out to Euler his observation that “every whole number greater than six seems to be the sum of three primes”. He checked it against thousands of cases and always found it to be true – but the whole numbers being infinite, only an abstract proof would cover the general case. This he could not find.

Euler immediately noticed that this statement – if true – breaks up into two:

a) Every even number is the sum of two primes.
b) Every odd number is the sum of three primes.

Today, the former is known by mathematicians as “Goldbach’s Conjecture” while the latter is known as “the second”, the “other” or the “weaker” GC.

The second GC was proven in the mid 1930’s by the great Russian number theorist, Ivan Vinogradov. But the first, or GC plain and simple, (“every even number greater than 2 is the sum of two primes”) has still to be cracked, even though some of the world’s greatest mathematicians have tried their hands at it.

Because of its notorious difficulty, GC is not the kind of problem that attracts many top class researchers today. Few people want to waste years and years working on a problem that in all probability they will not solve. Mathematics, like all scientific disciplines, is ruled by expediency and fashion, and the classical problems of number theory are not currently deemed ‘à la mode’. One more reason that a major breakthrough with GC seems unlikely in the foreseeable future.

The closest anyone has come to proving GC is a theorem of 1996 by the Chinese mathematician Chen Jing-Run. It proves that “every even number greater than 2 is the sum of a prime and an almost prime – ‘almost prime’ meaning a composite number that has at most two factors.” Although this may sound extremely close to GC, unfortunately there is no obvious step from one to the other.
Goldbach’s Conjecture
- Goldbach Conjecture Research (Mark Herkommer, Nov. 23, 1998)
- The Prime Glossary (Article on Goldbach’s Conjecture)
- Goldbach’s Conjecture (The Mac Tutor on Goldbach’s Conjecture)
Mathematicians & Biographies
- Kurt Gödel attended school in Brünn, completing his studies in 1923. He is best known for his Incompleteness Theorem. TIME Magazine has recently declared him to be the leading figure in mathematics in the twentieth century.
- G H Hardy was a pure mathematician who hoped his mathematics could never be applied. However in 1908, near the beginning of his career, he formulated a law describing the proportions of dominant and recessive genetic traits that would be propagated in a large population. Hardy considered it unimportant but it has proved of major significance in the study of blood group distribution.
- John Edensor Littlewood is best known for his collaboration with G H Hardy on summability, function theory and number theory.
- Srinivasa Ramanujan a poor clerk from India with little formal education, was one of the world’s great mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.
- Alan Turing held that computers would in time be programmed to acquire abilities rivaling human intelligence. His work was fundamental in the theoretical foundations of computer science.
- Andrew Wiles is the man who managed to prove Fermat’s Last Theorem. He first published a proof in 1993 but a subtle error was discovered. Although too old by mathematical standards (40 years old), he gave it another go and managed to prove the Theorem a year later.
- The Mac Tutor History of Mathematics Site contains the biographies of more than 1100 mathematicians, accessible from a selection of alphabetical or chronological indexes.
- Constantin Carathéodory considered to be the greatest modern Greek mathematician, made significant contributions to the calculus of variations, the theory of point set measure, and the theory of functions of a real variable.
More Mathematics
- Mathematics by Topic contains a host of links covering all the major areas of mathematics. In each section there are links to electronic journals, websites, databases and other relevant material.
- The American Mathematical Society was founded in 1888 to further mathematical research and scholarship. The Society currently has approximately 30,000 members throughout the United States and around the world. It fulfils its mission through programs that promote mathematical research, increase the awareness of the value of mathematics to society, and foster excellence in mathematical education.
- The Prime Pages contain links to a number of sites relating to Prime Numbers, including articles and programmes useful in proving primality.
- The Number Theory Web is an attempt to use the resources of the World Wide Web to collect and disseminate online information of interest to number theorists everywhere.
- Scientific American -
  ‘Petros Papachristos is…the invention of Apostolos Doxiadis. But the story of his life is enriched with so many authentic details from history in general and from science in particular that one feels tempted to look him up in a biographic dictionary. Doxiadis manages to keep the reader’s attention until the tragic end…’
- Booklist -
  ‘delightful and original…Although framed by math, the Uncle Petros story easily extends interest beyond the scientific minded.’
- Publishers Weekly -
  ‘intriguing debut…Doxiadis keeps the story engaging by focusing on the development of two compelling characters…the novel is captivating.’
- Kirkus Reviews -
  ‘An intellectual thriller that manages to convey the high drama and excitement involved in the pursuit of an answer to a mysterious…mathematical theorem…Delightful, fun, well-conceived and nicely executed.’
- Lexis -
  ‘Reads like a fascinating adventure story. Doxiadis has given to literature the mysterious, arcane and sometimes tragic world of abstract mathematics.’
- William Wall – Irish Examiner -
  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…
- Eric Wittmershaus – Flakmagazine -
  With “Uncle Petros & Goldbach’s Conjecture,” first-time author Apostolos Doxiadis has put together a stunning synthesis of mathematics and make-believe. In the grand tradition of science novels…
- J.A. – Barcelona Review -
  Greek author Doxiadis wrote this novel in 1992 and updated it slightly for the 2000 publication in English. It’s a delight to have it in translation at last because this is a riveting good story about pride, obsession and – gulp – mathematics…
- Professor Demetrios Christodoulou, Princeton University -
  ‘Uncle Petros offers many glimpses of the great superreal world of mathematical ideas, a world of eternal truths and of unspeakable beauty.’
- Professor Ken Ribet, University of California, Berkeley -
  ‘A compelling portrait of a talented young mathematician.’
- Sir Michael Atiyah, winner of the Fields Medal and world-renowned mathematician -
  “‘It is brilliantly written—a mathematical detective story of great charm—and it certainly succeeds in capturing much of the spirit of mathematical research.’
- 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…
- El Pais -
  ‘Doxiadis invites us into the universe of Number Theory, he gives us a glimpse of what the mathematical profession and community during the first decades of the 20th century was like and introduces us to fascinating persons, such as the mathematicians Hardy, Ramanujan, Turing and Godel. Above all, he introduces us to the subterranean, psychological world of mathematical thought and …continue reading…
- Jean-Michel Kantor – La Recherche (in French) -
  Enfin un livre qui parle de science et qui se devore comme un roman policier – un roman policier mathematique. C’est un recit plein de charme et de suspense qu’a ecrit Apostolos Doxiadis, homme de theatre et industriel grec forme aux mathematiques…
- Sophie Ratcliffe – The Times -
  “GREAT LOVES are often born of loneliness”, and this, the narrator concludes, is the case with his uncle’s affair with numbers. Petros has spent a lifetime searching for Goldbach’s Conjecture…
- Lawrence Goldstone – Miami Herald Tribune -
  At first blush, one could hardly think of a more dry and uninviting premise for a novel. But along comes applied-mathematics-student-turned film-maker, Apostolos Doxiadis, who with Uncle Petros and Goldbach’s Conjecture has given us a fascinating, captivating, intellectual joy ride…
- Bruce Schechter – New York Times -
  For those who want to be millionaires but shudder to contemplate facing a smirking Regis Philbin as he asks, “Is that your final answer?” the publishers of “Uncle Petros and Goldbach’s Conjecture,” a novel by Apostolos Doxiadis offer a challenging alternative…
- Polly Shulman – Newsday -
  BOY MEETS GIRL, perhaps; girl meets girl or boy, boy; occasionally boy or girl may even find perfect happiness with dog or horse: As a rule, love stories treat relationships among the animate. But “Uncle Petros & Goldbach’s Conjecture” describes a passion wholly of the mind…
- Keith Devlin – The MAA Online book review column -
  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 Ecole Pratique des Hautes Etudes in Paris…
- Nicholas Lezard – The Guardian -
  It is a matter of some concern over and above the purely literary when a publisher, in whom the present reviewer has to declare an interest, announces that it is prepared to give away a cool $1 million. And all the more so when, in the last financial year, it made a profit of only £256,000, a sum I had thought perfectly respectable until announcement of this damn fool publicity stunt was made…
- Geraldine Brennan – Times Educational Supplement -
  It is no longer fashionable to boast of innumeracy. Soon mathematicians will be courted at A-list gatherings and encouraged to stun the assembled celebs with their exquisite little problems. This slim novel from a writer previously unknown outside Greece (now translated into 15 languages) offers the non-mathematician of any age…
- Gilbert Adair – The Independent -
  In a letter to Leonhard Euler, dated 7 June 1742, Christian Goldbach, a not especially eminent mathematician, speculated that every even number greater than 2 was the sum of at least one pair of primes (a prime being an integer divisible solely by itself and 1). Thus 10 = 7+3, 32 = 13+19, 84 = 67+17, ad infinitum. To the great Euler, it probably seemed a trifling puzzle not worth racking his brain over…
- John Allen Paulos – ABCNEWS.com -
  One generally doesn’t speak the words “prime numbers” and “seven-figure prizes” in the same breath.
  
  But don’t tell that to the publishers of “Uncle Petros and Goldbach’s Conjecture”, an engaging first novel by Greek author Apostolos Doxiadis. The Story Behind the Math…
- Jane Shilling – The Times -
  One of the most attractive developments of the literature of the Nineties was the rapprochement between the arts and the sciences. A series of humane and graceful texts appeared whose purpose was to convey to an audience with no special scientific or mathematical competence some of the beauty and resonance of those subjects…
- George Steiner – The Observer -
  Pure maths is so technical that few have dared to use it as vehicle for fiction. Until Apostolos Doxiadis arrives with Uncle Petros and Goldbach’s Conjecture…
- Michael Frayn, author of Headlong and Copenhagen -
  ‘I very much enjoyed Uncle Petros and Goldbach’s Conjecture, and read it through compulsively to the end.’
- John Nash, Nobel Laureate, 1994, subject of A Beautiful Mind -
  ‘Paints a fascinating picture of how a mathematician could fall into a mental trap by devoting his efforts to a too difficult problem.’
- Oliver Sacks, M.D. -
  ‘A mathematical conjecture unsolved for two centuries; a mathematical genius uncle driven mad trying to solve it; an ambiguous relation with a mathematically-minded nephew; and acute human observation all come together in Uncle Petros to make a very funny, tender, charming and, to my mind, irresistible novel.’
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