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Summary: The obsession called mathematics
Review: I thoroughly enjoyed reading this book and could not put it down for even a moment.The books is the story of "two generations of obsession", the one is Uncle Petros' quest (more literally an obsession) for the solution to a mathematical problem, the other his nephew's search for the truth about his elusive uncle his family derides for having thrown away his life. What makes mathematicians tick, what drives them, their obsessions etc?. Uncle Petros' obsession "Goldbach's conjecture" is but a passing reference. The book is fun, and Uncle Petros' meetings with Caratheodory,Hardy,Littlewood,Ramanujam,Godel and Alan Turing make interesting reading. I was reminded about Andrew Wiles' assault on Fermat's last theorem (Simon Singh's book on Fermat's last theorem is strongly recommended!) Why did Uncle Petros squander away his whole life on Goldbach's conjecture?. Why did he eventually give up (or did he?) and why did he persuade his nephew to stay away from math?. This book should provide you with some partial answers.
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Summary: WHICH IS MORE IMPORTANT;TRUTH OR PROVABILITY?
Review: MAGNIFICANT BOOK.GODLE'S STATEMENT IS KNOWN TO BE TRUE-BUT UNPROVABLE.TRUE(PROBABLY) IN THE SENSE OF TARSKY(IT IS A THESIS,LIKE THE TURING THESIS,THAT THIS SENSE OF TRUTH COINCIDES WITH THE MATHEMATICIAN'S SENSE OF A TRUE THEOREM).HENCE IT FOLLOWS THAT IF GOLDBACH'S CONJECTURE IS UNDECIDABLE(OR EVEN NOT FORMALLY REFUTED IT IS TRUE.AFTER ALL GODEL's PAPER IS TITLED "FORMALLY .....".THE ARGUMENT GOES AS FOLLOWS:ASSUME NO FORMAL DISPROOF OF GOLDBACH.THEN IF WE EVER DID COME ACROSS A PRIME,NO MATTER HOW,THAT IS NOT THE SUM OF TWO PRIMES;THEN WE HAVE A TWO LINE FORMAL DISPROOF OF GOLDBACH.HENCE NO SUCH PRIME CAN EXIST.SO THERE MAY NOT BE A PROOF,BUT IF NO DISPROOF,GOLDBACH IS TRUE.THIS REASONING DOES NOT APPLY TO TWIN PRIMES,THE CONTINUUM HYPOTHESIS, NOR P=NP.SO THE (joke) INFIDEL MATHEMATICIAN DESIRES MORE THAN TRUTH, HE WANT'S PROOF.READ THIS BOOK.
Rating:
Summary: Outstanding
Review: One of the best books on the mathematical culture and the mathematical "passion".
Written as a novel makes it easy to read.
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Summary: Greek Tragedy without the Gods:
Review: Or rather, with the gods reborn in psychological terms as our inner motivators and inhibitors. At its simplest, this is a short, well written, light, detective story. It is a little like Sherlock Holmes, a set of stories read by Uncle Petros, with Mathematics as an environment rather than a subject. If taken at this level it is an enjoyable read that should have a wide audience. However, it is a multifaceted novel. For me it has its origins in Ancient Greece, its heart in the theme of 'Pride" (hubris) and is constructed in terms of Greek Tragedy, complete with protagonist (Uncle Petros) / antagonist (unnamed nephew narrator). It has all the intensity and economy needed to make a wonderful opera. There are many allusions to the myths, philosophy and history of Ancient Greece. Pythagoras, his mathematics (especially his opinion of the number 2 and the Pythagorean idea of rules imposing limits on the unlimited) and his views on beans seem to lie behind a several of the book's images. Plato is specifically referred to and the location of much of the story in Uncle Petros's semi-rural cottage is reminiscent of the original Academy. Of the myths, Oedipus is central: The solving of the sphinx's riddles (the second riddle, about two sisters, links with Petros's dream), Oedipus being destroyed by 'truth', his apotheosis at Colonus all have parallels in the novel. There are references to more recent literature and other arts forms: The choice of Isolde (Wagner's Eros driven opera), as the name of Petros's only human love is typical - and Hamlet, complete with ghost, make an appearance too. All this is treated with a light hand, there to be seen and enjoyed but not essential to understanding (unlike, for example, in TS Eliot!). Another major facet is an exploration of creativity and originality. Apostolos Doxiadis clearly demonstrates the visual imaging many great thinkers experience (Kekule and the tail-biting snake being a classic example) and reflects contemporary views on dreams and the role of the sub/unconscious. The book looks at the social and political consequences of original creativity: The tremendous self belief and lack of doubt needed to drive the mind to real creativity; the politics surrounding the individual in institutions and the need for peer recognition; the isolation from the family and the way we define "self". Scattered through the book are characters driven 'mad' by too close a knowledge of the pure form - the sad image of Kurt Godel in the 'shabby', 'genteel', Oppenheimer created Institute of Advanced Study is quite horrifying in some respects. Other real mathematicians appear, all 'The Greats' bent from the norms of the society they lived in in some way, all seeking immortality, a place in the museum of mathematics. The book opens with the bold claim (in a quote) that mathematicians have a greater chance of immortality than poets: It ends in the 'poetic' First Cemetery of Athens with Goldbach's Conjecture engraved, as a poem, on Uncle Petros's grave stone.
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Summary: A charming small novel
Review: Short, simple, and totally engaging. Just the thing to have with you on a trip, or to sit down with for a pleasant afternoon.
Rating:
Summary: A charming small novel
Review: Short, simple, and totally engaging. Just the thing to have with you on a trip, or to sit down with for a pleasant afternoon.
Rating:
Summary: An elegy on elusiveness
Review: This "anti-heroic" novel is centered around a man's changing attitudes toward the passion of his life: the man happens to be a Greek mathematician with a distinguished -- for a while -- career in early twentieth century Germany; and his passion is no other than an unsolved problem that even elementary school kids could understand (but not necessarily comprehend): is every even number the sum of just two odd numbers none of which is the product of smaller odd numbers? The Greek mathematician, Petros Papachristou, is fictional, but the problem, known as Goldbach's Conjecture, is very real and still (June 2000) unsolved, perhaps even unsolvable. This last word, "unsolvable", is indeed the novel's keystone: to most people it means "something that themselves, and possibly others as well, cannot solve", but to mathematicians it may also mean "something that cannot be solved" or, in more mathematical language, "something that cannot be decided"; more to the point, a mathematical problem is "undecidable" when its solution is elusive not because of the potential solvers' insufficient talent, effort or knowledge, but rather because of its "inner structure". Wonderfully, the first and most famous example of such an "undecidable" statement comes straight out of plane geometry and the world's second most read book, Euclid's "Elements": is it true for every straight line L and every point P not on L that there exists exactly one straight line that is parallel to L and passes through P at the same time? [If you think that the answer is an obvious "yes", imagine our universe as a sphere and then start thinking what "straight lines" and "parallel lines" on that sphere ought to be...] Papachristou's personal tragedy is precisely that he invested so much of himself on a goal that was not only extraordinarily ambitious, but quite likely profoundly unattainable as well: he worked on a mathematical problem that might have been, or even be, undecidable rather than merely unsolvable. Moreover, he started pursuing his goal at a time that it was not clear to him (or anyone else) how plentiful unattainable goals are: indeed it was only in 1930 that Czech mathematician Kurt Goedel (a real person!) stunned the world by proving that every mathematical system and theory (be it built on numbers or lines or whatever) hides deep inside it undecidable questions; that is, Euclid's undecidable "postulate" was far from an isolated "accident" in our intellectual history... Shattered by Goedel's discovery, Papachristou the brilliantly successful (but increasingly withdrawn) mathematics professor turns into "Uncle Petros": a social oddity living alone on family inheritance in an Athenian suburb, and visited by disapproving relatives every June 29 (his "name day"). But one of those visiting relatives is an angel (or devil?) of sorts, a young, bright nephew with a developing passion for Mathematics, completely unaware of his uncle's complicated past in the field (which is a sad story for the entire family): Uncle Petros feels obliged to discourage him from pursuing Mathematics by employing Goldbach's Conjecture in a sinister manner, and that's where the story begins to unravel... Skillfully, Doxiadis, himself withdrawn from a potentially brilliant career in mathematics, builds his novel around the parallel mathematical orbits of uncle and nephew and their encounter with the infamous problem. The emphasis is on human struggle and disillusionment rather than the mathematics itself, which, with the exception of Goedel's "philosophical" theorem, is kept on the story's periphery and on an intentionally, some times even naively so, accessible level. Another mathematical prodigy, a Brooklyn Jew mastering the immensely complicated field of Algebraic Topology in the novel's backstage, is cleverly thrown into the story as an unanticipated link between uncle and nephew. Those familiar with Doxiadis' first novel, "Parallel Lives" (1985, in Greek), may not be surprised by the novel's ending: Uncle Petros is eventually led back to his life's failed passion by his nephew's unforeseen love of mathematics ... in about the same way a random encounter involving a third person brings back to the "Parallel Lives"' old Christian ascetic his own youth's elusive goal (and very reason for his withdrawing into the Arabian desert) -- a beloved, unfaithful, much repented wife ravaged by old age... One story is centered around mathematical truth, the other one around Christian faith, but one thing Doxiadis seems to warn us about in both is that, long after we have shattered and buried the statues of our youth, the broken marbles may one day resurface to adorn our coffin...
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Summary: An exhilarating read!
Review: This book was a gift from a friend, and now he's a better friend! I have not enjoyed a book as much as I did this one in a long time. I am not a book critic nor a mathematician (although the subject and those who invent and create it certainly fascinate me) but the writing style was superb and the subject matter extremely interesting. The story craftily developed Uncle Petros' character and made you need to keep reading to hear his story. This was a fun book that can and should be enjoyed by all.
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Summary: We could be Zeroes...
Review: This is a highly stimulating novel about the mathematician as artist, following the trend laid down by 'Fermat's Last Theorem'. Moreover, it is attractive to watch artists suffering, as Petros Anargyros does here. For Petros dares solve Goldbach's Conjecture... This Conjecture states that "EVERY EVEN NUMBER GREATER THAN TWO IS THE SUM OF TWO PRIMES". This is an apparently simple mathematical problem, yet it has remained unsolved for two hundred and fifty years. The delight of this novel is that it seems to go over all the options in layman's terms. Doxiadis has chosen an excellent problem, in my view, for a mathematical novel, since Goldbach's Conjecture is a literary quandary as well as a numerical one. Indeed, math seems to have started off in language. I do have some literary complaint about Doxiadis though: he makes Petros more romantic than his successful peers, and the narrator writes his account in the style of a math paper. Goldbach's Conjecture may as well be a cryptic crossword clue (very apt in the case of one of the mathematicians Doxiadis mentions), with the answer lying in the body of the question. At first glance, it seems very appropriate that 2 (the only even prime), is mentioned in the conjecture. After all, it's common sense that there can only even be one even prime. If there was an even prime number larger than 2, then it could be divided by 2, and therefore it could not have been prime in the first place. Whenever I do a review of a novel, I'm also reviewing the novelist, trying to find out what makes them tick. I think that it's suitable to apply the same methods to Goldbach. Who was he? Why did he use these particular words? My task is slightly more difficult here, since Goldbach didn't write his conjecture in English, and adapted it from the time that he first mentioned it in a letter to Euler. But the grammar of the conjecture still gives us clues, and insights into his mind. Part of the conjecture is that "EVERY EVEN NUMBER IS THE SUM OF TWO PRIMES" with 2 being an exception, since 1 isn't a prime. This is true for 2+2=4, 3+3=6, 5+3=8, 7+3=10, 7+5=12. However, for even number 14, you can have both 11+3=14, or 7+7=14. This trend for having more than a single set of primes creating an even number continues beyond 14. This is probably what lies at the heart of Goldbach's Conjecture: he speculated that the bigger the even number, the more likely it would be that he was correct, since the number of chances would multiply. In this way, it seems, Goldbach's conjecture is very much dependent on the 'unnatural' operation of multiplication (as Petros sees it). He and Euler both knew and wrote about Fermat's work on chance. For Goldbach, this meant that he could quite happily make his conjecture, because the chances of his being proved wrong were so small. However, this is too simplistic. It is not true to say that the higher the even number, the higher the number of pairs of primes which constitute it. Therefore, this is where some doubt comes in to play, since it does not follow that the biggest even number ever created will have the largest number of prime number pairs in its construction. However, there does seem to be a pattern in the allocation of pairs. This is important, because it shows that prime numbers are not just random occurrences. The unwritten principle behind the Eratosthenes' Sieve, which Petros uses, is that prime numbers are predictable. Petros also mentions that Euclid proved that prime numbers are infinite. I want to go further and say that ALL PRIME NUMBERS ARE INFINITELY PREDICTABLE - which is probably why Doug Lenat's AM programme found Goldbach's Conjecture so boring. This is where Kurt Godel comes into Petros' story. His 'Incompleteness Theorems' state that some current mathematical problems can never be resolved, which is linked to his 'undecidability theorem'. Much of the drama in Doxiadis' novel comes from this disclosure. So, many mathematicians believe Goldbach to be unsolvable, because we are never going to be able to check every even number. Nevertheless, these mathematicians could take a lesson from literature and Doxiadis. There is left a certain element of doubt at the end of 'Uncle Petros', but there is also definite closure. What I'm saying is that it is not the numbers that are uncertain: it is we who have doubts. This is where the human factor comes into mathematics. If we want certainty in mathematics, then it is up to us to create that certainty. Could we not create new axioms? Do we want to be positive or negative? So, I say that Goldbach's Conjecture is true because it has been proved on the finite stage many times. I want to move the burden of proof away from 'we don't know whether this is true' to 'we know this to be true because it has not been proved otherwise'. Therefore, Goldbach's Conjecture is more likely to be true than most conjectures made today, because it has survived two hundred and fifty years without being disproved. Fermat's Last Theorem was a similarly famous problem, which Andrew Wiles proved positively after an even longer period of time. It is somewhat appropriate to include a time factor here, since Goldbach was an historian, as well as a mathematician. Geometry may well tell us all we need to know about a three dimensional sphere, but can it tell us how long that sphere may last? (Is there a math of entropy?). Time has been an important factor in the development of math, with some ideas lasting thousands of years, whilst others are instantly dismissed. Time, like math and language, is an artificial construct, which we have created in order for us to make some sophisticated sense of the world. We start from the finite, and head for infinity when we choose.
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Summary: Math story without equations = delight!
Review: This is a thoroughly enjoyable story with the ring of "fact" to it. The fact that its central character is actually the world of higher mathematical theorists should deter no one - there are almost no equations even mentioned in the book and none you need to be able to read, much less understand! This is an engaging story of a boy and his family relationships, particularly with his wunderkind uncle, who was a semi-successful and obsessed theoretician. It plays out against the competitiveness of the world of genius, the basest motives of very human beings, love of family, and modern European history. It plays out very well, I might add. Read this one and feel good, satisfied intellectually, and know that an excellent novelist is at work behind it all. It does add up.....
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