81. Leaderboard - Goldbach's Conjecture Leaderboard Goldbach s conjecture. To update your score, click on your score,or if you are not on the list, use the Update score link on the top of http://terje.perlgolf.org/wsp/pgas/score.pl?func=score&hole=41&season=1

82. Goldbach's Conjecture And that s why it is called a conjecture , my friends. A conjecture is a statementthat you think is probably true, at least based on all the information http://www.trottermath.net/numthry/goldbach.html

and his Conjectures Here's an "oldie but goodie" for you this time! Some time long ago a mathematician, named C. Goldbach, was playing around with prime numbers and noted the following oddity: All even numbers, greater than 2, can be expressed as the sum of two primes. This is really a simple idea, as these few examples will show: So what's so hard about that, you ask? Well, just try proving that it is true for ALL even whole numbers! There's the rub. Ever since Goldbach made this observation, mathematicians, professional and amateur alike, have tried to do that. But with no real success. And that's why it is called a "conjecture", my friends. A conjecture is a statement that you think is probably true, at least based on all the information at hand. But a "for sure" proof is not available. You see, it is not enough, as in a case like the one before us, to just say, "See! All the even numbers I've tested so far can all be expressed as the sum of a pair of primes. So all of them must behave the same way." Mathematics doesn't work that way. So where do we go from here, you ask? Well, one of my favorite activities for my students is to ask the question:

83. Encyclopedia: Goldbach's-conjecture Other descriptions of Goldbach sconjecture. In mathematics, Goldbach s conjectureis one of the oldest unsolved problems in number theory and in all of http://www.nationmaster.com/encyclopedia/Goldbach's_conjecture

Supporter Benefits Signup Login Sources ... Pies What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates List of songs with the word "song" in their title or lyrics List of songs whose title appears more than twenty times in the lyrics List of sexual slang List of sets of unrelated songs with identical titles#Rn_Rz ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: Goldbach's-conjecture Updated 7 days 21 hours 55 minutes ago. Other descriptions of Goldbach's-conjecture In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: This article describes some currently unsolved problems in mathematics. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Every even integer greater than 2 can be written as the sum of two primes . (The same prime may be used twice.) For example

84. Uncle Petros And Goldbach's Conjecture ºÒ§µÍ¹ ªÑé¹Ë¹Ñ§Ê×Í ªÇ¹ä»ÍèÒ¹ ¤×¹à×͹ ªÑé¹Ë¹Ñ§Ê×Í Uncle Petros and Goldbach sconjecture. book, UNCLE PETROS and GOLDBACH S conjecture Apostolos Doxiadis http://faylicity.com/book/book1/fstpetros.html

Uncle Petros and Goldbach's Conjecture UNCLE PETROS and GOLDBACH'S CONJECTURE : Apostolos Doxiadis One Every family has its black sheep - in ours it was Uncle Petros. My father and Uncle Anargyros, his two younger brothers , made sure that my cousins and I should inherit their opinion of him unchallenged. 'That no-good brother of mine, Petros, is one of life's failure,' my father would say at every opportunity. And Uncle Anargyros, during the family get-togethers from which Uncle Petros routinely absented himself, always accompanied mention of his name with snorts and grimaces expressing disapproval, disdain or simple resignation, depending on his mood. However, I must say this for them: both brothers treated him with scrupulous fairness in financial matters. Despite the fact that he never shared even a slight part of the labour and the responsibilities involved in running the factory that the three inherited jointly from my grandfather, Father and Uncle Anargyros unfailingly paid Uncle Petros his share of the profits. (This was due to a strong sense of family, another common legacy.) As for Uncle Petros, he repaid them inthe same measure. Not having had a family of his own, upon his death he left us, his nephews, the children of his magnanimous brothers, the fortune that had been multiplying in his bank account practically untouched in its entirety. Specially to me, his 'most favoured of nephew' (his own words), he additionally bequeathed his huge library which I, in turn, donated to the Helleinic Mathematical Society. For myself I retained only two of its items, volume seventeen of Leonard Euler's

85. Powell's Books - Uncle Petros And Goldbach's Conjecture: A Novel Of Mathematical Fermat s Last Theorem collides with Sophie s World in this novel of intellectualadventure and the exhilaration of pure mathematics http://www.powells.com/cgi-bin/biblio?inkey=17-1582341281-1

86. The Edge Online: Books. Apostolos Doxiadis -- Uncle Petros And Goldbach's Conjec Uncle Petros and Goldbach s conjecture Apostolos Doxiadis Faber trd pbk, 211pgs, £9.99 since reissued as a £6.99 Faber paperback http://www.theedge.abelgratis.co.uk/bookscd/unclepetros.htm

The Edge Index Uncle Petros and Goldbach's Conjecture Apostolos Doxiadis Faber trd pbk, 211 pgs, £9.99 since reissued as a £6.99 Faber paperback Review by Gerald Houghton (2000) "Every even number greater than 2 is the sum of two primes." Doxiadis' novel is as much a reader in rudimentary number theory as a sustained narrative, purporting to tell the story of Uncle Petros through the admiring eyes of his young Greek nephew. The Papachristos family don't usually talk about their black sheep, the former prodigy who gave it all away in a fit of hubris, determined to prove one of the last great mathematics puzzles, Goldbach's Conjecture. And failed. Doxiadis' storytelling is clumsy and his dialogue leaden. But that really isn't the point. His book is in love with mathematics and mathematicians, and with the "material for tragedy" that the form so often offers. He conspires to bring Petros to both Munich and Cambridge in the early part of the century, and to have him cross theoretical swords with real figures like the brilliantly incisive Indian mathematician Srinivasa Ramanujan (dead in his early thirties), and Alan Turing, the father of modern computing who was himself hounded to an early grave because of his homosexuality. If you don't make an impact in the field by your fourth decade, we're told, then you're a numerically spent force. "The psychological make-up of the true mathematician is closer to that of the poet or the musical composer," Doxiadis writes as Petros engages in his "Sisyphean task". His pursuit is beauty, although it's one as much driven by arrogance as purity. Failure was complete and humiliating. Doxiadis has little to offer in his writing, but in finding a compelling way in which to promote popular science

87. BookHq: Uncle Petros And Goldbach's Conjecture: A Novel Of Mathematical Obsessio Compare 24 bookstores with 1 click. Save! Why pay more? Search for new and usedbooks, college textbooks for all subjects, medical/medicine/law included. http://www.bookhq.com/compare/1582341281.html

Home Login Register Help Search: by ISBN # by Keyword Link directly to this book using: http://www.bookhq.com/compare/1582341281.html Book Information Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession Edition:n/a Pages: Book Format: ISBN:1582341281 Date Published:December2000 Publisher:Bloomsbury USA Remember to bookmark bookHq! Ctrl-D Tell your friends too! Qty: books in your list. View book list Pistachio Biscotti Search will take a maximum of 15 seconds. Problem? Retry the search. Click on the retailer name or the total to go directly to the book Best Price New : $3.25 @ Alibris Used : $0.75 @ Amazon US BookHq Listed : none Results Click on the Retailer name or the Price to buy the book Retailer Type Price Tax Total Avl + Ship = Total Notes Amazon US Used Enter your zipcode for availability information, the total price. zipcode: Half.com Used Abebooks.com Used Alibris New Powells Used TextbookX New eCampus New Walmart New Amazon US New Club* New Blackwells US New Powells New This book is not available in : Amazon CA Amazon UK Blackwells UK Chapters ... PickABook UK Search 24 bookstores with 1 click!

88. Birmingham Words - Uncle Petros And Goldbach's Conjecture Uncle Petros and Goldbach s conjecture. Apostolos Doxiadis. Faber and Faber 2000ISBN 0571202039. Mathematics does not seem the most promising subject for http://www.birminghamwords.co.uk/index.php?option=com_content&task=view&id=335&I

89. Uncle Petros Excerpt English edition to Uncle Petros and Goldbach s conjecture. Uncle Petros Goldbach sconjecture. From Uncle Petros and Goldbach s conjecture http://www1.greece.gr/CULTURE/Literature/UnclePetrosExcerpt.stm

Home Culture Literature English edition to Uncle Petros and Goldbach's Conjecture From Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis , pp. 64-67 (US edition) 'Every even number greater than 2 can be written as a sum of two primes.' 'You surely can't prove that', said the famous mathematician. 'Not yet,' answered Petros, 'although I'm sure it's a general principle. I've checked it up to 10,000!' 'What about the distribution of the prime numbers? Caratheodory asked. 'Can you figure a way to calculate how many primes there are lesser than a given number n?' 'No,' answered Petros, 'but as n approaches infinity the quantity gets very close to its ratio by the natural logarithm.' Caratheodory gasped. 'You must have read that somewhere!' 'No, sir, it just seems a reasonable extrapolation from my tables. Besides, the only books at my school are about geometry.' The Professor's previously stern expression now gave way to a beaming smile. He called Petros' father inside and told him that to subject his son to two more years of high school would be a complete waste of precious time. Denying his extraordinarily gifted boy the best that mathematical education had to offer would be tantamount, he said, to 'criminal negligence'. Caratheodory would arrange to have Petros immediately admitted to his university - if his guardian consented, of course.

90. Count On - The Sum Newpaper If you don t know what Goldbach s conjecture is, see the box below. In 1998,Goldbach s conjecture was shown by computer to be true for even numbers up http://www.counton.org/thesum/issue4/sunbottom.html

Prize Sparks Goldbach Fever PUBLISHING giant Faber and Faber is offering a prize of one million dollars to anyone who can prove the theory known as Goldbach's Conjecture within the next two years. The offer is part of the publicity drive for a new book by a Greek mathematician and author Apostolos Doxiadis called Uncle Petros and Goldbach's Conjecture in which a man dedicates his life to the challenge. The book has already been translated into 15 languages and Faber has high hopes of it becoming a bestseller, given the recent success of stories about great scientific quests like Dava Sovel's Longitude and Simon Singh's Fermat's Last Theorem. If you don't know what Goldbach's Conjecture is, see the box below. If you do, then there is a chance you may want to throw your hat into the ring and have a shot at the million dollar prize. Be warned though, the proof has to be published by a respectable mathematical journal within two years and proved correct by Faber's panel of experts. Faber has spent a five-figure sum insuring itself again a pay-out, but boss Tony Faber said he would be happy to hand over the prize. He said: "Now that we are insured, I'd love it if someone won."

91. Goldbach's Conjecture - Wikipedia, The Free Encyclopedia XGC movedAn eXtension of the Goldbach conjecture. Mathematica code. http://www.wikipedia.org/wiki/Goldbachs_conjecture

Goldbach's conjecture From Wikipedia, the free encyclopedia. (Redirected from Goldbachs conjecture In mathematics, Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics . It states: Every even integer greater than 2 can be written as the sum of two primes . (The same prime may be used twice.) For example, etc. Contents Origins Heuristic justification Rigorous results Trivia ... edit Origins In , the Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler in which he proposed the following conjecture: Every integer greater than 2 can be written as the sum of three primes. He considered 1 to be a prime number , a convention subsequently abandoned. So today, Goldbach's original conjecture would be written: Every integer greater than 5 can be written as the sum of three primes. Euler, becoming interested in the problem, answered with an equivalent version of the conjecture: Every even number greater than 2 can be written as the sum of two primes. The former conjecture is today known as the "ternary" Goldbach conjecture, the latter as the "strong" Goldbach conjecture. The conjecture that all odd numbers greater than 9 are the sum of three odd primes is called the "weak" Goldbach conjecture. Both questions have remained unsolved ever since, although the weak form of the conjecture is much closer to resolution than the strong one. edit Heuristic justification The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, at least for

92. Citebase - On Partitions Of Goldbach's Conjecture An approximate formula for the partitions of Goldbach s conjecture is derived A strong form of Goldbach s conjecture follows in the form of a lower http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:math/0010027

93. Number Theory Goldbach s conjecture and Integral Matrices. The order of a matrix, is the lowestpositive power that computes the identity matrix. So for example http://www.maths.uwa.edu.au/~john.bam/research/numtheory.html

Goldbach's Conjecture and Integral Matrices The order of a matrix, is the lowest positive power that computes the identity matrix. So for example has order 4 (html ain't so good at making matrices I'm afraid). We are concerned with the following question What are the possible orders of n x n invertible matrices with integer entries? Most people have heard of the Goldbach Conjecture . If you haven't, then you are missing out on the most amazing unsolved problem of mathematics. Goldbach conjectured in a letter to Euler that every number greater than 5 is the sum of three primes. Euler replied that this statement is equivalent to the conjecture "every even number greater than 2 is the sum of two primes". There has been good evidence for the following stronger conjecture which we call... The Strong Goldbach Conjecture: Every even number greater than 6 is the sum of two different odd primes. This is very cool. Grant Cairns, Devin Kilminster, and I have found that the following statement is equivalent to the Strong Goldbach Conjecture... For every even integer m greater than 4, there is an invertible integral matrix of size m with order a product of two different odd primes and no other invertible integral matrix of lesser size has this order.

94. Book Review %T Uncle Petros and Goldbach s conjecture %Ai Apostolos Doxiadis %I Faber andFaber Ltd %C London %D 1992, 2000 %G ISBN 0571-20511-9 %P 209 pp %K fiction http://www.accampbell.uklinux.net/bookreviews/r/doxiadis.html

Home Book Reviews Titles Authors ... Subjects Apostolos Doxiadis UNCLE PETROS AND GOLDBACH'S CONJECTURE It is difficult to bring about a successful blend of mathematics and fiction; indeed, not many people have attempted it. However, Doxiadis, who is himself a mathematician, has brought it off brilliantly here. The core of the book is the story of the narrator's uncle, the eponymous Petros. He is a reclusive, living just north of Athens (in a district I know well, as it happens, which makes the whole thing all the more vivid for me). Shunned by his brothers as a failure who threw away his position as a professor in Germany, he is in fact a mathematician of near-genius who has been acquainted with some of the most famous figures in twentieth-century mathematics (Hardy, Ramanujan, Godel). As a young man he became obsessed with the challenge of trying to prove Goldbach's Conjecture. This is one of the great unsolved problems in mathematics and, unlike most others of the kind, it can be stated quite simply: every even number greater than 2 is is the sum of two primes. If he could prove it, Petros would be recognized as one of the greatest mathematicians of all time. However, he failed, and the consequent sense of disappointment destroyed his life. A complex relationship, sometimes affectionate, sometimes resentful, and evolving over many years, develops between uncle and nephew. Inspired by their conversations, the nephew decides to become a mathematician himself; Petros tries to dissuade him, and finally sets him the notorious Goldbach challenge as a test, though without disclosing that this is what it is. The nephew fails, of course, but goes to the USA to study mathematics anyway, furious with his uncle for the trick he played on him. But in the end he finds he has not the talent or the wish to do original mathematical research and so he returns to Athens and goes into the family business with his father.

95. Student.math.hr - Èlanci Uncle Petros and Goldbach s conjecture is an inspiring novel of intellectual Goldbach s conjecture was first stated in 1742, in a letter written by the http://student.math.hr/clanci/clanci.html

Ovaj tekst je bio referat iz engleskog: nekakva vrsta recenzije na knjigu "Stric Petros i Goldbachova slutnja". Uncle Petros and Goldbach's conjecture 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. (G. H. Hardy, A mathematician apology) Apostolos C. Doxiadis was born in Brisbane, Australia, in 1953. He grew up in Athens, Greece. He was admitted to New York's Columbia University at the age of fifteen after submitting an original paper to the Department of Mathematics, and did postgraduate work in Applied Mathematics at the École Pratique des Hautes Etudes in Paris. Doxiadis also has directed for professional theatre and cinema, but his main activity is fiction writing. One of his books is ‘mathematical triller’ Uncle Petros and Goldbach's Conjecture, published in 1992. and translated into twelve languages. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, of proud genius and the exhilaration of pure mathematics. The book is fiction and it is written in I-personality. The writer is in the role of the nephew of main character, Petros Papachristos. Petros lives alone in a suburb of Athens, playing the odd game of 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 soon discovers, was once a celebrated mathematician. A brilliant mathematician who spent his life on solving a problem that wasn’t prooved for nearly three centuries called Goldbach’s conjecture.

96. Incompleteness Theorems. Related Results. By K.Podnieks Assume, you are a Platonist believing that Goldbach s conjecture is, Hence,if we could prove that Goldbach s conjecture is consistent with the axioms http://www.ltn.lv/~podnieks/gt6a.html

universal, formulas, statements, sentences, consistent, provable, Goldbach conjecture, Berry paradox, Goldbach, conjecture, paradox, Berry, incompleteness Back to title page Left Adjust your browser window Right 6.7. Consistent Universal Statements Are Provable Let us consider the famous Goldbach's Conjecture from 1742 by Christian Goldbach every even number greater than 2 can be expressed as a sum of two prime numbers . For example (the really interesting numbers are shown in bold), See also: Eric W. Weisstein . "Goldbach Conjecture." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/GoldbachConjecture.html Assume, you are a Platonist believing that Goldbach's Conjecture is, "in fact", true. I.e. if you take any even number n, it can be expressed as a sum of two primes. If it can, you can determine these two primes p + p = n simply by trying n = (n-3)+3, n=(n-5)+5, n=(n-7)+7, n=(n-11)+11, etc. up to n=k+k. Any particular true equality p + p = n, i.e. p times p times - n times can be proved in PA (see Exercise 3.4a

97. Buy UNCLE PETROS AND GOLDBACH'S CONJECTURE From Aarons Books Uk Looking for UNCLE PETROS AND GOLDBACH S conjecture by APOSTOLOS DOXIADIS? Buy ithere and get free delivery in the UK! http://www.aarons-books.co.uk/p/uncle-petros-and-goldbach-s-conjecture-057120203

Number of Items: UNCLE PETROS AND GOLDBACH'S CONJECTURE by APOSTOLOS DOXIADIS Title: BOUGUEREAU Purchase This Book An inspiring novel of intellectual adventure and the exhilaration of pure mathematics, this is also a story of the rivalry, antagonism and sense of impending failure which haunts those who pursue impossible goals. Should delight readers of 'Sophie's World', 'A Beautiful Mind' and 'Fermat's Last Theorem'. Huge review coverage guaranteed, one to watch! Author: APOSTOLOS DOXIADIS Published by: In: With: FABER AND FABER LTD paperback 224 pages Recommended Home View Basket New Titles Special Offers ... Privacy Aarons Books, c/o Black Books, PO Box 3875 Kidderminster, DY10 2WL

98. Weak Counterexamples: A Supplement To Luitzen Egbertus Jan Brouwer Being a still open problem, Goldbach s conjecture is by itself a weak counterexampleto Should Goldbach s conjecture one day be proved or disproved, http://plato.stanford.edu/entries/brouwer/weakcounterex.html

Stanford Encyclopedia of Philosophy Supplement to Luitzen Egbertus Jan Brouwer Citation Information Weak Counterexamples Here are four weak counterexamples. Consider a still open problem in mathematics, such as Goldbach's conjecture (the conjecture that every even number equal to or greater than 4 is the sum of two prime numbers). As an illustration of the technique that Brouwer used to generate weak counterexamples to other classically valid statements, we show three more weak counterexamples, adapted from the first Vienna lecture (Brouwer, 1929). They are based on a sequence of rational numbers a( n ), defined in terms of Goldbach's conjecture, as follows: a( n n if for all j n j +4 is the sum of two primes k if for some k n, 2 k +4 is not the sum of two primes The sequence of the a( n ) satisfies the Cauchy condition (the condition that for every rational number j )-a( k for all j k n , any two members of the sequence after a( n n of each other. Therefore the sequence converges and determines a real number From the way is constructed, it is clear that we can assert that

99. Newsleter Issue 10 Newsleter issue 10 Proof of Goldbach s conjecture. To promote the book UnclePetros and Goldbach s conjecture by Apostolos Doxiadis, the publishers, http://vedicmaths.org/Community/Newsletter/2000/newsletter_issue_10.asp

Community Newsleter issue 10 Home Page Newsletter VEDIC MATHEMATICS NEWSLETTER ISSUE No. 10 Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods. The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics. If you are working with Vedic Mathematics- teaching it or doing research- please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue. If you are learning Vedic Maths, let us know how you are getting on and what you think of this system. This issue's article: PROOF OF GOLDBACH'S CONJECTURE We are delighted to include an attachment with this Newsletter which contains a proof , according to Dr S K Kapoor who devised it, of Goldbach's Conjecture: that every even number over two can be expressed as the sum of two primes. The experts in number theory will soon tell us about the validity of Dr Kapoor's proof, which is neat and does not require very advanced mathematics to understand. This is contained in Dr Kapoor's book "Goldbach Theorem" ISBN 81-7063-113-0 and steps are being taken to have it published in a reputable journal.

100. Doxiadis - Page Redirected this page has moved click here to be redirected please update your links. http://www.maths.ex.ac.uk/~mwatkins/zeta/doxiadis.htm

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