Taniyama The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.geocities.co.jp/Technopolis/5346/taniyama.html
Extractions: 17 NOVEMBRE 1999 KEITH DEVLIN Teorema di Fermat Nel 1994 il matematico inglese Andrew Wiles , dimostrando il cosiddetto ultimo teorema di Fermat, pose il sigillo finale ad una saga iniziata nella seconda metà del Seicento. Come fa ogni esperto narratore, tuttavia, Wiles aveva lasciato in sospeso un inquietante enigma. Solo nel corso dell'estate appena trascorsa una équipe di quattro matematici ha trovato la risposta giusta a questo enigma. Mi stupisce che questo importante risultato, al contrario di quanto è successo con quello di Wiles, sia passato in sordina, perfino in molti ambienti di matematici di professione. Basandosi sui lavori dello stesso Wiles, Brian Conrad e Richard Taylor , di Harvard, Christophe Breuil dell'Università di Parigi-Sud, e Fred Diamond dell'Università Rutgers (nel New Jersey) hanno sobriamente annunciato di essere finalmente riusciti a dimostrare la correttezza della cosiddetta "congettura di Shimura Taniyama ". Questa congettura, che adesso diventa verità matematica incontestabile, era stata centralissima nella dimostrazione data da Wiles del teorema di Fermat. Per chiarezza, conviene tornare alle origini della saga, riassumendo una storia oramai ben nota.
The Mathematics Of Fermat's Last Theorem Actually, Theorem B was conjectured earlier (in a special form) by yutaka Taniyamaaround 1955, and increasingly more general forms since then by Goro Shimura http://www.mbay.net/~cgd/flt/fltmain.htm
Extractions: Welcome to one of the most fascinating areas of mathematics. There's a fair amount of work involved in understanding even approximately how the recent proof of this theorem was done, but if you like mathematics, you should find it very rewarding. Please let me know by email how you like these pages. I'll fix any errors, of course, and try to improve anything that is too unclear. If you have ever read about number theory you probably know that (the so-called) Fermat's Last Theorem has been one of the great unsolved problems of the field for three hundred and fifty years. You may also know that a solution of the problem was claimed very recently - in 1993. And, after a few tense months of trying to overcome a difficulty that was noticed in the original proof, experts in the field now believe that the problem really is solved. In this report, we're going to present an overview of some of the mathematics that has either been developed over the years to try to solve the problem (directly or indirectly) or else which has been found to be relevant. The emphasis here will be on the "big picture" rather than technical details. (Of course, until you begin to see the big picture, many things may look like just technical details.) We will see that this encompasses an astonishingly large part of the whole of "pure" mathematics. In some sense, this demonstrates just how "unified" as a science mathematics really is. And this fact, rather than any intrinsic utility of a solution to the problem itself, is why so many mathematicians have worked on it over the years and have treated it as such an important problem.
Developing A General 2nd Degree Diophantine Equation X2 + P = 2n Methods to solve these equations.Category Science Math Number Theory Diophantine Equations true. In 1987, Kenneth Ribet came up with a simple connection betweenYutaka taniyamas conjecture and Fermats Last Theorem. In http://www.biochem.okstate.edu/OAS/OJAS/thiendo.htm
Extractions: It is fun to experiment with numbers and exciting to discover patterns. Number theory played an important role in the Diophantine Equation. In this project, I consider a family of Diophantine equation: x + p = 2 n for various odd primes p. Using methods of congruences, I have shown that if p = 3 there is only one positive solution (1,2), and if p is any other odd prime not congruent to 7 mod 8, there are no solutions. The explanation of this general 2 nd degree equations solutions has not been previously determined as a result of the complication. This equation is solved uniquely by using congruences in modulo 2 and modulo 8. In the branch of number theory concerned with determining the solutions in integers of algebraic equations with two or more unknowns, Greek algebra and number theory played an important role in the appearance of the Arithmetica written by Diophantus. Diophantus was interested in exact solutions rather than the approximate solutions considered perfectly appropriate. Diophantus found interest in polynomial equation in one or more variables for which it is necessary to find a solution in either integers or rational numbers. This polynomial equation bears the name: Diophantine Equation Diophantuss edition of the Arithmetica caught the attention of Pierre de Fermat (1601-1665), known as the prince of amateur mathematician. He discovered and developed many theorems in number theory. The most famous of Fermats assertion is the equation
The Whole Story The incident which began everything happened in postwar Japan, when yutaka Taniyamaand Goro Shimura, two young academics, decided to collaborate on the study http://www.simonsingh.net/owtasite/147
Fermats Last Theorem Simon Singh The Quest To Solve The The incident which began everything happened in postwar Japan, when yutaka Taniyamaand Goro Shimura, two young academics, decided to collaborate on the study http://www.prometheus.demon.co.uk/01/01fermat.htm
Extractions: In 1963 a ten-year-old boy borrowed a book from his local library in Cambridge, England. The boy was Andrew Wiles, a schoolchild with a passion for mathematics, and the book that had caught his eye was The Last Problem by the American mathematician Eric Temple Bell. The book recounted the history of Fermat's Last Theorem, the most famous problem in mathematics, one which had baffled the greatest minds on the planet for over three centuries. There can be no problem in the field of physics, chemistry or biology that has so vehemently resisted attack for so many years. Indeed E.T. Bell predicted that civilisation would come to an end as a result of nuclear war before Fermat's Last Theorem would ever be resolved. Nonetheless young Wiles was undaunted. He promised himself that he would devote the rest of his life to addressing the ancient challenge. The seventeenth century mathematician Pierre de Fermat created the Last Theorem while studying Arithmetica , an ancient Greek text written in about AD 250 by Diophantus of Alexandria. Although mathematicians in India and Arabia had since made significant contributions to the subject, mathematics had remained largely frozen since Diophantus, and Fermat and his contemporaries were attempting to resurrect the subject and discover new truths. However, Fermat conducted his research largely in isolation, living near Toulouse in southwest France, far from the salons of Paris where intellectuals gathered to discuss their ideas.
Mathematician/Scientist Links Mathematicians/Scientists. The names below are possible candidatesfor research for the second quarter interdisciplinary project http://www.rialto.k12.ca.us/frisbie/mathematicians.html
The Radical Exponent 19.2 A completely different approach to the problem had its origins in 1955 when YutakaTaniyama conjectured that all elliptic curves of a certain type have the http://www.nwmissouri.edu/~math/radexp192.html
Extractions: Volume XIX, Number 2, April 1995 Even though it may seem impossible, an advance in mathematical theory has been reported in the newspapers and popular magazines several times during the past two years. This unusual appearance of mathematics in the news came about because of the solution of a problem that has intrigued mathematicians for over three centuries. In this article we will briefly summarize the historical attempts and recent success in solving this long-standing mystery. Pierre de Fermat was a French lawyer who lived 1601-1665, spending most of his life in Toulouse. His career as a professional jurist won him little notoriety, but his career as an amateur mathematician has placed his name forever among the great ones in the history of mathematics. Sometime in the mid-1630's, Fermat was reading a book called the
LULTIMO TEOREMA DI FERMAT (49) Translate this page Anni prima (più precisamente negli anni 50) due matematici giapponesi, YutakaTaniyama e Goro Shimura, studiando le curve ellittiche e le Forme Modulari http://www.lalimonaia.pisa.it/news/fermat.doc.htm
Extractions: LULTIMO TEOREMA DI FERMAT FERMATS LAST THEOREM Regia : John Lynch e Simon Singh Produzione BBC Horizon Gran Bretagna, 1998 Fermat era un giudice francese vissuto nel 600 appassionato di matematica, abilissimo nel proporre enigmi matematici, di cui spesso non dava la soluzione. Mentre studiava il libro II dell Arithmetica di Diofanto, alle pagine dedicate ai problemi e alle osservazioni intorno al Teorema di Pitagora, Fermat scrisse una nota a margine del libro: Al termine della sua nota Fermat aggiunge: " Esigenza di una dimostrazione Gli studi di Andrew Wiles e alcuni sviluppi della matematica del XX secolo Curve Ellittiche. x e y ciambella. le Forme Modulari z Andrew Wiles e LUltimo Teorema di Fermat
Fermat's Last Theorem The summary for this Korean page contains characters that cannot be correctly displayed in this language/character set. http://www.postech.ac.kr/math/study/read/read002-Fermat_last_thm.html
Dinoj Surendran Dinoj's Science Writing Page. The Kepler Conjecture draft of article Published inthe MAA magazine Math Horizons in April 2001. zipped postscript file, 350K. http://people.cs.uchicago.edu/~dinoj/sciwrit.htm
Extractions: The Kepler Conjecture draft of article Published in the MAA magazine Math Horizons in April 2001. [zipped postscript file, 350K] Science, or rather Math, writing is something I really enjoyed as an undergraduate. Here's some of what I wrote for Zimaths, which is a magazine aimed at Zimbabwean High School students and teachers. Tawanda Gwena and myself founded it in August 1996 and the editor is Dr Gavin Hitchcock of the U of Zimbabwe Math Department. In retrospect I should have spent less time on this stuff and more time on my academic work, but I was younger and naiver then. My perception of mathematics has also changed since I wrote some of these articles but... anyway, live and learn. Don't expect to find high powered mathematics here! I also compiled short biographies of Escher Mary Boole Hypatia Emmy Noether ... Newton and the Bernoullis Another article, regarding certain graph theory conjectures, was published in the February 1999 issue of the Indian magazine
Untitled The summary for this Greek page contains characters that cannot be correctly displayed in this language/character set. http://ieee.ntua.gr/articles/Fermat's last theorem.htm
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