Fermat's Last Theorem yutaka taniyama asked some questions about elliptic curves, ie curves of theform y = x +ax + b for constants a and b. Further work by Weil and Shimura http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Frmtslst.htm
Extractions: Pierre de Fermat died in 1665. Today we think of Fermat as a number theorist, in fact as perhaps the most famous number theorist who ever lived. It is therefore surprising to find that Fermat was in fact a lawyer and only an amateur mathematician. Also surprising is the fact that he published only one mathematical paper in his life, and that was an anonymous article written as an appendix to a colleague's book. There is a statue of Fermat and his muse in his home town of Toulouse: Because Fermat refused to publish his work, his friends feared that it would soon be forgotten unless something was done about it. His son, Samuel undertook the task of collecting Fermat 's letters and other mathematical papers, comments written in books, etc. with the object of publishing his father's mathematical ideas. In this way the famous 'Last theorem' came to be published. It was found by Samuel written as a marginal note in his father's copy of Diophantus Arithmetica Fermat's Last Theorem states that x + y = z Fermat wrote I have discovered a truly remarkable proof which this margin is too small to contain.
Újság Frey kimutatta, hogy Fermat sejtése a leheto legszorosabb kapcsolatban áll egymásik híres sejtéssel, a két fiatal japán, yutaka taniyama és Goro http://www.gdf-ri.hu/UjsagInfo/10/fermat.htm
Extractions: Hírek Telefonkönyv Vizsgajelentkezés Index kezelés ... GDF FERMAT CSODÁLATOS SEJTÉSE Dr. Vargha Magdolna A mai matematika többnyire távol a nyilvánosságtól zajlik, tekintve, hogy a kutatás annyira specializálódott, hogy nemhogy a laikusok, de még a kutatók közül is csak azok értenek meg egy-egy új bizonyítást, akik közvetlenül azon a szakterületen dolgoznak. 1993-ban és 94-ben a matematika mégis a lapok címoldalára került. Ennek oka az volt, hogy Andrew Wiles, a princetoni egyetem professzora végre megnyugtatóan képes volt bebizonyítani azt a több száz éves sejtést, amelyet Pierre de Fermat, egy XVII. századi francia törvényszéki bíró és amatõr matematikus, egy ókori szerzõ, Diophantes aritmetika könyvének margójára írt le elsõként. Pierre de Fermat egy gazdag bõrkereskedõ fiaként jött a napvilágra 1601. augusztus 20-án, éppen 400 éve. A Toulouse-i egyetemen tanult, majd Toulouse tanácsnoka és bírája lett. Munkáját a fennmaradt iratok szerint lelkiismeretesen végezte, annyira, hogy John Wallis, egy kortárs angol matematikus egy ízben hiába utazott Toulouse-ba pusztán azért, hogy Fermat-val találkozzon, mert az éppen egy hivatásával visszaélõ pap máglyára küldésével volt elfoglalva. A matematika Fermat-nak csupán a hobbija volt. Szabadidejében, avatott és avatatlan szemektõl távol, saját szórakoztatására matematikai tételeket talált ki és megpróbálta azokat, saját állítása szerint többnyire sikerrel, bizonyítani. Aztán a tételeket megküldte a kortárs matematikusoknak, anélkül, hogy elárulta volna bizonyításait.
Resenha - O Último Teorema De Fermat Translate this page Em 1955, yutaka taniyama e Goro Shimura, dois jovens matemáticos talentosos, desenvolveramuma conjectura que, sem perceberem, seria o grande passo para a http://www.ime.usp.br/~cesar/projects/lowtech/teoremadefermat/resenha.html
Ein Wahrhaft Wunderbarer Beweis ... [sciencegarden - Magazin Für Junge Forschun Translate this page der sich nie entscheiden konnte, ob er nun Mathematiker oder aufständischer Republikanersein wollte yutaka taniyama und Goro Shimura japanische Mathematiker http://www.sciencegarden.de/fundstuecke/200204/bxuchtipp/buchtipp.php
Extractions: Osteuropa April 2002 Im März hat Frank Berzbach auf Bücher zum Thema Bildung und Naturwissenschaften hingewiesen. Ein Buch, dass Naturwissenschaften und Mathematik durch spannende Themen und interessante Menschen näher bringt ist Simon Singhs "Fermats letzter Satz". Wer immer schon der Meinung war, Mathematik sei spannend, der wird dieses Buch lieben. Wer schon immer der Meinung war Mathematik sei langweilig, den wird dieses Buch vielleicht vom Gegenteil überzeugen. Und wer eigentlich gar keine Meinung zur Mathematik hatte, der wird sich durch dieses Buch sicher eine bilden. Fermats Behauptung Im Mittelpunkt aller Berichte steht Fermats letzter Satz - ein Behauptung, die Generationen von Mathematikern in ihren Bann gezogen hat. Pierre de Fermat, geboren 1601, gilt als "Fürst der Amateure. Selbst Jurist, betrieb er Mathematik aus Spaß und Liebhaberei in seiner Freizeit. Er war genial, ohne dass er allzu viele seiner Mitmenschen daran teilhaben ließ. Er liebte es, Rätsel zu lösen, war jedoch zu ungeduldig, um Lösungen sauber zu dokumentieren. Beim "Spielen" mit der pythagoreischen Gleichung kam er zu der neuen, der pythagoreischen sehr ähnlichen Gleichung
Ultimo Teroema De Fermat Translate this page En realidad, el Teorema 2 fue conjeturado anteriormente (en una forma especial)por yutaka taniyama cerca de 1955, y en una forma mucho más general por Goro http://www.itcr.ac.cr/revistamate/ContribucionesV4n3/Fermat/
Extractions: Monterey Bay Introducción Si usted ha leído alguna vez acerca de la teoría de números, usted probablemente conoce que el llamado Ultimo Teorema de Fermat ha sido uno de los grandes problemas no resueltos en este campo en los últimos trecientos cincuenta años. Usted probablemente sabrá que una solución del problema fue anunciada recientemente, en 1993. Y, después de unos pocos meses muy tensos tratando de resolver una dificultad que fue encontrada en la prueba original, expertos en el campo ahora creen que el problema ya está definitivamente resuelto. En este trabajo, vamos a presentar una reseña algunas de las matemáticas que han sido desarrolladas a través de años para tratar de resolver el problema (directa o indirectamente) o que se han sido encontradas relevantes. El énfasis será el "vistazo general" antes que los detalles técnicos (por supuesto, hasta que usted empiece a ver el vistazo general, muchas cosas pueden parecer como detalles técnicos). Veremos que esto involucra una sorprendentemente gran cantidad de matemáticas "puras". En cierto sentido, esto demuestra simplemente que tan unificada es la matemática como ciencia. Y este hecho, más que cualquier utilidad intrnseca de la solución del problema en s mismo, es el porqué de que muchos matemáticos hayan trabajado en él a través de los años y lo hayan considerado como un problema importante.
1601 e mai dimostrato 1954, , yutaka taniyama propone una congettura 1980, inizi http://www.viandante.it/sito24/XVII secolo/1601.php
My First HomePage yutaka taniyama asked some questions about elliptic curves, ie curves of the formy2 = x3 +ax + b for constants a and b. Further work by Weil and Shimura http://iml.umkc.edu/PACE_Online/wdd/StudentsWS2004/YuE-2/yue7.htm
Search Results For Conjecture - Encyclopædia Britannica mathematician Leonhard Euler. Includes links to definitions of Diophantineequations. yutaka taniyama University of St. Andrews Biography of http://www.britannica.com/search?query=conjecture&submit=Find&source=MWTEXT
El Enigma De Fermat Translate this page En el corazón de la crucial conjetura de taniyama-Shimura estaba la trágica vidade yutaka taniyama en el Japón de posguerra, cuya historia tuve la suerte http://www.elementos.buap.mx/num38/htm/fermat.html
Theoreme Kenneth Ribet. Jean Pierre Serre. André Weil. Goro Shimura. yutaka taniyama. http://www.cdg82.fr/beaumont/fermat/theoreme.htm
Extractions: L a conjecture de Fermat a n + b n = c n s'énonce simplement,.ce qui explique le nombre d'étudiants et damateurs qui se soient attaqués au problème. Nombre de mathématiciens et non des moindres ont consacré beaucoup de temps à tenter de résoudre cette énigme sans y parvenir complètement. Elle a même en engendré de nouvelles branches des mathématiques grâce aux différentes tentatives de résolution. D u XVIIème au XIXème siècles, ce sont les plus grands noms des mathématiques qui ont tenté de résoudre l'énigme : Léonard Euler, Sophie Germain, Adrien Legendre, Gustave Lejeune-Dirichet, Gabriel Lamé, Lebesgue, Ernst Kummer. Ils sont parvenus à démontrer le théorème pour certaines valeurs en fournissant un contre exemple mais non dans la généralité.
CheatHouse.com - The History Of Fermats Last Theorem of Fermat Fermat So close The Current Status Of Fermat 1801 Carl Friedrich Gauss1824 Niels Henrik Abel 1846 1922 Louis J 1955 yutaka taniyama 1977 Barry Mazur http://www.cheathouse.com/eview/11032-the-history-of-fermats-last-theorem.html
Extractions: An Introduction to Fermats Last Theorem Fermat claimed to have found a proof of the theorem at an early stage in his career. Much later he spent time and effort proving the cases n=4 and n=5. Had he had a proof to his theorem earlier, there would have been no need for him to study specific cases. I Note! The sentences in this essay are shuffled, making this essay unusable
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/FLT_the_whole_story.html
Extractions: This is it the entire story of Fermats Last Theorem in a couple of thousand words. The essay on this page is an edited version of an article that I wrote for Prometheus magazine , but if you feel that even this is too long to read, then you might want to read the whole story in 100 words instead. On the other hand, if you want to read more, then visit some of the other pages in the Fermats Last Theorem section (e.g., Who was Pierre de Fermat? Who is Andrew Wiles? ) and visit some of the links to other websites about Fermats Last Theorem In 1963 a 10-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 mathematician Eric Temple Bell. The book recounted the history of Fermats Last Theorem, the most famous problem in mathematics, which had baffled the greatest minds on the planet for over three centuries.
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.
Fermats Last Theorem 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.
Search Results For Conjecture - Encyclopædia Britannica Frobenius s conjecture, group theory, and coding theory. yutaka TaniyamaUniversity of St. Andrews Biography of the 20thcentury http://www.britannica.com/search?query=conjecture&submit=Find&source=MWTAB
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
Fermat There were no major development in proving the Last Theorem until 1955. YutakaTaniyama and Goro Shimura had a bold idea while studying modular functions. http://www.geocities.com/galois_e/page/fermat.html
Extractions: Fermat's Last Theorem x n + y n = z n has no positive integer solution if n For 350 years, hundreds of mathematicians had tried to prove the Fermat's Last Theorem. But none succeed. For the past couple hundred years, this theorem has inspired thousands of people to study mathematics. New braches of mathematics were generated from the attempts to prove it. It remained unsolved until 1994. Pierre de Fermat The story began with Pierre de Fermat (1601-1665), a French lawyer by profession. However he spent most of his spare time doing mathematics. In fact he is remembered today for his mathematical accomplishments. He is "the Prince of Amateur Mathematicians". He was one of the founders of probability and calculus. Not to mention his numerous contribution to number theory. While studying Diophantus's Arithmetica , he came across the well known Pythagorean theorem, x + y = z . He wrote down the most enigmatic margin note in the history of mathematics. "It is impossible for a cube to be written as a sum of two cubes, or a fourth power as the sum of two fourth powers, or in general, for any number which is a power greater than the second to be written as the sum of two like powers. I have a truly marvelous demonstration of this proposition but this margin is too narrow to contain it." (Of course, the original note was in Latin.) Well, Fermat was a man who did mathematics for the joy of it and never had any intention of having fame with his many brilliant observations. He never published anything himself. After his death, his son collected his margin notes and observations and published them. One by one, most of his observations were proven to be correct, with a few proven to be erroneous. And the last one remained to be proven or disproved is the above observation, and thus its name, the Last Theorem. For the next few centuries, people believed he was correct. Yet no one could prove his statement. Nor could anyone find a counterexample to disprove it. Proving or disproving the theorem would bring someone instant fame.
