41. Published Sources On The History Of The Modularity Conjecture Shimura, G. yutaka taniyama and his time. Very personal recollections, {\it Bull.Lon. Math. Soc.} 21 (1989), 186196. taniyama s problems are in {\it http://math.albany.edu:8010/g/Math/topics/fermat/bib-goss

42. History Of Fermat S Last Theorem % By Andrew Granville % A Version with a question posed by the Japanese mathematician yutaka taniyama \ Could one taniyama was fairly specific about these very special curves (the http://math.albany.edu:8010/g/Math/topics/fermat/granville.hist

43. Science.ca Profile Henri Darmon Back in 1955, two Japanese mathematicians, yutaka taniyama and Goro Shimuraclaimed that elliptical curves were related to another mathematical idea called http://science.ca/scientists/scientistprofile.php?pID=357

44. Benutzer DiskussionExxu - Wikipedia Translate this page Bei yutaka taniyama war mindestens ein Zweitsatz erforderlich. Zu yutakataniyama Irgendwie muss der Leser doch dazu kommen, gerade dieses Lemma zu http://de.wikipedia.org/wiki/Benutzer_Diskussion:Exxu

45. Goro Shimura -- Facts, Info, And Encyclopedia Article Shimura was a colleague and a friend of (Click link for more info and facts aboutyutaka taniyama) yutaka taniyama. They wrote a book (the first book http://www.absoluteastronomy.com/encyclopedia/g/go/goro_shimura.htm

Goro Shimura [Categories: Number theorists, 21st century mathematicians, 20th century mathematicians, Japanese mathematicians, American mathematicians, 1930 births] Goro Shimura (A constitutional monarchy occupying the Japanese Archipelago; a world leader in electronics and automobile manufacture and ship building) Japan ese- (A native or inhabitant of the United States) American (A person skilled in mathematics) mathematician , and currently a (Someone who is a member of the faculty at a college or university) professor of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics at (A university in New Jersey) Princeton University Shimura was a colleague and a friend of (Click link for more info and facts about Yutaka Taniyama) Yutaka Taniyama . They wrote a book (the first book treatment) on the (Click link for more info and facts about complex multiplication of abelian varieties) complex multiplication of abelian varieties , an area which in collaboration they had opened up. Shimura then wrote a long series of important papers, extending the phenomena found in the theory of complex multiplication and

46. The Mathematics Of Fermat's Last Theorem Theorem B was conjectured earlier (in a special form) by yutaka taniyama Theorem B and more general forms of the taniyamaShimura Conjecture can be http://cgd.best.vwh.net/home/flt/fltmain.htm

The Mathematics of Fermat's Last Theorem 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. Introduction 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.

47. Science -- Sign In In 1955, a young Japanese mathematician named yutaka taniyama first suggestedusing such modular functions to describe all rational points on an elliptic http://www.sciencemag.org/cgi/content/full/285/5425/178a

You do not have access to this item: Full Text : Mackenzie, MATHEMATICS:Fermat's Last Theorem Extended, Science You are on the site via Free Public Access. What content can I view with Free Public Access If you have a personal user name and password, please login below. SCIENCE Online Sign In Options For Viewing This Content User Name Password this computer. Help with Sign In If you don't use cookies, sign in here Join AAAS and subscribe to Science for free full access. Sign Up More Info Register for Free Partial Access including abstracts, summaries and special registered free full text content. Register More Info Pay per Article 24 hours for US $10.00 from your current computer Regain Access to a recent Pay per Article purchase Need More Help? Can't get past this page? Forgotten your user name or password? AAAS Members activate your FREE Subscription

48. Fermat yutaka taniyama and Goro Shimura had a bold idea while studying modular functions.They conjectured that every rational elliptical curve is a modular http://www.geocities.com/galois_e/page/fermat.html

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.

49. Fermat S Last Theorem - Taniyama-Shimura Conjecture It was raised for the first time by yutaka taniyama, in the form of a problemposed to the participants of an international conference on algebraic number http://www.geocities.com/fermatnow/flt/flt8.htm

Previous chapter: There are failures too Next chapter: Here is the proof! Table of contents Taniyama-Shimura conjecture Elliptic curves are not ellipses but Diophantine equations, of the form y =Ax +Bx +Cx+D. The two dimensional graphical representation of these equations look like a hump with an egg on top. The graphical representation of these equations in complex numbers is what mathematicians call a torus and the rest of the word calls a bagel. Diophantine equations of this class appear in Fermat's work. He had shown, for example, that the equation y =x-x has three rational solutions: (0,0), (1,0) and (-1,0). In the twentieth century elliptic curves were an important research topic in number theory, and a lot of knowledge was accumulated about them ("One can write endlessly about elliptic curves" wrote Serge Lang in the preface to his book Elliptic Curves - Diophantine Analysis (published in 1973). In last few years elliptic curves are used in cryptography. More about the use of elliptic curves in cryptography see at Online ECC Tutorial , Certicom.

50. Retiro Cultural - O Último Teorema De Fermat yutaka taniyama, whose insights would ultimately lead to the solution, Em 1954 dois jovens matemáticos japoneses, yutaka taniyama e Goro Shimura, http://www.angelfire.com/ab/geloneze/fermat.html

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "angelfire.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Angelfire Star Wars Share This Page Report Abuse Edit your Site ... Next Retiro Cultural - O Último Teorema de Fermat Matematicoterapia 1 Matematicoterapia 2 A história da demonstração da conjectura mais famosa da Matemática Um problema que desafiou os matemáticos por mais de 300 anos Baseado nos livros "O Último Teorema de Fermat" de Simon Singh, edição brasileira pela Editora Record, 1998, e no livro "Fermat’s Last Theorem:Unlocking the Secret of an Ancient Mathematical Problem" By Amir D. Aczel Delta - Trade Paperbacks "This is a captivating volume ... The brilliant backdoor method used by Mr. Wiles as he reached his solution, along with the debt he owed to many other contemporary mathematicians, is graspable in Mr. Aczel’s lucid prose. Equally important is the sense of awe that Mr. Aczel imparts for the hidden, mystical harmonies of numbers, and for that sense of awe alone, his slender volume is well worth the effort." —The New York Times "For more than three centuries, Fermat’s Last Theorem was the most famous unsolved problem in mathematics; here’s the story of how it was solved ... An excellent short history of mathematics, viewed through the lens of one of its great problems — and achievements."

51. Brendandawes.com / Good Mistakes Goro Shimura and yutaka taniyama were 2 talented mathematicians at the Universityof Tokyo back in 1954. But the two had very different methods of working. http://www.brendandawes.com/mt/archives/000142.html

@import "/layout.css"; @import "/main.css"; home headshop sketches about ... downloads Good Mistakes Having recently read Fermats Last Theorem by Simon Singh, one particular paragraph stayed with me. Goro Shimura and Yutaka Taniyama were 2 talented mathematicians at the University of Tokyo back in 1954. But the two had very different methods of working. To quote from the book: While Shimura was fastidious, Taniyama was sloppy to the point of laziness. Surpisingly this was a trait that Shimura admired: 'He was gifted with the special capability of making many mistakes, mostly in the right direction. I envied him for this and tried in vain to imitate him, but found it quite difficult to make good mistakes.' Good mistakes. I've always been a fan of mistakes in creativity and when trying to generate ideas, which is nothing new. But I love the idea of "good mistakes". The two together seem at first to contradict each other but actually are a powerful notion - maybe that's the basis of all creative ideas? The root of creativity is the idea... Generating new ideas is really my problem, I always get this feeling of copying others work but I oftenly feel that's not in my track... I'm getting stuck sometimes and don't know where to start and produce ideas that would somehow incorporate new style. I didn't know that good mistakes could also lead into creativity.

52. WalkerBooks.com - Books yutaka taniyama, whose insights would ultimately lead to the solution, tragicallykilled himself in 1958. On the other hand, Paul Wolfskehl, a famous German http://www.walkerbooks.com/books/catalog.php?key=63

53. Yutaka Taniyama The extraordinary story of Fermat s Last TheoremGoro Shimura and yutaka taniyama began to examine socalled modular forms, avariety of objects which are special because of their immensely high level of http://www.algebra.com/algebra/about/history/Yutaka-Taniyama.wikipedia

Yutaka Taniyama Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Yutaka Taniyama Yutaka Taniyama Yutaka Taniyama November 12 November 17 ) was a Japanese mathematician, best known for conjecturing the Taniyama-Shimura theorem after a meeting with Andr© Weil , whose statement he subsequently refined in collaboration with Goro Shimura . The names Taniyama, Shimura and Weil have all been attached to this conjecture, but the idea is essentially due to Taniyama. In Ribet proved that if the conjecture held, then so would Fermat's last theorem , which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem. Due to the pioneering contribution of Wiles and the efforts of a number of mathematicians the conjecture was finally proven in For reasons he was unable to explain, even to himself, Taniyama committed suicide . He left a note explaining how far he had gotten with his teaching duties, and apologizing to his colleagues for the trouble he was causing them. His mystifying suicide note read

54. QED in the late 1950 s the Japanese mathematicians yutaka taniyama and Goro Later, others showed that if the taniyamaShimura conjecture were true, http://www.nytimes.com/books/97/11/30/reviews/971130.30penrost.html

55. November 2004 yutaka taniyama, 13 Max Wilhelm Dehn. 14 Robert Moore, 15 Michel Chasles,16 Eugenio Beltrami, 17 August Möbius, 18 Albert Wangerin, 19 http://mathforum.org/~judyann/calendar/November2004.html

November 2004 Can you identify the pictured Mathematicians? Sunday Monday Tuesday Wednesday Thursday Friday Saturday Andrzej Mostowski George Boole Martin Wilhelm Kutta Johann(III) Bernoulli James Glaisher Giovanni Plana Thomas De Lagny Edmond Halley Hermann Weyl Elwin Bruno Christoffel John Henry Whitehead Yutaka Taniyama Max Wilhelm Dehn Robert Moore Michel Chasles Eugenio Beltrami Albert Wangerin Nina Karlovna Bari Benoit Mandelbrot Georg Scheffers Giusto Bellavitis John Wallis Duncan Sommerville Norbert Wiener Anatoly Ivanovich Malcev John Wishart Ernest William Brown Sir Henry Savile A quotation for November: Hermann Weyl (1885 - 1955) Logic is the hygiene the mathematician practices to keep his ideas healthy and strong. The American Mathematical Monthly, November, 1992 This calendar is available in a printable PDF format.

56. Math Forum: Alejandre: Mathematician/Scientist Links Ramanujan, Srinivasa Russell, Bertrand ShihChieh, Chu Somerville, MaryFairfax taniyama, yutaka Turing, Alan Woods, Granville T. http://mathforum.org/alejandre/workshops/mathematicians.html

Mathematicians/Scientists The names below are possible candidates for research for the second quarter interdisciplinary project for Team 8-1. Select one from the specific list or look at the general list and find one of your own. Read about the person and note: full name date of birth place of birth where educated contribution(s) to mathematics and/or science date of death how studying this person has benefited your life Specific List Agnesi, Maria al'Khwarizmi, Abu Ja'far Muhammad ibn Musa Banneker, Benjamin Bolyai, Janos ... Hypatia again Just, Ernest Khayyam, Omar Kovalevsky, Sonya Kowa, Seki ... Lovelace, Ada Byron again Morgan, Garrett Noether, Emmy Nunez, Pedro Raman, Chandrasekhra Venkata ... Young, Grace Chisholm General List 4000 Years of Women in Science - Time Ordered List African Americans in the Sciences Alphabetical Index of Women Mathematicians Biographies of African-Americans from Maryland ... Help http://mathforum.org/ Please mail comments and suggestions to Suzanne Alejandre

57. Biography-center - Letter T taniyama, yutaka wwwhistory.mcs.st-and.ac.uk/~history/Mat hematicians/taniyama.html;Tanner, Joseph R. www.jsc.nasa.gov/Bios/htmlbios/tanner.html http://www.biography-center.com/t.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish T 366 biographies T humamah ibn Uthal, www.usc.edu/dept/MSA/history/biographies/sahaabah/bio.THUMAMAH_ IBN_UTHAL.html T ishler, Max www.invent.org/hall_of_fame/145.html T rotter, William Monroe www.triadntr.net/~rdavis/trotter.htm T urchi, Alessandro www.kfki.hu/~arthp/bio/t/turchi/biograph.html Tabern, Donalee L. www.invent.org/hall_of_fame/142.html Tacquet, Andrea www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tacquet.html Taetzsch, Lynne lynnetaetzsch.com Taft, Helen Herron www.whitehouse.gov/WH/glimpse/firstladies/html/ht27.html Taft, Wi lliam Howard odur.let.rug.nl/~usa/P/wt27/about/taftbio.htm Tagore, Rabindranath www. nobel.se/literature/laureates/1913/tagore-bio.html Tahir, ibn

58. Powell's Books - Fermat's Enigma: The Epic Quest To Solve The World's Greatest M yutaka taniyama, whose insights would lead directly to the ultimate solution toFermat, tragically killed himself in despair. On the other hand, http://www.powells.com/cgi-bin/biblio?show=hardcover:sale books:0802713319:7.98

59. Steve's Place - Scientists Goro Shimura (1930) and yutaka taniyama (1927-1958) were the mathematicians thatproposed the infamous taniyama-Shimura conjecture, whose proof by Andrew http://www.steve.gb.com/science/scientists.html

Science Major topics Acids, bases and pH Atomic structure ... Water potential Essays Agrobacteria SAR GM drugs Reference Consensus Domains Genetic code Geological timeline ... Molecules About science Essays Practicals Talks Learning ... Scientific papers Worksheets BLAST Esters Fruitful DNA Internet ... Menagerie Scientists They're not all beardy old men in white coats Pythagoras, father of mathematics, ran a secret society of mathematicians. Women were welcomed into the 'brother'hood. The numerals we now use are ultimately derived from the Arabic numeral system (top row), via the Indian (Devanagari) numerals (middle row). Science didn't start with the Renaissance For starters, it wasn't until 200 BCE that someone got an inkling that there ought to be a number to represent nothingness. It was the Babylonians that first got this inkling, but it took another thousand years before the Hindus finally nailed down the idea, symbol and name for this new invention. The word zero is ultimately derived from the Hindi for 'void' ( sunya ). Negative numbers had a similarly drawn-out birth. The slowness of the acceptance of negatives and zero is one of the reasons that the Western calendar lacks a year nought: 1 BCE changes to 1 CE, much to the suprise of today's more numerate historians.

60. Writing Activities Srinivasa; Russell, Bertrand; ShihChieh, Chu; Somerville, Mary Fairfax;taniyama, yutaka; Turing, Alan; Woods, Granville T. Young, Grace Chisholm http://www.math.wichita.edu/history/activities/writing-act.html

Writing Activity Home Historical Mathematicians Writing Project Grades 5-12 Introduction: Small student groups will use the Internet and other traditional sources to research historically significant mathematicians, write a paper, and creatively present research in class. Prior Knowledge Research skills Paper Writing Skills Word Processing Skills Internet Site Location Skills Student Project Guidelines This in an integrated cooperative learning project for grades 5-12 which allows students to research through Internet sites and traditional methods a historically significant mathematician. Students research the mathematician's personal background and upbringing, education, and their significant contribution to mathematics. Students gain a clearer understanding of a great mathematical discovery and the person behind it. The last component is a creative class presentation/lecture by each group. Learning Advice: As groups work in class, monitor how the groups are working together. I suggest that a teacher schedule 1 or 2 short conferences with the groups to help keep the groups focused and on track. If computer access is limited, I suggest that teachers assign groups a block of time to begin.

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