21. Zimaths Fermat S Last Theorem But progress was made, notably by the Japanese mathematicians yutaka taniyama (whokilled himself in 1958) and Goro Shimura (who s a professor at Princeton http://uzweb.uz.ac.zw/science/maths/zimaths/flt.htm

22. List Of People By Name: Ta-Tb China, (died 649); Tange, Kenzo, architect; Tani, Daniel, astronaut;taniyama, yutaka, (19271958), mathematician; Tanizaki, Junichiro http://www.fact-index.com/l/li/list_of_people_by_name__ta_tb.html

Main Page See live article Alphabetical index List of people by name: Ta-Tb List of people by name A B C ... S T U V W X ... Z Ta-Tb Tc-Td Te Tf-Th Ti ... Tz Ta Tabor, June, musician Tabori, George, dramatist, author Tacer, Ales, poet Tacitus, Publius (or Gaius) Cornelius , (AD 56-120), . Roman historian, ethnologist Tacitus, M. Claudius , (200 AD-276 AD), Roman Emperor Tacuma, Jamaaladeen , (born 1957), jazz musician Taft, Robert Alphonso Senator from Ohio Taft, William Howard President of the United States Chief Justice of the United States Taggard, Geneviere, (Calling Western Union) Tagle, Francisco Ruiz, president Taglioni, Fabio Italian motorcycle engineer Tagore, Rabindranath , (1861-1941), poet Tailleferre, Germaine , (1892-1983), French composer Taimanov, Mark, chess player Taimur Bin Faisal, (1913-1932), Oman sultan Taira no Kiyomori , (1118-1181), samurai warlord Taisho, emperor of Japan Taisuke, Itagaki , Japanese liberal activist Tait, Archibald Campbell , (1811-1882), Archbishop of Canterbury Takagi, Teiji , (1875-1960), mathematician Takakura, emperor of Japan Takaloo, world ranked boxer Takamine, Jokichi

23. Biography-center - Letter T Bios/htmlbios/tani.html; taniyama, yutaka wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/taniyama.html;Tanner, Joseph R. www 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 361 biographies Tabern, Donalee L. www.invent.org/hall_of_fame/142.html Tacca, Ferdinand www.getty.edu/art/collections/bio/a451-1.html Tacquet, Andrea www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tacquet.html Taft, Helen Herron www.whitehouse.gov/WH/glimpse/firstladies/html/ht27.html Taft, William Howard odur.let.rug.nl/~usa/P/wt27/about/taftbio.htm Tagore, Rabindranath www.nobel.se/literature/laureates/1913/tagore-bio.html Tahir, ibn www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Baghdadi.html Taiga, Marton www.kirjasto.sci.fi/taiga.htm Taillandier, Vincent www.getty.edu/art/collections/bio/a1075-1.html Tait, Peter Guthrie www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tait.html Takacs, Karoly

24. Auteur - Taniyama, Yutaka Translate this page Auteur taniyama, yutaka, 2 documents trouvés. Ajouter au panier, Imprimer,Envoyer par mail, Liste détaillée. Ouvrage Complex multiplication http://bibli.cirm.univ-mrs.fr/Auteur.htm?numrec=061944891912660

25. Editeur - The Mathematical Society Of Japan taniyama, yutaka (Co-auteur) The http://bibli.cirm.univ-mrs.fr/Reference.htm?numrec=191920079910280

26. Yutaka Taniyama Definition Meaning Information Explanation yutaka taniyama definition, meaning and explanation and more about yutaka taniyama.FreeDefinition - Online Glossary and Encyclopedia, yutaka taniyama. http://www.free-definition.com/Yutaka-Taniyama.html

27. A Brief History Of Fermat's Last Theorem yutaka taniyama presented several problems at a conference for mathematiciansthat dealt with the relationship between elliptic curves and modular forms. http://www.missouri.edu/~cst398/fermat/contents/theorem.htm

The Theorem Origins Fermat Euler Germain ... Wiles Fermat's Last Theorem is considered the greatest problem to ever enter into the theory of numbers. Its origins date back to the ancient Babylonians. Around 2000 B.C., the Babylonians had discovered the fact that some square numbers could be written as the sum of two smaller square numbers. In the sixth century B.C., Pythagoras of Samos founded a brotherhood that is now known as the Pythagoreans. It was through the efforts of members of this group that the Pythoagorean Theorem was developed. This theorem, which is probably one of the most commonly known throughout the world, states that the equation x^2 + y^2 = z^2 has solutions exactly when x, y, and z are the lengths of the sides of a right triangle (z being the hypotenuse and x and y being the two legs). The theorem can be and has been easily proven in many different ways. Here is an example of one such proof. Pythagoras' ideas about so-called "Pythagorean Triples," or values of x, y, and z that satisfy the Pythagorean Theorem, would later be recorded and analyzed by other famous Greeks, including Euclid and Diophantus. Euclid introduced a proof that demonstrated the fact that there are infinitely many Pythagorean triples. This idea would later be analyzed by Diophantus, who is commonly referred to as the "father of algebra." Diophantus, who lived somewhere around 250 A.D., was extremely fond of numbers. He created and solved a host of problems that dealt with the nature and behavior of numbers. Eventually, Diophantus compiled many of his problems into a mutli-volumed work known as the

28. Yutaka Taniyama - Japanese Mathematician yutaka taniyama Japanese mathematician. yutaka taniyama ( ?,November 12, 1927 - November 17, 1958) was a Japanese mathematician. http://www.japan-101.com/culture/yutaka_taniyama.htm

29. Goro Shimura - Japanese-American Mathematician Shimura was a colleague and a friend of yutaka taniyama. They wrotea book (the first book treatment) on the complex multiplication http://www.japan-101.com/culture/goro_shimura_japanese-american_mathematician.ht

30. Yutaka Taniyama Article on yutaka taniyama from WorldHistory.com, licensed from Wikipedia,the free encyclopedia. Return to Article Index yutaka taniyama. http://www.worldhistory.com/wiki/Y/Yutaka-Taniyama.htm

World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Yutaka Taniyama Yutaka Taniyama November 12 November 17 ) was a Japanese mathematician. He is known for his Taniyama-Shimura conjecture Taniyama was born in Kisai, Saitama (north of Tokyo ), Japan. His first name was actually Toyo, but many people misinterpreted his name as Yutaka, and he came to accept that name. In high school, he became interested in mathematics inspired by Teiji Takagi 's modern history of mathematics. Taniyama studied mathematics at the University of Tokyo after the end of World War II , and here he developed a friendship with another student named Goro Shimura . He graduated in . He remained there as a 'special research student', then as an associate professor. His interests were in algebraic number theory . He wrote Modern number theory ) in Japanese , jointly with Goro Shimura. Although they planned an English language version, they lost enthusiasm and never found the time to write it before Taniyama's death. But before all, they were fascinated with the study of

31. Fermat S Last Theorem - Taniyama-Shimura Conjecture It was raised for the first time by yutaka taniyama, in the form of a problem posedto the participants of an international conference on algebraic number http://fermat.workjoke.com/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.

32. Fermat S Last Theorem - Bibliography Discover, January 1989. Goro Shimura, yutaka taniyama and His Time VeryPersonal Recollections, Bull. London Math. Soc., 1989. B. Mazur http://fermat.workjoke.com/flt11.htm

Previous chapter: Is this the proof we were expecting? Table of contents Bibliography L. J. Mordell: Three Lectures on Fermat's Last Theorem, 1921. E. T. Bell: Men of Mathematics E. T. Bell: The Last Problem, 1961. C. B. Boyer: A History of Mathematics W. W. Rouse Ball: Mathematical Recreations and Essays M. S. Mahoney: The Mathematical Career of Pierre de Fermat Harold M. Edwards: Fermat's Last Theorem - A Genetic Introduction to Algebraic Number Theory Paulo Ribenboim: 13 Lectures on Fermat's Last Theorem Number Theory - An approach through history Simon Singh: Fermat's Enigma: The Quest to Solve the World's Greatest Mathematical Problem Ian Stewart: The Problems of Mathematics, 1987. Keith Devlin: Mathematics: The New Golden Age Charles J. Mozzochi: The Fermat Diary L. E. Dickson, Fermat's Last Theorem and the Origin and Nature of the Theory of Algebraic Numbers, Annals of Math. Fermat's Method of Infinite Descent, American Mathematical Monthly, 1918 , p. 333. Alonzo Church, An unsolvable problem of elementary number theory, American J. of Mathematics

33. Re: Shimura-Taniyama Conjecture By Antreas P. Hatzipolakis of a specific matter. yutaka taniyama (1927 1958) Pleasetell the source of this taniyama quote. (There seem to be so http://mathforum.org/epigone/math-history-list/glexzhangdwimp/v01540B06630B9D985

Re: Shimura-Taniyama Conjecture by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Re: Shimura-Taniyama Conjecture Author: xpolakis@otenet.gr Date: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Taniyama.html As for the second: The only one reference the authors of the biography above, have in the "References for Yutaka Taniyama" is: G Shimura: Yutaka Taniyama and his Time. Very Personal Recollections. Bull. London Math. Soc. 21 (1989) 186-196. So, most likely the original source is Shimura's article. Antreas The Math Forum

34. Shimura-Taniyama-Weil Conjecture (was: John Baez: This Week's....) By Antreas P. myself, but it is not the result of a particular incident, nor of aspecific matter. yutaka taniyama (1927 1958) The Math Forum http://mathforum.org/epigone/math-history-list/gangloxphel

Shimura-Taniyama-Weil Conjecture (was: John Baez: This Week's....) by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to math-history-list Subject: Shimura-Taniyama-Weil Conjecture (was: John Baez: This Week's....) Author: xpolakis@otenet.gr Date: http://news2.thls.bbc.co.uk/hi/english/sci/tech/newsid_527000/527914.stm Read also the online articles: Frank Morgan's Math Chat TANIYAMA-SHIMURA CONJECTURE PROVED (July 1, 1999) http://www.maa.org/features/mathchat/mathchat_7_1_99.html Ivars Peterson's MathTrek Curving Beyond Fermat (November 22, 1999) http://www.maa.org/mathland/mathtrek_11_22_99.html Antreas Until yesterday I had no definite intention of killing myself. ... I don't quite understand it myself, but it is not the result of a particular incident, nor of a specific matter. Yutaka Taniyama (1927 - 1958) The Math Forum

35. Math@Net - O Último Teorema De Fermat Translate this page Em 1954 dois jovens matemáticos japoneses, yutaka taniyama e Goro Shimura,iniciaram uma amizade porque Shimura ficara sabendo que o volume 24 do http://www.net-rosas.com.br/~cvidigal/math/fermat.htm

O Último Teorema de Fermat 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 A história mais famosa da Matemática Andrew Wiles demonstrou em 1994, finalmente, o Último Teorema de Fermat (UTF), um fato que se compara à descoberta de que o átomo é divisível ou à a descoberta da estrutura do ADN como observou John Coates, matemático de Cambridge, Inglaterra, ex-orientador de Andrew. Gerações de matemáticos foram envolvidos nesta batalha de cerca de 350 anos que influenciou, praticamente, toda a Matemática. Para Andrew o problema mais famoso da Matemática nestes últimos quatro séculos tornou-se uma obsessão desde quando, aos 10 anos de idade, pôs as mãos no livro de Eric Temple Bell, "O Último Problema". Este problema parecia tão simples mas os grandes matemáticos destes quatro séculos não puderam resolvê-lo. Andrew achou que tinha que ser ele a resolvê-lo. Pierre de Fermat era um Conselheiro da Câmara de Requerimentos de Toulouse, na França de 1631. Sua responsabilidade estava ligada à condenação de pessoas à morte na fogueira e porisso não podia ter muitas amizades. Em seu tempo livre dedicava-se à Matemática. Fermat ficou conhecido como o "Príncipe dos Amadores" por ter descoberto as leis da probabilidade, os fundamentos do cálculo diferencial e elegantes e difíceis teoremas sobre números inteiros.

36. Writing Activities Bertrand; ShihChieh, Chu; Somerville, Mary Fairfax; taniyama, yutaka;Turing, Alan; Woods, Granville T. Young, Grace Chisholm. Evaluation 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.

37. Ivars Peterson's MathTrek -Curving Beyond Fermat In the 1950s, Japanese mathematician yutaka taniyama (19271958) proposed that everyrational elliptic curve is a disguised version of a complicated, impossible http://www.maa.org/mathland/mathtrek_11_22_99.html

Search MAA Online MAA Home Ivars Peterson's MathTrek November 22, 1999 Curving Beyond Fermat When Andrew Wiles of Princeton University proved Fermat's last theorem several years ago, he took advantage of recently discovered links between Pierre de Fermat's centuries-old conjecture concerning whole numbers and the theory of so-called elliptic curves. Establishing the validity of Fermat's last theorem involved proving parts of the Taniyama-Shimura conjecture. Four mathematicians have now extended this aspect of Wiles' work, offering a proof of the Taniyama-Shimura conjecture for all elliptic curves rather than just a particular subset of such curves. Mathematicians regard the resulting Taniyama-Shimura theorem as one of the major results of 20th-century mathematics. It establishes a surprising, profound connection between two very different mathematical worlds and, along the way, has important consequences for number theory. An elliptic curve is not an ellipse. It is a solution of a cubic equation in two variables of the form y x ax b (where a and b are fractions, or rational numbers), which can be plotted as a curve made up of one or two pieces.

38. Ivars Peterson's MathTrek - The Amazing ABC Conjecture That conjecture dates back to 1955, when it was published in Japaneseas a research problem by the late yutaka taniyama. Goro Shimura http://www.maa.org/mathland/mathtrek_12_8.html

Search MAA Online MAA Home Ivars Peterson's MathTrek December 8, 1997 The Amazing ABC Conjecture In number theory, straightforward, reasonable questions are remarkably easy to ask, yet many of these questions are surprisingly difficult or even impossible to answer. Fermat's last theorem, for instance, involves an equation of the form x n y n z n . More than 300 years ago, Pierre de Fermat (1601-1665) conjectured that the equation has no solution if x y , and z are all positive integers and n is a whole number greater than 2. Andrew J. Wiles of Princeton University finally proved Fermat's conjecture in 1994. In order to prove the theorem, Wiles had to draw on and extend several ideas at the core of modern mathematics. In particular, he tackled the Shimura-Taniyama-Weil conjecture, which provides links between the branches of mathematics known as algebraic geometry and complex analysis. That conjecture dates back to 1955, when it was published in Japanese as a research problem by the late Yutaka Taniyama. Goro Shimura of Princeton and Andre Weil of the Institute for Advanced Study provided key insights in formulating the conjecture, which proposes a special kind of equivalence between the mathematics of objects called elliptic curves and the mathematics of certain motions in space. The equation of Fermat's last theorem is one example of a type known as a Diophantine equation an algebraic expression of several variables whose solutions are required to be rational numbers (either whole numbers or fractions, which are ratios of whole numbers). These equations are named for the mathematician Diophantus of Alexandria, who discussed such problems in his book

39. Taniyama-Shimura Theorem :: Online Encyclopedia :: Information Genius The taniyamaShimura theorem states All elliptic curves over Q are modular. .This theorem was first conjectured by yutaka taniyama in September 1955. http://www.informationgenius.com/encyclopedia/t/ta/taniyama_shimura_theorem.html

Quantum Physics Pampered Chef Paintball Guns Cell Phone Reviews ... Science Articles Taniyama-Shimura theorem Online Encyclopedia The Taniyama-Shimura theorem establishes an important connection between elliptic curves, which are objects from algebraic geometry , and modular forms , which are certain periodic holomorphic functions investigated in number theory If p is a prime number and E is an elliptic curve over Q , we can reduce the equation defining E modulo p ; for all but finitely many values of p we will get an elliptic curve over the finite field F p , with n p elements , say. One then considers the sequence a p n p p , which is an important invariant of the elliptic curve E . Every modular form also gives rise to a sequence of numbers, by Fourier transform . An elliptic curve whose sequence agrees with that from a modular form is called modular . The Taniyama-Shimura theorem states: "All elliptic curves over Q are modular." This theorem was first conjectured by Yutaka Taniyama in September . With Goro Shimura he improved its rigor until . Taniyama died in . In the it became associated with the Langlands program of unifying conjectures in mathematics, and was a key component thereof. The conjecture was picked up and promoted by

40. Timeline Of Fermat's Last Theorem 1955, yutaka taniyama (19271958) Goro Shimura, taniyama and Shimura helpedorganize the Tokyo-Nikko Symposium on Algebraic Number Theory. http://www.public.iastate.edu/~kchoi/time.htm

Drink to Me (Carolan, sequenced by Barry Taylor) Timeline of Fermat's Last Theorem when who what 1900 BC Babylonians A clay tablet, now in the museum of Columbia University, called Plimpton 322, contains 15 triples of numbers. They show that a square can be written as the sum of two smaller squares, e.g., 5 circa 530 Pythagoras Pythagoras was born in Samos. Later he spent 13 years in Babylon, and probably learned the Babylonian's results, now known as the Pythagorean triples. Pythagoras was also the founder of a secret society that studied among others "perfect" numbers. A perfect number is one that is the sum of its multiplicative factors. For instance, 6 is a perfect number (6 = 1 + 2 + 3). Pythagoreans also recognized that 2 is an irrational number. circa 300 BC Euclid of Alexandria Euclid is best known for his treatise Elements circa 400 BC Eudoxus Eudoxus was born in Cnidos, and became a colleague of Plato. He contributed to the theory of proportions, and invented the "method of exhaustion." This is the same method employed in integral calculus. circa 250 AD Diophantus of Alexandria Diophantus wrote Arithmetica , a collection of 130 problems giving numerical solutions, which included the Diophantine equations , equations which allow only integer solutions (e.g, ax + by = c, x

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