21. References For Taniyama References for the biography of yutaka taniyama. G Shimura, yutaka taniyamaand his time. Very personal recollections, Bull. London Math. Soc. http://www-groups.dcs.st-and.ac.uk/~history/References/Taniyama.html

References for Yutaka Taniyama Version for printing Articles: G Shimura, Yutaka Taniyama and his time. Very personal recollections, Bull. London Math. Soc. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR February 1997 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Taniyama.html

22. Taniyama, Yutaka (1927-1958) -- From Eric Weisstein's World Of Scientific Biogra Shimura, G. yutaka taniyama and His Time. Very Personal Recollections. Bull.London Math. Soc. 21, 186196, 1989. Shimura, G. and taniyama, http://scienceworld.wolfram.com/biography/Taniyama.html

Branch of Science Mathematicians Nationality Japanese Taniyama, Yutaka (1927-1958) Japanese mathematician who was a colleague of Shimura who tragically died by his own hand while still at the peak of his creativity. His name is most widely known through the important Taniyama-Shimura conjecture which connects topology and number theory and includes Fermat's last theorem as a special case. This "conjecture" was finally proved in its entirety in 1999. Shimura Additional biographies: MacTutor (St. Andrews) References Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. New York: Hyperion, p. 196, 1998. Shimura, G. "Yutaka Taniyama and His Time. Very Personal Recollections." Bull. London Math. Soc. Shimura, G. and Taniyama, Y. Complex Multiplication of Abelian Varieties and Its Applications to Number Theory. Tokyo: Mathematical Society of Japan, 1961.

23. Talk:Yutaka Taniyama - Wikipedia, The Free Encyclopedia I have not been able to verify that yutaka taniyama committed suicide by leapingout of a window. Can anyone help me corroborate this statement? http://en.wikipedia.org/wiki/Talk:Yutaka_Taniyama

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. Talk:Yutaka Taniyama From Wikipedia, the free encyclopedia. I have not been able to verify that Yutaka Taniyama committed suicide by "leaping out of a window." Can anyone help me corroborate this statement? I deleted the above phrase from the article, after finding the following sentence on page 186 of Fermat's Enigma, by Simon Singh, referring to Taniyama's death: "On the morning of Monday, November 17, 1958, the superintendent of his apartment found him dead in his room with a note left on his desk." John M. Singleton Retrieved from " http://en.wikipedia.org/wiki/Talk:Yutaka_Taniyama Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 22:02, 13 March 2005. All text is available under the terms of the GNU Free Documentation License (see for details).

24. 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

25. 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

Home Tokyo Guide Travel Culture ... Next Yutaka Taniyama - Japanese mathematician Yutaka Taniyama 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 1953. 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 (1957) 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 modular forms, which are objects that exist in complex space that are peculiar because of their inordinate level of symmetry.

26. Ivars Peterson's MathTrek -Curving Beyond Fermat In the 1950s, Japanese mathematician yutaka taniyama (19271958) proposed thatevery rational A brief biography of yutaka taniyama can be found at 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.

27. Ivars Peterson's MathTrek - The Amazing ABC Conjecture In particular, he tackled the Shimurataniyama-Weil conjecture, when it waspublished in Japanese as a research problem by the late yutaka taniyama. 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

28. Yutaka Taniyama Biography yutaka taniyama biography and related resources. yutaka taniyama ( ?,November 12, 1927 November 17, 1958) was a Japanese mathematician. http://www.biographybase.com/biography/Taniyama_Yutaka.html

Biography Base Home Link To Us Search Biographies: Browse Biographies A B C D ... Z Yutaka Taniyama Biography Yutaka Taniyama 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 1953. 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 (1957) 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 modular forms, which are objects that exist in complex space that are peculiar because of their inordinate level of symmetry. Taniyama's fame is mainly due to two problems posed by him at the symposium on Algebraic Number Theory held in Tokyo in 1955 (His meeting with Weil at this symposium was to have a major influence on Taniyama's work). There he presented some problems that dealt with the relationship between modular forms and elliptic curves. He had noticed some extremely peculiar similarities between the two types of entities. Taniyama's observations led him to believe that every modular form is somehow matched up with some elliptic curve. Shimura later worked with Taniyama on this idea that modular forms and elliptic curves are linked and this form the basis of the Taniyama-Shimura conjecture:

29. VACETS Technical Column - Tc58 In 1955, taniyama proposed a conjecture about elliptic curves. The taniyamaShimuraconjecture, introduced by the Japanese yutaka taniyama in 1955 and http://www.vacets.org/sfe/fermat.html

VACETS Regular Technical Column "Science for Everyone" "Science for Everyone" was a technical column posted regularly on the VACETS forum. The author of the following articles is Dr. Vo Ta Duc . For more publications produced by other VACETS members, please visit the VACETS Member Publications page or Technical Columns page The VACETS Technical Column is contributed by various members , especially those of the VACETS Technical Affairs Committe. Articles are posted regulary on vacets@peak.org forum. Please send questions, comments and suggestions to vacets-ta@vacets.org Mon, 24 Oct 1994 FERMAT'S LAST THEOREM In the [SCIENCE FOR EVERYONE] column last week, I had three bonus problems posted and no one had solved any of them. All I heard was all kinds of discussion about the first bonus, the Fermat's last theorem. It asserts that "For any integer n greater than 2, the equation (a^n + b^n = c^n) has no solutions for which a, b, and c are integers greater than zero." The discussion was interesting. Actually, I had heard that someone had found a solution to the theorem sometime last year. A few months ago, I heard that the proof had some holes in it; some are small like pin-holes and some are as big as black holes. All the pin-holes, potholes, manholes were filled, but the biggest hole, the black hole, was not filled. I guess that there is no way to fill a black hole. It just swallows everything you throw at it and gets bigger. I didn't pay much attention until last week when I saw that many people were discussing it. I decided to do some research into it, and here is what I found. This story is rather long, so I'm going to present it in an unusual way by summarizing the results first. This is so people who do not have time to follow the whole story, grasp at least grasp some idea.

30. 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

31. Math Lessons - Yutaka Taniyama Math Lessons yutaka taniyama. yutaka taniyama ( ?, November 12, 1927 –November 17, 1958) was a Japanese mathematician, best known for http://www.mathdaily.com/lessons/Yutaka_Taniyama

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Number theorists Yutaka Taniyama Yutaka Taniyama November 12 November 17 ) was a Japanese mathematician, best known for conjecturing the Taniyama-Shimura theorem after a meeting with André 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

32. Math Lessons - Yutaka Taniyama Math Lessons yutaka taniyama. yutaka taniyama. (Redirected from taniyama).yutaka taniyama ( ?, November 12, 1927 – November 17, http://www.mathdaily.com/lessons/Taniyama

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Number theorists Yutaka Taniyama (Redirected from Taniyama Yutaka Taniyama November 12 November 17 ) was a Japanese mathematician, best known for conjecturing the Taniyama-Shimura theorem after a meeting with André 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

33. The Whole Story when yutaka taniyama and Goro Shimura, two young academics, He was unableto prove the Shimurataniyama conjecture, but he was able to link it with http://www.simonsingh.com/FLT_the_whole_story.html

34. FLT -The Book The Japanese genius yutaka taniyama killed himself in despair, while the Germanindustrialist Paul Wolfskehl claimed Fermat had saved him from suicide. http://www.simonsingh.com/Fermats_Last-Theorem_The_Book.html

The Book Back to Fermat Corner Reviews of FLT Birth of the Book Read an Excerpt ... Overseas Editions Fermat's Last Theorem (aka Fermat's Enigma in America) The Book In 1997 I published my first book, a biography of a mathematical theorem. In this section of the website, you can read reviews and an extract, and you can also find out about the background to the book. Below is a very brief summary what it is about. 'I have discovered a truly marvellous proof, which this margin is too narrow to contain... With these tantalising words the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. Fermat's Last Theorem looked simple enough for a child to solve, yet the finest mathematical

35. Elliptic Curves, Modular Forms And The Taniyama-Shimura Conjecture taniyama. yutaka taniyama. yutaka taniyama and Goro Shimura were students atTokyo University. In postwar Japan, many university lecturers were out of http://people.bath.ac.uk/ma3fmr/ma10126/maths.html

The purpose of this page is to explain some of the basic maths that is referred to on the other pages of this site. It is in no way a definitive explanation but there are many sources where you can find this sort of information. Links click here to go to the relevant section of the page: Elliptic Curves Modular Forms Taniyama-Shimura Conjecture Elliptic Curves When you hear/read "Elliptic Curves", you will most likely think that it is something to do with ellipses or other graphs. Unfortunately, the name doesn't mean very much and elliptic curves are just equations of the form y = x + ax + bx + c where a,b and c are any constants These equations look pretty straight-forward but it is very difficult to work out how many whole-number solutions they have. It is possible to find solutions, but proving that they are the only ones is very difficult. To make their lives easier, mathematicians try to find out how many solutions there are in clock arithmetic. This probably doesn't sound like it's any easier but trust me it is! Clock arithmetic is something you use every day when talking about time. If you want to know what the time is 6 hours after 10 o'clock, you don't say it is 16 o'clock, it is 4 o'clock. This is because when you add one to twelve, you go back to one. 12 is the same as 0. Mathematicians use exactly the same idea but they don't always use 12. you can use any number you like for the size of the clock. Finding the number of solutions to an elliptic equation using clock arithmetic is much easier than it is when you use the entire number line as you have much fewer possibilities to check.

36. Shimura-Taniyama-Weil Conjecture yutaka taniyama. Born 12 Nov 1927 in Kisai (north of Tokyo), Japan. Died 17Nov 1958 in Tokyo, Japan. Let E be an elliptic curve whose equation has http://people.bath.ac.uk/ma2wyec/taniyama.html

A very general and important conjecture (and now theorem) connecting topology and number theory which arose from several problems proposed by Taniyama in a 1955 international mathematics symposium. Yutaka Taniyama Born: 12 Nov 1927 in Kisai (north of Tokyo), Japan Died: 17 Nov 1958 in Tokyo, Japan Let E be an elliptic curve whose equation has integer coefficients , let N be the so-called conductor of E and, for each n , let a n be the number appearing in the L -function of E . Then, in technical terms, the Taniyama-Shimura conjecture states that there exists a modular form of weight two and level N which is an eigenform under the Hecke operators and has a Fourier series a n q n In effect, the conjecture says that every rational elliptic curve is a modular form in disguise. Or, more formally, the conjecture suggests that, for every elliptic curve y = Ax + Bx + Cx + D over the rationals, there exist nonconstant modular functions f(z) and g(z) of the same level N such that [f(z)] = A[g(z)] + Cg(z) + D Equivalently, for every elliptic curve, there is a modular form with the same Dirichlet L -series.

37. Here Are Some Articles Related To Fermat S Last Theorem. Be Aware yutaka taniyama and his time very personal recollections , by Goro Shimura;Bulletin of the London Mathematical Society, Volume 21 (1989), pages 186196. http://www.math.wisc.edu/~propp/courses/491/articles

38. Goro Shimura: Information From Answers.com Shimura was a colleague and a friend of yutaka taniyama. They wrote a book (thefirst book treatment) on the complex multiplication of abelian varieties, http://www.answers.com/topic/goro-shimura

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Goro Shimura Wikipedia Goro Shimura Goro Shimura Goro Shimura -) is a Japanese American mathematician , and currently a professor of mathematics at Princeton University Shimura was a colleague and a friend of Yutaka Taniyama . They wrote a book (the first book treatment) on the complex multiplication of abelian varieties , an area which in collaboration they had opened up. Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication and modular forms to higher dimensions (amongst other results). This work (and other developments it provoked) provided some of the 'raw data' later incorporated into the Langlands program . It equally brought out the concept, in general, of Shimura variety ; which is the higher-dimensional equivalent of modular curve . Even to state in general what a Shimura variety is quite a formidable task: they bear, roughly speaking, the same relation to general Hodge structure s as modular curves do to elliptic curves Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms. He also argues for a 'romantic' approach, something he finds lacking in the younger generation of mathematician. The central 'Shimura variety' concept has been tamed (by application of

39. Fermat's Last Theorem: Definition And Much More From Answers.com which would provide a counterexample to the taniyamaShimura conjecture. Wall-Sun-Sun prime yutaka taniyama open problem Richard Taylor http://www.answers.com/topic/fermat-s-last-theorem

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Dictionary Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Fermat's last theorem Dictionary Fer·mat's last theorem fĕr-m¤z n. The theorem that the equation a n b n c n has no solutions in positive integers a, b, c if n is an integer greater than 2. It was stated as a marginal note by Pierre de Fermat around 1630 and not proved until 1994 by the British mathematician Andrew Wiles (born 1953). Wikipedia Fermat's last theorem Pierre de Fermat Fermat's last theorem (sometimes abbreviated as FLT and also called Fermat's great theorem ) is one of the most famous theorems in the history of mathematics . It states that: There are no positive integers x y , and z such that in which n is a natural number greater than 2. The 17th-century mathematician Pierre de Fermat wrote about this in in his copy of Claude-Gaspar Bachet 's translation of the famous Arithmetica of Diophantus : "I have discovered a truly remarkable proof of this theorem that the margin of this page is too small to contain". (Original

40. Yutaka Taniyama Université Montpellier II Translate this page yutaka taniyama (1927-1958). Cette image et la biographie complète en anglaisrésident sur le site de l’université de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1873

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