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Wiles's Proof Of Fermat's Last Theorem
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Sir Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove using previous knowledge by almost all living mathematicians at the time. Wiles first announced his proof on 23 June 1993 at a lecture in Cambridge entitled "Modular Forms, Elliptic Curves and Galois Representations". However, in September 1993 the proof was found to contain an error. One year later on 19 September 1994, in what he would call "the most important moment of isworking life", Wiles stumbled upon a revelation that allowed him to correct the proof to the satisfaction of the mathematical community. The corrected proof was published in 1995. Wiles's proof uses many techniques from algebraic geometry and number theory and has many ramificatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Wiles1-3
Andrew is the English form of the given name, common in many countries. The word is derived from the , ''Andreas'', itself related to ''aner/andros'', "man" (as opposed to "woman"), thus meaning "manly" and, as consequence, "brave", "strong", "courageous", and "warrior". In the King James Bible, the Greek "Ἀνδρέας" is translated as Andrew. Popularity In the 1990s, it was among the top ten most popular names given to boys in English-speaking countries. Australia In 2000, the name Andrew was the second most popular name in Australia after James. In 1999, it was the 19th most common name, while in 1940, it was the 31st most common name. Andrew was the first most popular name given to boys in the Northern Territory in 2003 to 2015 and continuing. In Victoria, Andrew was the first most popular name for a boy in the 1970s. Canada Andrew was the 20th most popular name chosen for male infants in 2005. Andrew was the 16th most popular name for infants in British Columbia i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John H
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerhard Frey
Gerhard Frey (; born 1 June 1944) is a German mathematician, known for his work in number theory. Following an original idea of , he developed the notion of Frey–Hellegouarch curve, Frey–Hellegouarch curves, a construction of an elliptic curve from a purported solution to the Fermat's Last Theorem, Fermat equation, that is central to Wiles's proof of Fermat's Last Theorem. Education and career He studied mathematics and physics at the University of Tübingen, graduating in 1967. He continued his postgraduate studies at Heidelberg University, where he received his PhD in 1970, and his Habilitation in 1973. He was assistant professor at Heidelberg University from 1969–1973, professor at the University of Erlangen-Nuremberg, University of Erlangen (1973–1975) and at Saarland University (1975–1990). Until 2009, he held a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg-Essen, campus Essen. Frey was a visiting scientist at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is due both to his original contributions to a remarkably broad spectrum of mathematical theories, and to the mark he left on mathematical practice and style, through some of his own works as well as through the Bourbaki group, of which he was one of the principal founders. Life André Weil was born in Paris to agnostic Alsatian Jewish parents who fled the annexation of Alsace-Lorraine by the German Empire after the Franco-Prussian War in 1870–71. Simone Weil, who would later become a famous philosopher, was Weil's younger sister and only sibling. He studied in Paris, Rome and Göttingen and received his doctorate in 1928. While in Germany, Weil befriended Carl Ludwig Siegel. Starting in 1930, he spent two academic years at Aligarh Mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Modular Curve
In number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation :, such that is a point on the curve. Here denotes the -invariant. The curve is sometimes called , though often that notation is used for the abstract algebraic curve for which there exist various models. A related object is the classical modular polynomial, a polynomial in one variable defined as . The classical modular curves are part of the larger theory of modular curves. In particular it has another expression as a compactified quotient of the complex upper half-plane . Geometry of the modular curve The classical modular curve, which we will call , is of degree greater than or equal to when , with equality if and only if is a prime. The polynomial has integer coefficients, and hence is defined over every field. However, the coefficients are sufficiently large that computational work with the curve can be difficult. As a polynomial in with coefficients in , i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also called the field of rationals or the field of rational numbers. It is usually denoted by boldface , or blackboard bold A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Form
In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modular forms has origins in complex analysis, with important connections with number theory. Modular forms also appear in other areas, such as algebraic topology, sphere packing, and string theory. Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group \mathrm_2(\mathbb Z) \subset \mathrm_2(\mathbb R). Every modular form is attached to a Galois representation. The term "modular form", as a systematic description, is usually attributed to Erich Hecke. The importance of modular forms across multiple field of mathematics has been humorously re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yutaka Taniyama
was a Japanese mathematician known for the Taniyama–Shimura conjecture. Life Taniyama was born on 22 November 1927 in Kisai, a town in Saitama. He was the sixth of eight children born to a doctor's family. He studied at Urawa High School (present-day Saitama University) after graduating from Fudouoka Middle School. He suspended his college for two years due to his medical condition, but finally graduated in 1950. During Taniyama's college years, he aspired to be a mathematician after reading Teiji Takagi's work. In 1958, Taniyama worked as an Associate Professor after years of assistant at the University of Tokyo. He also obtained his doctorate from the University in May. In October, Taniyama was engaged to be married to , while the Institute for Advanced Study in Princeton, New Jersey offered him a position. On 17 November 1958, Taniyama committed suicide by poisoning himself with gas. He left a note explaining how far he had progressed with his teaching duties, and apolog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goro Shimura
was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem. Biography Gorō Shimura was born in Hamamatsu, Japan, on 23 February 1930. Shimura graduated with a B.A. in mathematics and a D.Sc. in mathematics from the University of Tokyo in 1952 and 1958, respectively. After graduating, Shimura became a lecturer at the University of Tokyo, then worked abroad — including ten months in Paris and a seven-month stint at Princeton's Institute for Advanced Study — before returning to Tokyo, where he married Chikako Ishiguro. He then moved from Tokyo to join the faculty of Osaka University, but growing unhappy with his funding situation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norwegian Academy Of Science And Letters
The Norwegian Academy of Science and Letters (, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick University in Christiania was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Trondhjem had no university, but had a learned society, the Royal Norwegian Society of Sciences and Letters, established in 1760. The purpose of a learned society in Christiania was to support scientific studies and aid publication of academic papers. The idea of the Humboldt-inspired university, where independent research stood strong, had overtaken the instrumental view of a university as primarily a means to produce civil servants. The city already had societies for specific professions, for instance the Norwegian Medical Society, which was founded in 1833. However, these societies were open to both academics within medicine as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
