NationMaster - Encyclopedia: Emil Artin

Emil Artin (March 3, 1898-December 20, 1962) was an Austrian mathematician born in Vienna who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Indiana University 1938-1946, and Princeton University 1946-1958. He was the father of Michael Artin, an American algebraist currently at MIT. March 3 is the 62nd day of the year in the Gregorian Calendar (63rd in leap years). ... 1898 (MDCCCXCVIII) was a common year starting on Saturday (see link for calendar) of the Gregorian calendar (or a common year starting on Monday of the 12-day-slower Julian calendar). ... December 20 is the 354th day of the year (355th in leap years) in the Gregorian calendar. ... 1962 (MCMLXII) was a common year starting on Monday (link will take you to calendar). ... This article is in need of attention from an expert on the subject. ... Vienna (German: Wien [viËn]; Slovenian: Dunaj, Hungarian: BÃ©cs, Czech: VÃdeÅˆ, Slovak: ViedeÅˆ, Romany Vidnya; Croatian and Serbian: BeÄ) is the capital of Austria, and also one of the nine States of Austria. ... It has been suggested that this article or section be merged into Nazism. ... 1937 (MCMXXXVII) was a common year starting on Friday (link will take you to calendar). ... The Indiana University system, technically founded in 1820, is an eight-campus university system in the state of Indiana. ... Princeton University, incorporated as The Trustees of Princeton University, located in Princeton, New Jersey, is the fourth-oldest institution to conduct higher education in the United States. ... Michael Artin is an American mathematician, known for his contributions to algebraic geometry. ... The Massachusetts Institute of Technology, or MIT, is a research and educational institution located in the city of Cambridge, Massachusetts, USA. MIT is a world leader in science and technology, as well as in many other fields, including management, economics, linguistics, political science, and philosophy. ...

He was one of the leading algebraists of the century, with an influence larger than might be guessed from the one volume of his Collected Papers edited by his students Serge Lang and John Tate. He worked in algebraic number theory, contributing largely to class field theory and a new construction of L-function. He also contributed to the pure theories of rings, groups and fields. He developed the theory of braids as a branch of algebraic topology. Serge Lang (May 19, 1927â€“September 12, 2005) was a mathematician known for his work in algebra and for writing a variety of mathematics textbooks, including the very influential Algebra. ... You may be looking for John Tate (boxer) John Torrence Tate, born March 13, 1925 in Minneapolis, Minnesota, is an American mathematician, distinguished for many fundamental contributions in algebraic number theory and related areas in algebraic geometry. ... In mathematics, an algebraic number field (or simply number field) is a finite field extension of the rational numbers Q. That is, it is a field which contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and these days... In mathematics, class field theory is a major branch of algebraic number theory. ... The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary number theory. ... In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have similar (but not identical) properties to those familiar from the integers. ... In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ... In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ... In topology, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalisations. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ...

He was also an important expositor of Galois theory, and of the group cohomology approach to class field theory (with John Tate), to mention two theories where his formulations became standard. The influential treatment of abstract algebra by van der Waerden is said to derive in part from Artin's ideas, as well as those of Emmy Noether. He wrote a book on geometric algebra that gave rise to the contemporary use of the term, reviving it from the work of W. K. Clifford. In mathematics, Galois theory is a branch of abstract algebra. ... In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. ... You may be looking for John Tate (boxer) John Torrence Tate, born March 13, 1925 in Minneapolis, Minnesota, is an American mathematician, distinguished for many fundamental contributions in algebraic number theory and related areas in algebraic geometry. ... Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ... Bartel Leendert van der Waerden ( February 2, 1903 – January 12, 1996) was a Dutch mathematician who born in Amsterdam, Netherlands and died in Zürich, Switzerland. ... Emmy Noether (born NÃ¶ther) (March 23, 1882 â€“ April 14, 1935) was one of the most talented mathematicians of the early 20th century, with penetrating insights that she used to develop elegant abstractions which she formalized beautifully. ... Geometric algebra is a Clifford algebra given a geometric interpretation which makes it useful in an exceptionally wide range of physics problems, particularly those that involve rotations, phases or imaginary numbers. ... William Kingdon Clifford. ...

He left two conjectures, both known as Artin's conjecture. The first concerns Artin L-functions for a linear representation of a Galois group; and the second the frequency with which a given integer a is a primitive root modulo primes p, when a is fixed and p varies. These are unproven; Hooley proved a result for the second conditional on the first. In mathematics, particularly in number theory, the Artin conjecture on Artin L-functions concerns the region of the complex plane in which an Artin L-function is an analytic function. ... In mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation Ï of a Galois group G. These functions were introduced in the 1920s by Emil Artin, in connection with his research into class field theory. ... Representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. ... In mathematics, the Artin conjecture is a conjecture on the set of primes p modulo which a given integer a > 1 is a primitive root. ... A primitive root modulo n is a concept from modular arithmetic in number theory. ...

Emil Artin died in 1962, in Hamburg, Germany. This article is about the city in Germany. ...

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