Robert Langlands (born 1936 in Canada) is one of the most significant mathematicians of the 20th century, with profound insights in number theory and representation theory. 1936 (MCMXXXVI) was a leap year starting on Wednesday (link will take you to calendar). ... A mathematician is a person whose primary area of study and research is mathematics. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999 in the... Number theory is the formal study of numbers. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ...

Langlands attended the University of British Columbia as an undergraduate and received his PhD from Yale University in 1960. During the early 1960s he developed the general theory of Eisenstein series for discrete groups, initiated by Atle Selberg; this, roughly speaking, is the continuous spectrum theory of automorphic forms, for arithmetic groups in semisimple groups. Though his work was strong, he was not offered tenure at Princeton University. He spent a year in Turkey, working in isolation, during which time he had profound insights. His subsequent work shook mathematics (in a famous anecdote, André Weil complained that a conversation with Langlands had induced a headache). He has been a permanent member of the Institute for Advanced Study since the early 1970s. The University of British Columbia (UBC) is a public university with its main campus located at Point Grey, in the University Endowment Lands adjacent to Vancouver, British Columbia, Canada and another smaller campus known as UBC Okanagan located in Kelowna, British Columbia. ... Yale University is a private university in New Haven, Connecticut. ... 1960 (MCMLX) was a leap year starting on Friday (the link is to a full 1960 calendar). ... The 1960s decade refers to the years from 1960 to 1969, inclusive. ... In mathematics, Eisenstein series are particular modular forms with infinite series expansions that may be written down directly. ... In mathematics, a discrete group is a group G equipped with the discrete topology. ... Atle Selberg (born June 17, 1917) is a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory. ... In mathematics and physics, continuous spectrum is, roughly speaking, a non-countable set of eigenvalues of an operator. ... In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms. ... In mathematics, an arithmetic group (arithmetic subgroup) in a linear algebraic group G defined over a number field K is a subgroup Γ of G(K) that is commensurable with G(O), where O is the ring of integers of K. Here two subgroups A and B of a group... In mathematics, the term semisimple is used in a number of related ways, within different subjects. ... Tenure commonly refers to academic tenure systems, in which professors (at the university level)—and in some jurisdictions schoolteachers (at primary or secondary school levels)—are granted the right not to be dismissed without cause after an initial probationary period. ... Princeton University is a coeducational private university located on an extensive campus in and around suburban Princeton, New Jersey. ... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ... The 1970s decade refers to the years from 1970 to 1979, inclusive. ...

Langlands is the author of the Langlands program, a deep web of conjectures connecting number theory and representation theory. In mathematics, the Langlands program is a web of far-reaching and influential conjectures that connect number theory and the representation theory of certain groups. ... In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. ...

Langlands understood that the theory of automorphic representation offers a generalization of class field theory, a central topic in algebraic number theory. Thus, in crude terms, to every representation of a Galois group there should be associated an automorphic form. Taken to its logical and organisational conclusion, this leads to his famous functoriality conjecture, which altered the understanding of key issues in number theory. In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms. ... In mathematics, class field theory is a major branch of algebraic number theory. ... 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, a Galois group is a group associated with a certain type of field extension. ...

To give evidence for this idea, by working out special cases, Hervé Jacquet and Langlands developed an idea of the Russian mathematicians, that representation theory is the setting for the theory of automorphic forms. Using every tool at their disposal, they gave a surprisingly complete theory of automorphic forms on the general linear group GL(2), establishing important cases of functoriality. In mathematics, the general linear group of degree n over a field F (such as R or C), written as GL(n, F), is the group of n×n invertible matrices with entries from F, with the group operation that of ordinary matrix multiplication. ...

Subsequently Langlands and James Arthur developed the Selberg trace formula as a method of attacking functoriality in general. In mathematics, the Selberg trace formula is a central result, or area of research, in non-commutative harmonic analysis. ...

The functoriality conjecture is far from proved, but a special case (the octahedral Artin conjecture, proved by Langlands and Tunnell) was the starting point of Andrew Wiles' attack on the Taniyama-Shimura conjecture and the proof of Fermat's last theorem. 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. ... Sir Andrew John Wiles (born April 11, 1953) is a British mathematician living in the United States. ... 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. ... Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats last theorem (edition of 1670). ...

Since the mid-1980s he has turned his attention to physics, where his contributions have been less influential than his earlier work. The 1980s decade refers to the years from 1980 to 1989, inclusive. ... A Superconductor demonstrating the Meissner Effect. ...

In 1996, Langlands received the Wolf Prize for his work on the Langlands program. 1996 (MCMXCVI) was a leap year starting on Monday of the Gregorian calendar, and was designated the International Year for the Eradication of Poverty. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples, irrespective of nationality, race, colour, religion, sex or political views. The prize is awarded in Israel by the Wolf Foundation, founded by Dr. Ricardo...

External links

• The work of Robert Langlands