Robert Phelan Langlands, CC FRS FRSC (/ˈlæŋləndz/; born October 6, 1936) is a Canadian mathematician.

He is emeritus professor and occupied Albert Einstein's office at the Institute for Advanced Study in Princeton, until 2020 when he retired.

In 1945, his family moved to White Rock, near the US border, where his parents had a building supply and construction business.

His first accomplishment in this field was a formula for the dimension of certain spaces of automorphic forms, in which particular types of Harish-Chandra's discrete series appeared.

This work led in turn, in the winter of 1966–67, to the now well known conjectures[14] making up what is often called the Langlands program.

Very roughly speaking, they propose a huge generalization of previously known examples of reciprocity, including (a) classical class field theory, in which characters of local and arithmetic abelian Galois groups are identified with characters of local multiplicative groups and the idele quotient group, respectively; (b) earlier results of Martin Eichler and Goro Shimura in which the Hasse–Weil zeta functions of arithmetic quotients of the upper half plane are identified with

These conjectures were first posed in relatively complete form in a famous letter to Weil,[14] written in January 1967.

, establishing among other things the Jacquet–Langlands correspondence showing that functoriality was capable of explaining very precisely how automorphic forms for

Subsequently, James Arthur, a student of Langlands while he was at Yale, successfully developed the trace formula for groups of higher rank.

This has become a major tool in attacking functoriality in general, and in particular has been applied to demonstrating that the Hasse–Weil zeta functions of certain Shimura varieties are among the

In 1995, Langlands started a collaboration with Bill Casselman at the University of British Columbia with the aim of posting nearly all of his writings—including publications, preprints, as well as selected correspondence—on the Internet.

In recent years he has turned his attention back to automorphic forms, working in particular on a theme he calls "beyond endoscopy".

[28] Among other honorary degrees, in 2003, Langlands received a doctorate honoris causa from Université Laval.

[30][31] On January 10, 2020, Langlands was honoured at Semiahmoo Secondary, which installed a mural to celebrate his contributions to mathematics.

Langlands spent a year in Turkey in 1967–68, where his office at the Middle East Technical University was next to that of Cahit Arf.