Langlands received his PhD from Yale University in 1960. During the 1960's he developed the theory of Eisenstein series, initiated by Selberg. Though his work was strong, he failed to receive 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. He has been a permanent member of the Institute for Advance Study since the early 1970's.
Langlands understood that the theory of automorphic forms gives a generalization of class field theory, a central topic in algebraic number theory. Thus to every representation of a Galois group there should be associated an automorphic form. Taken to its logical conlusion, this leads to his famous functoriality conjecture, which altered our understanding of what the key issues are in number theory. To give evidence for this idea, 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 GL(2) establishing important cases of functoriality. Subsequently Langlands and James Arthur developed the Selberg trace formula as a method of attacking functoriality in general. 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 Wiles' attack on the Shimura Taniyama conjecture and the proof of Fermat's last theorem.
Langlands has not worked in number theory since the mid-1980's having turned his attention to physics, where his contributions have been less influential than his earlier work.
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