Editorial Comments: This essay was posted here in 2016 and published in August 2018 in the book Langlands 纲领和他的数学世界. (Langlands program and his mathematical world.) The essay appeared in English and was also translated into Chinese.
Robert P. Langlands
Author's comments: The text on the genesis and gestation of functoriality was for an informal lecture at the Tata Institute of Fundamental Research in Bombay delivered on short notice at the suggestion of Venkataraman. It has been suggested to me that the first four pages, a brief summary of the development of the theory of automorphic forms before 1960, roughly as it affected my initial reflections, manage to be simultaneously trite and eccentric and might be best omitted.
Author's Comments: This letter was written from Berkeley.
There are at several aspects of Harish-Chandra, his life, and his work on which one can reflect: his personality; the nature of his contributions and their position in mathematics; his relation to the land of his birth.
Author's comments: This essay, entitled "A letter to Turkish readers from Robert Langlands" appears in the Turkish translation of the extremely popular book "Love and Math" by Edward Frenkel. It does not refer to the book but comments in an informal manner on my relations with Turkey and Turkish mathematicians. The two photographs were taken by the Turkish authorities when we applied for a residence permit for a year's stay in 1967/68. I am very fond of the one with the children.
Author's comments: There are one or two comments I neglected to make in the course of the lecture or matters that were inadequately explained.
Author's comments: These terse comments were intended as a suggestion not to read the Mostow lecture or listen to it with preconceptions about the nature of a geometric theory.
Author's comments: The book La formule des traces tordue needed no introduction from me, but I did write it at the authors' request, in part because I was troubled by the circumstances of its appearance. I have, I believe, as a mathematician led a much richer intellectual life than the circumstances of my childhood would have normally permitted. So I am distressed by the diminishing possibilities of our profession and cannot always resist expressing my uneasiness and disappointment in a somewhat dyspeptic voice.
Author's comments: Problems of endoscopy first arose as I began the study of Shimura varieties in Bonn during the academic year 1970/71. I reflected on them for a long time, in part in collaboration with Labesse, in part in collaboration with Shelstad. I presented a fairly mature form of my reflections in the Paris lectures, Les débuts d'une formule des traces stable, in which the presence of a major obstacle, overcome considerably later through the efforts of a number of mathematicians, in particular Waldspurger and Ngô, was clearly described.