Introduction to a book of Labesse-Waldspurger

Robert P. Langlands
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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.

Although I do not fully understand the nature of the difficulties surrounding the book's publication, presumably all related to the ever increasing reluctance, perhaps even refusal, of publishers to accept technical books in the vernacular, I do know that in the end its publication, not in France, not by a Quebec editor, but by the American Mathematical Society was possible largely, perhaps only, thanks to the fortunate, and probably rare, circumstance that the then president of the Society was a francophile and was willing to use his good offices with the Society's publication branch. Although grateful to the president, I found the incident a sad sign of a serious intellectual decay, not in the USA but in Europe --- and perhaps in Quebec as well.

A final comment. There are very many mathematicians who have made important contributions in recent decades to the analytic theory of automorphic forms. Those of James Arthur and of Jean-Loup Waldspurger are I believe, even among these, outstanding. I do not think that they have received from the mathematical community the recognition they deserve.

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