October 16, 2007

  • Deep Beauty, continued:

    In memory of
    Harish-Chandra,
    who died at 60
    on this date in 1983


     
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    Harish-Chandra in 1981

    (Photo by Herman Landshof)


    Recent Log24 entries have parodied the use of the phrase "deep beauty" as the title of the Oct. 3-4 physics symposium of that name,
    which was supported by a grant from the John Templeton Foundation and
    sponsored by the Department of Philosophy at
    Princeton University.
    Such parody was in part suggested by the symposium's sources of
    financial and academic support. This support had, in the
    view of some, the effect of linking the symposium's topic, the
    mathematics of quantum theory, with both religion (the Templeton Foundation) and philosophy (a field sometimes associated in popular thought-- though not at Princeton-- with quantum mysticism.)

    As a corrective to the previous parodies here, the following material
    on the mathematician Harish-Chandra may help to establish that there
    is, in fact, such a thing as "deep beauty"-- if not in physics,
    religion, or philosophy, at least in pure mathematics.

    MacTutor History of Mathematics:

    "Harish-Chandra worked at the Institute of Advanced Study at Princeton from 1963. He was appointed IBM-von Neumann Professor in 1968."

    R. P. Langlands (pdf, undated, apparently from a 1983 memorial talk):

    "Almost immediately upon his arrival in Princeton he began working at a ferocious pace,
    setting standards that the rest of us may emulate but never achieve. For us there is a welter
    of semi-simple groups: orthogonal groups, symplectic groups, unitary groups, exceptional
    groups; and in our frailty we are often forced to treat them separately. For him, or so it
    appeared because his methods were always completely general, there was a single group. This
    was one of the sources of beauty of the subject in his hands, and I once asked him how he
    achieved it. He replied, honestly I believe, that he could think no other way. It is certainly true
    that he was driven back upon the simplifying properties of special examples only in desperate
    need and always temporarily."

    "It is difficult to communicate the grandeur of Harish-Chandra's
    achievements and I have
    not tried to do so. The theory he created still stands-- if I may be
    excused a clumsy simile-- like a Gothic cathedral, heavily buttressed
    below but, in spite of its great weight, light and
    soaring in its upper reaches, coming as close to heaven as mathematics
    can. Harish, who was
    of a spiritual, even religious, cast and who liked to express himself
    in metaphors, vivid and
    compelling, did see, I believe, mathematics as mediating between man
    and what one can only
    call God. Occasionally, on a stroll after a seminar, usually towards
    evening, he would express
    his feelings, his fine hands slightly upraised, his eyes intent on the
    distant sky; but he saw as
    his task not to bring men closer to God but God closer to men. For
    those who can understand his work and who accept that God has a
    mathematical side, he accomplished it."

    For deeper views of his work, see

    1. Rebecca A. Herb, "Harish-Chandra and His Work" (pdf), Bulletin of the American Mathematical Society, July 1991, and
    2. R. P. Langlands, "Harish-Chandra, 1923-1983" (pdf, 28 pp., Royal Society memoir, 1985)