Thursday, July 23, 2015

Robert Langlands on his early career

Langlands is a distinguished mathematician, professor at the Institute of Advanced Study. Here is he giving some background on his career, preliminary to discussing some of main mathematical concerns for a video for an Oxford conference. My quotations here, from that essay, are selective.

That topic became mathematics not out of a strong preference for that subject, but because it pretty much required no preparation, only native ability.

then I went on to Yale, a fortunate choice: the quality was high, although somewhat specialized; I had no obligations as any kind of teaching assistant, so that my time was my own; and, in contrast with, say, Princeton or Harvard, there were no fellow students with superior preparation eager to intimidate me. The few courses or seminars I had were helpful and instructive, so that I had a great deal of time on my own to spend in the library.

None the less, more by good luck than by good management, both [thesis work on semi-groups and a paper on Eisenstein series, written while a graduate student] were important in my career. The first came to the attention of Edward Nelson, who, then an assistant professor at Princeton, found enough merit in the first that I was offered, sight unseen and with no documentation, a position as instructor at Princeton. I had wanted to stay at Yale, and a number of the faculty would have been content to offer me a similar position, but fortunately the resident probabilist had taken a dislike to me, and he blocked the appointment. So I went to Princeton, where, asked to speak in a small analysis seminar, I spoke on the Eisenstein series paper. Bochner was favorably impressed, largely by the circumstance that I had already been thinking about a topic with no relation to my thesis

he [Bochner] had also encouraged, one could even say forced, me to give a graduate-course on class field theory. I knew nothing about it and was scared stiff, but could not refuse. I learned a great deal. So did a few students. It is impossible to overestimate the debt I owe to Bochner

I had — in the shape of the department chairman, also a probabilist — another stroke of luck. Fancying himself as a Hercules whose task was to cleanse the department of the deadwood accumulated under the influence, in particular, of Bochner, he took it upon himself to drive a number of us out. The story is complicated, but the upshot was that I returned to Yale, where I was very happy, but I could not resist the offer of an appointment to the Institute, an offer that at the time would not, because of a gentleman’s agreement between the two institutions, have been possible if I had remained at the University. This offer I owe, I am certain, principally to Harish-Chandra

So these early years were free of anxiety, but not of discouragement. Mathematics, if one is at all ambitious, is difficult. I was free to give it up, free to ignore any constraining demands, from deans or chairmen, free for example not to apply for grants, to write or publish only what I cared to write or publish and only when I felt it appropriate, willing to continue in modest circumstances in out-of-the-way places, but not willing to abandon the goals I had set for myself, or that, say, Bochner had encouraged me to set.

It was only when completely discouraged by my attempts to find the elusive non-abelian class field theory or the elusive automorphic L-functions that I began to think that the time had come to abandon mathematical research. Largely as a consequence of a chance acquaintance with a Turkish visitor to Princeton, the economist Orhan T¨urkay, unfortunately recently deceased, that I decided, as a first, mildly adventurous, step to spend a year or more in Turkey with my family.

I had recovered from my discouragement and had a great many mathematical ideas to deal with, so that it was just as well that I and my family were not dealing with too difficult an adaptation. There were difficulties, but they were overcome

Nevertheless, I wanted to express clearly my sentiment that thanks to circumstances of time and place I was never constrained by my profession as a mathematician, never forced to any kind of submission. I could always, without great reserves of moral courage, do as I wanted.

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