How to be a pro (Halmos)

Friday August 20, 2021

This is a section (pages 264-268) from I want to be a mathematician, by Halmos.

Anna, one of the mathematics department secretaries at Chicago, complained to me once when we met at a party and she had already consumed several gin and tonics. She was a good typist, and she didn't have much trouble picking up the art of technical, mathematical, typing—but she hated every minute of it. You have to look at every symbol separately, you have to keep changing "typits" or Selectric balls, you have to shift a half space up or down for exponents and subscripts, and you have no idea what you're doing. "I'm not going to spend my life flipping that damned carriage up and down", she said.

Another time Bruno, a well-known mathematician, asked me: "How did you manage to make your ten lectures at the CBMS conference all the same length? Isn't it true that some things take longer? When I did it, some of my talks were 45 minutes, and some 75."

More recently still I asked Calvin, a colleague, "Can you give a graduate student a ride to this month's Wabash functional analysis seminar?" "No", he said, "you better get someone else. I've been away, giving colloquium talks twice this month, and that's enough travelling."

I didn't make up any of this (except the names). Do you see what these three stories have in common? To me it's obvious, it jumps to the eye, and it horrifies me. What Anna, Bruno, and Calvin share and express is widespread and bad: it's the "me" attitude. It is the attitude that says "I do only what's important to me, and I am more important to me than the profession."

I think an automobile transmission mechanic should try to be the best automobile transmission mechanic he has the talent to be, and butlers, college presidents, shoe salesmen, and hod-carriers should aim for perfection in their professions. Try to rise, improve conditions if you can, and change professions if you must, but as long as you are a hod-carrier, keep carrying those hods. If you set out to be a mathematician, you must learn the profession, every part of it, and then work at it, profess it, live it as best you can. If you keep asking "what's there in it for me?", you're in the wrong business. If you're looking for comfort, money, fame, and glory, you probably won't get them, but if you keep trying to be a mathematician, you might.

I didn't preach to Calvin, but if I had done so, my sermon would have said that you support an activity such as the Wabash seminar (I'll tell more about that seminar later) without even thinking about it—it's an integral part of professional life. You go to such seminars the way you get dressed in the morning, nod amiably to an acquaintance you pass on the street, or brush your teeth before you go to bed at night. Sometimes you feel like doing it and sometimes not, but you do it always—it's a part of life and you have no choice. You don't expect to get rewarded if you do and punished if you don't, you don't think about it—you just do it.

A professional must know every part of his profession and (we all hope) like it, and in the profession of mathematics, as in most others, there are many parts to know. To be a mathematician you have to know how to be a janitor, a secretary, a businessman, a conventioneer, an educational consultant, a visiting lecturer, and, last but not least, in fact above all, a scholar.

As a mathematician you will use blackboards, and you should know which ones are good and what is the best way and the best time to clean them. There are many kinds of chalk and erasers; would you just as soon make do with the worst? At some lecture halls you have no choice—you must use the overhead projector, and if you don't come prepared with transparencies, your audience will be in trouble. Word processors and typewriters, floppy disks and lift-off ribbons—ignorance is never preferable to bliss. Should you ditto your preprints, or use mimeograph, or multilith, or xerox? Who should make decisions about these trivialities—you, or someone who doesn't care about your stuff at all?

From time to time you'll be asked for advice. A manufacturer will consult you about the best shape for a beer bottle, a dean will consult you about the standing of his mathematics department, a publisher will consult you about the probably sales of a proposed textbook on fuzzy cohomology. Possibly they will be genteel and not even mention paying for your service; at other times they will refer delicately to an unspecified honorarium that will be forthcoming. Would they treat a surgeon the same way, or an attorney, or an architect? Would you? Could you?

I am sometimes tempted to tell people that I am a real doctor, not the medical kind; my education lasted a lot longer than their lawyer's and cost at least as much; my time and expertise are worth at least as much as their architect's. In fact, I do not use tough language, but I've long ago decided not to accept "honoraria" but to charge fees, carefully spelled out and agreed on in advance. I set my rates some years back, when I was being asked to review more textbooks than I had time for. I'd tell the inquiring publisher that my fee is $1.00 per typewritten page or $50.00 per hour, whichever comes to less. Sometimes the answer was: "Oh, sorry, we didn't really want to spend that much", and at other times it was, matter-of-factly, "O.K., send us your bill along with your report". The result was that I had less of that sort of work to do and got paid more respectably for what I still did. My doctor, lawyer, and architect friends tell me that prices have changed since I established mine. The time has com, they say, to double the charges. The answers, they predict, will remain the same: half "no" and half "sure, of course".

A professional mathematician talks about mathematics at lunch and at tea. The subject doesn't have to be hot new theorems and proofs (which can make for ulcers or ecstasy, depending)—it can be a new teaching twist, a complaint about a fiendish piece of student skullduggery, or a rumor about an error in the proof of the four color theorem. At many good universities there is a long-standing tradition of brown-bag (or faculty club) mathematics lunches, and they are an important constituent of high quality. They keep the members of the department in touch with one another; they make it easy for each to use the brains and the memory of all. At a few universities I had a hand in establishing the lunch tradition, which then took root and flourished long after I left.

The pros go to colloquia, seminars, meetings, conferences, and international congresses—and they use the right word for each. The pros invite one another to give colloquium talks at their universities, and the visitor knows—should know—that his duty is not discharged by one lecture delivered between 4:10 and 5:00 p.m. on Thursday. The lunch, which gives some of the locals a chance to meet and have a relaxed conversation with the gues, the possible specialists' seminar for the in-group at 2:00, the pre-lecture coffee hour at 3:00, and the post-lecture dinner and evening party are essential parts of the visitor's job description. It makes for an exhausting day, but that's how it goes, that's what it means to be a colloquium lecturer.

Sometimes you are not just a colloquium lecturer, but the "Class of 1909 distinguished Visitor", invited to spend a whole week on the campus, give two or three mathematics talks and one "general" lecture, and, in between, mingle, consult, and interact. Some do it by arriving in time for a Monday afternoon talk, squeezing in a Tuesday colloquium at a sister university 110 miles down the road, reappearing for a Wednesday talk and a half of Thursday (spent mostly with the specialist crony who arranged the visit), and catching the plane home at 6:05 p.m. Bad show—malfeasance and nonfeasance—that's not what the idea is at all. When Bombieri came to Bloomington, I understood much of his first lecture, almost none of the second, and gave up on the third (answered my mail instead)—but I got a lot out of his presence. I heard him hold forth on meromorphic functions at lunch on Monday, explain the Mordell conjecture over a cup of coffee Wednesday afternoon, and at dinner Friday evening guess at the probably standing of Euler and Gauss a hundred years from now. We also talked about clocks and children and sport and wine. I learned some mathematics and I got a little insight into what makes one of the outstanding mathematicians of our time tick. He earned his keep as Distinguished Visitor, not because he is a great mathematician (that helps!) but because he took the job seriously. It didn't take his talent to do that; that's something us lesser people can do too.

Mathematical talent is probably congenital, but aside from that the most important attribute of a genuine professional mathematician is scholarship. The scholar is always studying, always ready and eager to learn. The scholar knows the connections of his specialty with the subject as a whole; he knows not only the technical details of his specialty, but its history and its present standing; he knows about the others who are working on it and how far they have reached. He knows the literature, and he trusts nobody: he himself examines the original paper. He acquires firsthand knowledge no only of its intellectual content, but also of the date of the work, the spelling of the author's name, and the punctuation of the title; he insists on getting every detail of every reference absolutely straight. The scholar tries to be as broad as possible. No one can know all of mathematics, but the scholar can succeed in knowing the outline of it all: what are its parts and what are their places in the whole?

These are the things, some of the things, that go to make up a pro.