Personal History
The first out-of-town conference I attended was at the University of Arkansas in April 1988. There was a mini-course of 5 lectures by Harold Shapiro on Quadrature Domains, and individual lectures by
other senior operator theorists and complex analysts (in those days, graduate students rarely traveled to conferences, and never gave talks). My adviser, Donald Sarason, had arranged for several of his students to go, and to share a room in a hotel (a Hilton! I had heard of the luxury hotel brand, but had never set foot in one, let alone slept in one.)
This conference turned out to be the most important event of my professional life. I found it terribly exciting—real mathematicians talking about their work and progress on interesting problems. I could understand the statements, even if the proofs were complicated. Outside the talks, the professors talked to the graduate students as if we were real people.
Allen Shields even invited me to join a group for dinner. (Unfortunately I was too shy to accept—a foolish mistake).
At the conference banquet, I sat at a table with several professors who chatted with us, and Philip Davis gave a fairly long after-dinner speech that was witty, interesting, and for me the high-light of the evening.
Before I went to the conference I was feeling somewhat desperate. I was in my fourth year as a Ph.D. student at Berkeley, had no results, and every time I sat down to work the sense that I had to prove something RIGHT NOW caused my anxiety and blood pressure to spike, making progress even more difficult. I was starting to believe that I would never finish my degree.
After I came back, I was newly enthused about mathematics, and within two weeks had proved a theorem that turned into my thesis. It wasn’t a very good theorem, but it was good enough for my adviser to sign off on my thesis. As soon as he did, with the psychological burden lifted, I became a much better mathematician, and I proved a theorem in the summer I graduated of which I am still proud.
Quadrature domains, which I had never heard of before the mini-course, have turned up in my professional life in unexpected and interesting ways. Many of the people I met at that conference became friends.
Since then, I have attended numerous conferences and organized several. Some have been more enjoyable than others.
Here are my personal opinions on what makes for a good conference.
The participants
Mathematics is a human activity (see https://www.math.wustl.edu/wp/mccarthy/publication/journal-of-xenomathematics/ for my thoughts on this), and a social activity. We may prove theorems on our own, but we need to communicate with others. Conferences serve several social functions, the relative importance of which change over one’s career.
- They serve to educate—we learn from the talks, we learn from discussions, and we learn from conversations at meals. We learn both mathematics, and mathematical culture.
- They serve to advertise—here is my new theorem! Let me explain why it is interesting!
- They serve to socialize. When you go to your first conference, you probably only know a few people from your own university. But over time you get to keep meeting people you have met before, some of whom become friends, even close friends.
- They serve to network. This is like socializing, but there is a subtext of helping you professionally. After all, you are much more likely to get a job offer from a university if someone on the faculty there has seen you talk.
- They serve to energize. I am really impressed by the theorem the speaker is telling us about. Next year I want to be on the stage talking about my own impressive theorem!
Conference attendees are a heterogeneous group—graduate students, postdocs, junior faculty, senior faculty, some mathematicians who are close to the core theme of the conference, some who are quite far from it, occasionally undergraduates and non-professionals. They all bring different things, and want different things from the conference. For the conference to be successful, they must all cooperate.
Conference Talks
There are several excellent articles on giving mathematical talks; see for example the essays by B. Kra https://www.ams.org/notices/201302/rnoti-p242.pdf and T. Tao https://terrytao.wordpress.com/career-advice/talks-are-not-the-same-as-papers/ on talks in general, and the post by W. Ross https://blog.richmond.edu/wross/2008/03/26/how-to-give-a-good-20-minute-math-talk/ on 20 minute talks in particular. My views on colloquium talks are here https://www.ams.org/profession/leaders/workshops/gcoll.pdf. In this essay, I will confine myself specifically to conference talks.
- The best medium for most mathematics talks is a blackboard, perhaps with some interruptions for graphics. This is for two reasons. The mathematical one is that blackboards allow far more material to be visible, so the audience can check back on definitions and statements. The psychological one is that it forces the speaker to proceed slowly, since it takes time to write. (See V. Peller’s essay https://arxiv.org/pdf/1204.5141v1.pdf for the advantages of the blackboard).
- At many conferences blackboards are unavailable. If you are giving a Beamer talk:
- GO SLOWLY and don’t write too much.
- Theorem: For an N minute talk, the optimal number of slides is N/2 (You get the title page for free.) Any number larger than
is malpractice. It takes much longer for the audience to absorb ideas and statements than most speakers realize (I find my ability to absorb decreases over the course of the conference, as I get more tired.) - Never put a full paragraph on a slide. Write the minimum necessary—it does not have to be in full sentences. We are all conditioned to read whatever is put in front of us. Time spent reading is time not spent listening to the speaker.
- Do not end with a slide that just says Thank you. Your last slide should contain your main result(s), so that audience members can look at it while absorbing your talk and thinking about questions.
(You can put “Thank You” on the last line if you want—a good use of the \pause command in Beamer.)
- There may well be people in the audience who heard you talk on a similar theme before. Don’t let this influence your presentation. Many other people in the audience haven’t attended your talk before, and even the ones who did attend don’t remember very much about it.
- Know the mathematical range of the audience. Try to make the talk worthwhile for all of them, not just a couple of experts.
- Everybody in the audience has chosen to attend your talk, instead of spending their time proving a theorem (or whatever else humans do when they are not attending talks). It is your responsibility to make sure their faith in you is justified, and the time at your talk is well-spent.
- A good talk takes a lot of preparation. Don’t cheat your audience by not preparing properly. Do not use slides or notes from another talk—make a fresh preparation for this particular audience. Of course, there may be significant overlaps with prior talks, but your emphasis should shift depending on who the audience is (and what the theme of the conference is). Two thirds of a good 60 minute talk is not a good 40 minute talk.
- Iff you like the talk, tell the speaker. Everybody likes positive feedback. And if nobody is coming up to you after your talk to tell you they liked it, perhaps you should wonder what you should be doing differently.
- Sadly, not every speaker will have taken the lessons of the previous section to heart, and some talks will be boring. If you get lost in a talk, it is perfectly acceptable to take out a pad of paper and work on your own mathematics. But don’t type on a keyboard—this is distracting for the audience around you.
Social Behavior
- Go to talks, not just by well-known mathematicians.
- Most conferences have plenary lectures (this means no other talk is scheduled simultaneously) and parallel sessions. The purpose of plenary talks is to inform—they should be like colloquia, but aimed at the audience designated by the conference. (So at an AMS meeting, a plenary talk should be just like a colloquium. At a conference on Hilbert Function spaces, the speaker can assume that the audience already believes that Hilbert Function spaces are inherently interesting, though still should try to convince the audience that the speaker’s particular subtopic is itself interesting.) Plenary talks close to you educate you about your current area of research. Plenary talks far from your current interests may educate you about your future area of research, or at least help you see a bigger picture of where your work fits.
- Parallel sessions have a range of speakers, from senior mathematicians to people giving their first ever conference talk. Attend talks in the parallel sessions too. Remember, everybody needs an audience. You want people to come to your talk, don’t you?
- Talk to people, at coffee breaks and meals. Go out to eat with other attendees at lunch and dinner. Do this in manageable groups. Having 20 odd mathematicians walk down the street looking for a restaurant for lunch where they can all sit together is ridiculous. Once the group exceeds 6 or 8 you can only talk to those sitting close to you anyway, so you may as well start in a smaller group.
- Introduce yourself to people you don’t already know, and talk to them. This is hard, especially if you are junior, but do it anyway. Some of these people will become your friends and collaborators, some will tell you interesting stories.
- If it is a themed conference, there will probably be a banquet. Go to the banquet. Try and ensure that some of the people sitting at your table are people you don’t already know (If you already know everybody at the conference, good for you! I have nothing to teach you.)
- Conference Organizers: Try to have the banquet in a venue where everybody at a table can hear verybody else near them. This means not too much background noise, and either small round tables (8 people maximum, 6 is better) or rectangular tables.
- It is traditional for the first speaker at the conference to give a speech at the banquet, or to tap somebody else to do so. This speech doesn’t have to be long, but it should have some message in addition to thanking the organizers.
- Organizing a conference is a lot of work. Don’t make unreasonable requests of the organizers.
- Organizing a conference is a lot of work. Thank the organizers!
Summary
Conferences are central to the practice of mathematics. Their success relies on your efforts as an attendee. This includes being a good audience member, being a good
speaker if you have the privilege of speaking at the conference, and making an effort to socialize, especially with people you don’t know, or who seem to need some help gaining entree. Done right, conferences are enjoyable and stimulating, and you will go home with a renewed enthusiasm to do mathematics.