We have a problem. I feel like we’re just not communicating properly. I hear you, but I don’t understand you. I appreciate that you have something to say, I just don’t like the way you’re saying it. I’m not angry, it’s just that I know you can do better. Don’t worry, I’m not going to leave you. But, dear speaker, I just wish you would do better.

In 1992 the physicist N. David Mermin wrote an article for Physics Today, in which he describes Physics talks saying, “the only pleasure it affords is the relief that washes over you as you realize, finally, that perhaps the end is in sight.” In math, we tend to suffer from a similar disaffectedness. Talks that just go on and on interminably and it’s not clear that a single person in the room knows what’s going on. Sometimes it even feels like that’s just the acceptable norm.

A few years ago one of those really validating bits of research came out confirming that boring speakers really do go on longer than exciting ones. Being exciting is hard. We can’t reasonably expect exciting speakers all the time. But keeping an eye on the time is not only easy, it’s a minimum display of respect that you can demonstrate for your audience.

The matter of giving a talk that your audience can actually understand, is a different thing altogether.

If you’ve been invited to give a colloquium talk, Sara Malec blogged 5 tips to give a good colloquium talk for the PhD Plus Epsilon Blog. For seminar talks, Jordan Ellenberg gives tips for giving talks on his blog Quomdocumque, and on What’s New, Terry Tao explains the important difference between writing a talk and writing a paper.

It’s been my experience that in the culture of mathematics, there is a certain fear of giving a talk that can be perceived as too elementary, causing speakers to whiplash too far in the other direction. Myriad are the talks I’ve seen aimed at the “experts” in the room, and typically the “experts” in the room consist of a cohort of 0 to 1 individuals who would likely be very happy to speak with you privately for 20 minutes after your talk.

And I guess it’s ok for only one person in the room to understand you by the very end, but everyone in the room should understand the first 5 minutes, half of people should understand the first 30 minutes (I know, ambitious) and, ok, from there I guess you can go nuts. And I use the word “understand” quite loosely here, give us definitions, give us notation, give us a chance. I’m talking to you, colloquium speaker who opened with “Let G be the k-dimensional Grassmanian on V.”

And I say this all with an understanding that a Colloquium, an Algebra, Combinatorics, and Geometry Seminar, and a Number Theory Seminar will likely have a different expectation of prerequisite knowledge.

As the imaginary Professer Mozart in Mermin’s article suggests, “strive to place as far as possible from the beginning the grim moment when more than 90% of your audience is able to make sense of less than 10% of anything you say.”

Having said all of this, the burden doesn’t rest entirely on the shoulders of the speaker. It’s also important to be a good audience member. When I was a graduate student someone pointed me towards the “3 Things” exercise that Ravi Vakil wrote about many years ago. The idea is, from any good talk you should be able to write down three things. Whether definitions, questions, ideas, theorems, or the like, these should be things that are interesting to you. In a way, these things represent hand-holds. These are places where, regardless of how divergent your research area is from the speaker, you are able to catch a little relatable tidbit that you can put in the context of your own knowledge.

This worked well for me as a graduate student. It certainly made me more attentive during talks, and had an added (perhaps unintended) bonus, that when I wasn’t able to find three things in a talk, I would walk around feeling righteously indignant for having sat blamelessly, martyrlike, through a terrible talk.

Since then, in my wisdom and maturity, I’ve added two more components to the exercise. I try to write down a single one-sentence “goal” at the end of the talk. If a talk is good (and I pay close attention) it should always be possible to write down at least one goal or large overarching purpose of the research described. I also try to write down one purposeful question. If you haven’t done it before, this is good training for being a session chair, a position in which (in my opinion) it is your duty to be armed with a question after every talk, just in case.

And finally, as I always tell a young friend of mine when she complains about going to church, they can make you go, but they can’t make you listen. If it’s boring, congratulations, you’ve just earned yourself 45 minutes to daydream and think about other problems that are more interesting to you, or failing that, daydream about your fantasy tiny home or whatever.

A seminar is like a special gift exchange between the speaker and the listener. So please join me in this pledge to always take only the allotted time, throw your audience a lifeline early and often, strive to be exciting — and failing that, aim for just being excited — and commit to hunting for interesting things for as long as you possibly can. If you have some more thoughts about this, ideas about giving better talks, tips and tricks for being an active listener, or if you totally disagree with me, feel free to let me know @extremefriday.