How to give a talk

I was recently reminded of an old answer I posted on Math.SE with advice on how to give a talk. I wrote that answer in 2012 when I was only finishing my masters, and while I had given a couple of seminar talks by that points, it's 13 years later and I look at this post and it looks like the advice a toddler gives an infant.

And so, now, with much more experience, I figured that it's a good time to revisit that piece of advice. And let me begin by saying that the advice that you can find in that answer is absolutely great, it is still valid, and even now after all my experience, it is still a good fundamental starting point.

If you've been to any of my talks you know that there are essentially three types of talks that I tend to give, which to an extent is the general three types of talks. Let me break my advice here based on those three types.

Type I: Lectures

Lectures are a specific type of a talk, usually in the sense of teaching "learners", and they usually lack the general context. In these talks your role is to convey knowledge which you have. I am going to skip this one type, but it is worth mentioning. Let me just reiterate previous advice that I gave elsewhere many a time before, and mention that the history of knowledge gives is another dimension. It is worth repeating this. When I took Calculus I in my freshman year we went from Rolle's theorem to Lagrange's Intermediate Value in the course of two hours. That was dreadful and boring. At no point there was any excitement about how we are journeying through centuries of mathematical progress!

Even in set theory we often forget that from Cantor's seminal paper to König's mistaken contradiction (known to us today as König's theorem) there were decades of work and struggle.

I'll give one more piece of advice here, given to me by Uri Onn, who was the best teacher I've had in my undergraduate degree. You are telling a story, and you need to keep the audience engaged and guessing, without giving too much too quickly.

But, this isn't really what we're here to talk about. We're here to talk about research talks. So, let's move on to the next type.

Type II: Seminars

Seminars generally present you with the opportunity to talk about research to an audience which will generally know about some of it and will be able to place it in a context. Mind you, this is not always the case. If you are invited to a School of Departmental seminar or colloquium, the expectation is that most people can follow you and the job is now to provide the context rather than to talk about the research. In those cases you want to focus on the context of a theorem: what led us to it, why is it interesting, why is it useful, and why do we even care?

In research-oriented seminars, however, you're facing an audience of your hardcore research fellows. You're expected to give away the goods. Proofs, details, definitions, to whatever extent time permits. In some countries research seminars will take an hour (where you can't really go into too many details and you need to be more picky) and I gave a three hours talk once in Prague, going into a lot of details on the Bristol model to a small group of people.

This is also a story that you're telling. You're presenting a story. You want to keep your audience engaged. Go on tangents, yes, even often, but you want to start by giving suitable context and stating your main purpose here. An abstract, if you will. Then you want to get into the bog and dig into it. The context's details, the theorem and proof, applications. There are many ways to give a good seminar lecture, so many that it's nearly impossible to give a good general advice.

As far as general advice go: mind your time, mind your audience, and mind yourself. It is okay to skip a proof by providing intuition for it, if it is done in favour of a bigger picture.

Type III: Conferences

Conferences are different from seminars, and my experience tells me that not enough people understand that distinction. When people go to a conference, to go to absorb a lot of ideas in a single day, possible for a few days in a row. Compare that to a seminar, where people have their attention devoted in its entirety to your talk. While it is possible, it is generally unwise to get into too many details when speaking in a conference.

It is generally easier for someone to lose their attention if they already listen to six different talks that day, on six very different subjects, or if they anticipate five other talks coming. Sometimes you will see people telling you to find your "person" in the audience who is the expert, and simply talk to them. But that's not what you want. In a conference, you want to inform the audience on your new research, but not necessarily in a way that alienates 90% of your colleagues.

Menachem, my supervisor, used to quote "no talk can be too short or too elementary". I do not recall who said that. But it is a very wise piece of advice. When you get into a proof, you will lose people, and eventually, you will lose almost everyone in your audience. It requires experience and talent (which can be developed!) to give good conference talks, where some details are given, but not so much that everyone loses you, and that the talk feels like eternity.

Conclusions

There is no other way to get good at talks than to give a lot of talks and to attend a lot of talks. Find speakers you liked, try to figure out what it was that made their talks great. Go and tell them that you enjoyed the talks. It feels good to hear from someone that they liked you talk. I recently heard from a colleague who liked my talk that they felt a bit lost when I was proving something technical, but they really liked the part afterwards where I tied it back to the start of the talk without getting into any significant details.

If speaking is hard, find a few very friendly people and practice. Remember that people are very forgiving when the intention is right. And that over time people will remember just a vague gist of your talk, if that. Unless you did something horrible, like eating baba ghanoush with a spoon continuously between sentences the entire time (I mean, why would you do that?) and even then, they will remember the thing rather than the talk.

So, this is a small addition, not even a revision, to an old and wildly premature piece of advice, that happened to be spot on. I'm looking forward to seeing you all give talks, real soon.