Last week, Tadashi Tokieda came to Chicago to give a colloquium. If you have seen him speak, you will not be surprised to learn that it was absolutely delightful talk. I carried the talk around with me in my mind for many days afterwards, not only for its content, but also with the nagging question: how I can I make my own talks better?
I think it’s very easy to feel that our subject (mathematics) is so technical that no talk can both convey depth and yet be accessible. But then why did this talk feel otherwise? There is certainly room for carving out exceptions, and arguing that some problems in mathematics are easier to explain than others, but that does seem to me to be making excuses.
I have always felt that conveying the idea behind a proof is more imporant than the details. Almost all results in mathematics are special cases (of special cases) of more general problems, and many talks start with the implicit assumption that the audience is not only aware of these special cases but also understands why one should care about them, and see how they fit into the broader picture of mathematics. But that is rarely the case. Sometimes it’s even the case that the speaker themselves doesn’t really seem to have a bigger picture of what they are doing.
I want listeners in my talks to come away with some satisfying idea in their mind of what is going on. I feel as time goes on that has lead me to give softer and softer talks. I think this has sometimes worked, but it’s certainly not perfect. I think it may have been Kai Wen who spoke to me after I gave a colloquium style talk at Barry Mazur’s 80th birthday conference and said he was a little sad because he was hoping to learn something about the details of my paper in the talk. This was a perfectly valid complaint, although one has to accept that in any talk you have to disappoint some people. But maybe that’s just another excuse.
I’ve seem Manjul Bhargava give some wonderful talks which made me feel like I understood everything. But that feeling dissipated on closer inspection. More concretely, there are a number of technical issues concerning lattice points near cusps of locally symmetric spaces where some key technical steps take place, but those parts of the story never really get top billing during the talk. But this is not a criticism! Not everything can be explained in an hour, and in Manjul’s case there were plenty of other new insights which were easier to convey in a talk setting.
I used to think Henri Darmon was an amazing speaker. But then I once saw Jan Vonk give a great talk on some joint work with Darmon and I started to think: “well maybe Henri just does great math and that’s why his talks are so good” and then I wasn’t sure. But at the very least it’s easier to give a better talk when the mathematics is more interesting.
Perhaps I did at least come to one conclusion from thinking about Tadashi’s talk that I feel I can take away with me. His talk was delivered in a very easy going intuitive manner which I also strive (in my way) to reach. But another thing that is very clear is that his talk was also exceptionally well prepared. I often spend a lot of time thinking about a talk before I give it; but I think I have been most successful when my preparation actually involves deciding exactly (more or less) what I am going to say in advance. I feel that using Beamer is helpful in this way by constraining in advance the direction of the talk. Another lesson I have leanrt is that when wants to give some broad brushstrokes about some technical subject it is tempting to be vague; but actually there is often more clarity in being precise. In practice, this means that instead of being vague about some complicated argument, one can often be very precise about some baby version of the same argument, and still get across some sense of the methods involved.
In the end, talks can be good for different people in many different ways, but for most of us there are not many people who are going to read our papers in any detail, and a talk is one of the few opportunities we get to really communicate our ideas to others. So I think reflecting on how to give better talks is time well spent.
Tadashi Tokieda gives amazing talks