A couple of weeks ago at the farmer’s market I ran into some undergrads who were doing science demonstrations on Capitol Square. I tried to get CJ to drop the ball into the beaker and displace some liquid, but he was too shy. While I was there, another guy wandered by to see what was happening — turned out he too was in the science popularization biz, and is running a series of science pub nights at Brocach downtown. This July 26, the guest is UW bio-anthro prof John Hawks, an expert in population genetics of early humans.

As it happened, CJ demanded we eat lunch at Brocach the same day. I’d never been in there before and wasn’t sure if it was OK to bring him in, but in fact the place is packed with strollers at Saturday lunchtime, and they have a kids’ menu. I had the corned beef hash, which was good, but — and coming from me, this means a lot — too big.

If you were a mathematician and you were going to talk at a science pub, what would you talk about?

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I’m not sure exactly how a “science pub” works, but I imagine it has to be something in which the results are “testable” by hand. For example, the “290” theorem of Conway about representations by quadratic forms…hmm, maybe too complicated. Oh, maybe the fact that every number can be written as the sum of four squares, but not three squares. And then you can talk about Waring’s problems, with 9 cubes etc. Especially interesting here is that the (real) cube problem is essentially unsolved — how many cubes does it take to represent a sufficiently large integer? The conjecture is 4, but the best known result is something pretty crappy (with respect to the answer, of course, the result is pretty good) like 7 cubes. Then give the elkies/zagier example with a^4 + b^4 = c^4 + d^4. Stuff like that.

This sounds very much like “science cafes”:

http://www.sciencecafes.org/

I like the inclusive subjunctive in your last sentence. It suggests that the mathematician readers need not constrain themselves to speaking on their own research.

Some topics that come to mind include 2-manifolds with boundary, knots, and maybe cryptography. If I knew more about it, I would possibly say something about small-world phenomena in social networks, after Kleinberg et al.

Depending on how well you can work an audience, you might want to try a “Consider a prison with 100 prisoners, and suppose the warden decides to play the following game…” routine.

You have to consider the sophistication and interests of the audience, and in order to do that you need to have some idea of who they are or who you could attract. Maybe discussion with the organizers and past presenters would be helpful in getting a picture.