I've noticed over the years that different numbers have their own "personalities". If you're a mathematician doing a calculation and you get the answer 248, it means something completely different than if you get 247 — because the number 248 shows up in all sorts of amazing places, while 247 is just dull. So when I was invited to give the Rankin Lectures in Glasgow, I thought it would be fun to explain this idea with some examples. I decided to give separate talks on three of my favorite numbers: 5, 8, and 24.
The first one should be quite easy for everyone. After that they get harder, but they're still meant to be expository and fun, Here you can see streaming videos of my talks — and also my slides, which have links to references that fill in the details.