I was asked, at rather short notice, to give a talk at the Colégio Planalto in Lisbon.
We arrived there to a very friendly welcome and an excellent lunch and conversation before my talk.
This school has some very able pupils, and the prospect of addressing them was a bit daunting. So I took the easy way out, and used some of the examples and problems that have come up in Mathematical Structures. So we had two problems about parties, two about ants, two about cards with something on each side, and various other logical and mathematical challenges. Some of them were only there for description, but most of them were there for the audience to puzzle over.
There was a serious purpose as well. Mathematics is a good career preparation, in my view largely because of the good habits of thought and techniques of problem-solving it encourages; I wanted to get some of this across.
Clearly their English was infinitely better than my Portuguese, but probably I stretched their knowledge to the limit with questions such as whether the statement
You can’t square the circle unless everyone is singing from the same sheet
with its combination of mixed metaphors and slightly contorted logic, is true or false.
The slides were only produced the night before, and are certainly not guaranteed free of misprints. But I think that all of the examples are fairly accessible; the boys at the lecture certainly engaged with them.
Altogether a rewarding and enjoyable experience for me; I hope the pupils found it so as well. In some ways, it was a practice run for the Gresham talk.
It was good to report, too, that my ubuntu laptop performed perfectly, and had no qualms about connecting to the projector.
I produced a handout, which I have put here. If you look at it, it has some of the answers at the back (I didn’t include these in the lecture), so no cheating!