Passing the CUP bookshop, I couldn’t resist picking up a copy of Béla Bollobás’ brand new The Art of Mathematics: Coffee Time in Memphis — no less than 157 mathematical problems and their solutions, problems (he says) of the kind that would have delighted Littlewood and Erdös.
Here’s the very first in the book. A lion and a Christian in a closed circular Roman arena have equal maximum speeds. Must the Christian in the end be caught by the lion? Here’s another later one: Is an infinite family of nested subsets of a countable set necessarily countable. (These are fun, because it is difficult to shake off the temptation to say that the answer in each case is “yes” when it is “no”.) Hours of amusement to be had here.
But I suspect that there are two kinds of mathematicians, puzzle-setters and puzzle-solvers on the one hand, and (for want of a better word) more philosophically minded mathematics who want to see the deep interconnections between Big Ideas. Erdös vs. Gödel, perhaps. Once upon a time I used to be fairly good at the puzzling; but these days, it’s Gödel for me.