It’s genuinely difficult to write an innovative maths book, something that’ll teach even the most grizzled and cynical of tutors a thing or two, but @standupmaths1 has done exactly that.
Most popular maths books, my own included, tread a pretty familiar path through the history of maths, throw out a few nice pictures of fractals, and make a big thing out of maths’s one romantic hero (who was clearly an idiot). Things to Make and Do in the Fourth Dimension doesn’t do that.
There are familiar pieces, of course: explorations of Euler’s other identity ($F+V-E=2$ for a 3D object, a simple variant of the Beveridge-Longcope equation), the Tower of Hanoi and finding primes are well-trodden; however, as a good guide can turn a walk around your home town into something amusing and entertaining, Parker presents it all freshly, while avoiding most of the obvious jokes.
The value of TMD4D for me is for where it digs into the less-machete-ed bits of the mathematical jungle: from @cperfect’s Perfect-Herschel Enneagon to an explanation of Tupper’s self-referential formula, to the four-dimensional Platonic solids, allowing the book to live up to its name.
While @standupmaths is obviously a comedian, it’s not (just) the humour that makes the book for me: it’s the have-a-go attitude. It’s full of suggestions to have a go at something yourself, or to try and figure out what’s going on before you read on. It’s hard to think of any point in my reading life when I wouldn’t have lapped this up.
This is a strongly recommended buy for anyone with an interest in maths, but especially for an A-level student whose eyes are beginning to open to its beauty.