I absolutely loved the title, although in a way it's a bit of a let down, as their are relatively few things to 'make and do' here - it is mostly straightforward recreational mathematics - though you certainly can't fault the promise of dealing with the fourth dimension, as well as the fifth, sixth and 196,883rd dimension (and that not one of the joky bits - this is genuinely significant).
Like most rec maths books, while it's clear that the author finds it all fascinating I found some captivating, some vaguely interesting and some a touch 'meh'. But as long as you accept that not all of it will work for you and you might have to skip a few bits and pieces, it has some absolute gems. From interesting ways to cut up pizzas via computers made with dominos (see my blog post on mechanical computing) and those many dimensional shapes to networks, variants of Möbius strips I've never seen before and an equation that plots as the equation itself there's truly mind boggling stuff. I particularly loved the bit about the secret checking mechanisms in barcodes and VAT numbers (but that's just me) and I'm sure you'll have your own favourites.
Perhaps the weakest parts of the book are the dips into mathematical history. Parker falls for the usual problem of over-egging what was done in 'programming' the non-existent Analytical Engine, and his quick whiz through some of the big names of maths towards the end of the book seems a little out of place with the rest. He acknowledges maths history is a 'bit like herding porridge', but I'm not sure this section adds a lot to the book.
It's interesting to compare TtMaitFD with the work of the hyper-productive Ian Stewart, probably our best known living maths populariser. Despite his light style, Parker took significant risks in going into more depth than Stewart often does in his rec maths books, and I think the gamble pays off, though it may bamboozle some readers. Parker certainly gives Stewart a run for his money and packs plenty in. Recreational maths doesn't work for everyone, but for the naturally geeky this book has a distinct appeal.
Review by Brian Clegg