This is an entertaining little romp through various seasonal quandaries — turkey-roasting, gift-wrapping, organising secret Santa schemes, cracker-pulling, stringing tinsel around the tree, winning Monopoly games, cutting the cake, predicting what will be in the Queen's speech, and so on — as well as a look at the existence and calorie-consumption of the man himself, with an eye to showing us to what extent maths can help us to deal with these. It's mainly harmless: things like partial differential equations and Markov chains get mentioned, but you don't really need to know what they are to follow the discussion. It's all at the sort of level you would expect if you watch the occasional Numberphile video. If you watch a lot of Numberphile videos you will already be familiar with most of what's in the book, and you'll probably be buying it to give to someone else whilst putting a little money in the authors' pockets.

Good fun for a couple of hours on a dark December day. And nicely produced, apart from the embarrassing eight-pointed snowflakes that seem to have been added by a rogue graphic designer whilst the authors were looking the other way. ( )

I picked up The Indisputable Existence of Santa without knowing anything about it when browsing at a book store a month before Christmas. I am glad I did.

This short book (135 pages) is quite a charming mix of math, Christmas and humour. The two authors use math to analyse various aspects of Christmas, such as how to wrap presents using as little wrapping paper as possible, how to decorate the Christmas tree, and how to win playing Monopoly.

The mathematical concepts used include Markov chains, graphs, probability theory and the Prisoner’s Dilemma, as well as some physics. The mathematical explanations are easy to follow, with plenty of illustrations. In some cases there are also end notes with extra details and tips for further reading.

In particular I liked the Queen’s Christmas speech, where the authors explain how to use a two-step Markov chain to generate gibberish. I knew about this technique before, but it is explained well here (and the results are always hilarious). I also enjoyed the Secret Santa chapter – on how to set it up to avoid the problem of giving a present to yourself. The analysis of how to win at Monopoly was also very interesting. Finally, from the chapter on how to decorate the tree, I liked the proof that there are only five platonic solids.

The book is also very funny. For example, here is a quote from the Monopoly chapter: “Officially, Monopoly ends when all players but one go bankrupt. In reality, it ends when your sister accuses one or all of you of cheating, flips the board across the room and storms off in a shower of miniature plastic houses.” I don’t often laugh aloud when reading books, but here I did many times.

I really enjoyed reading The Indisputable Existence of Santa. For anybody interested in maths, it is a perfect little book for a cosy Christmas evening. ( )

If you like Hannah Fry (I do), and numbers (I do), and silly what-if sorts of musings about what temperature Santas sled might reach at the speed he needs to go... then youll enjoy this. Otherwise I fear this is going to be a bit too geeky for most people. However, as an introduction to some basic numbers and physics deduction process, it would probably suit many a young teenager who shows some maths/physics leanings. ( )

Interesting but repeats a lot of content which is on the Numberphile YouTube channel. ( )