# FUNdamental mathematics

Comedy and mathematics are to most "ordinary" people concepts that belong to two different well separated worlds. Everybody can appreciate a good joke and a laugh from time to time, while mathematics to many is just blood sweat and tears. Of course some teachers and many authors of popular math books have used puns and humour to give the mathematics some sugar coating. However, their main subject is nevertheless serious mathematics. There do exist humorous novels about mathematicians. Two examples are *Goldman's Theorem* by Ron J. Stern (2008) and *A mathematician's shiva* by Stuart Rojstaczer (2014). And there is Jorge Cham, cartoonist and creator of *PhD Comics* who wrote *We have no idea* (2017) together with Daniel Whiteson about still open physical-mathematical problems. It has text that is richly illustrated with cartoons. The text has some slapstick kind of humour that approaches a bit the style of the book under review. But in fact I do not know of any book that is similar to *FUNdamental mathematics*, (which does not mean that such books do not exist). The capitalized FUN in the title is essential and it is further specified by the subtitle *a voyage into the quirky universe of maths and jokes*. Think of Monty Python brought by a stand-up comedian that goes on for over 300 pages, and who gets his inspiration in mathematics. There is indeed mathematics in this book but there are even more absurd jokes about mathematics, mathematicians, and about almost anything that the author has ever experienced. It is sometimes hard to know where exactly is the boundary between the mathematics and the nonsensical joke. There exist rules that stand-up comedy or sitcoms should have 4-6 laughs per minute. Eelbode applies a similar rule in this book with a joke every few paragraphs. To avoid an overdose, the reader should consume the book in limited portions. It's like with alcoholic beverages: read, but read wisely. As the author himself advises in his introduction, it should be administered a few pages at a time.

So if we sieve out the mathematical content, what are then the subjects that are covered? Well, there are quite a few and here is a grasp of some of them. We find the Hairy Ball Theorem, Fermat's last theorem, the parallel axiom, the abc-conjecture, Hilbert's hotel, Russell's paradox and Gödel's incompleteness theorems, the kissing number, conditional probability, the travelling salesman problem and P vs NP, topology, game and graph theory, the cube and sphere in high dimensions, the Gamma function, etc. This list is not exhaustive and some of these topics are (in between the jokes) somewhat seriously discussed, while others are more briefly mentioned and considered too advanced to go into details.

Some of the quirky characteristics of the book are that every chapter ends with a suggested music playlist. Music that can be listened to while reading the book or perhaps that the author was listening to while writing it. Hence it requires a taste that is somewhat similar to the author's preferences since it contains heavy metal with names like Iron Maiden and Metallica, but also dance, rap and plain rock. The last chapter has eleven exercises that look like mathematical multiple choice problems. They are followed by solutions that are again a kind of jokes that comment on every possible choice.

Another fun-element is that there are a lot of numbered, formal looking definitions, but almost none of these define something mathematical. I give an example of a short one (definition 18) "sandals: A rather special kind of footwear, often worn by mathematicians and people who believe that this will help to reduce their ecological footprint". Other definitions can be very long and they can take up several pages. Very occasionally, there is a theorem with a proof, but again this is not really mathematics. For example (theorem 2): "Music festivals are miniature copies of India" or (theorem 3): "Polar bears are colour blind". The proofs take about two pages each. There are also many cartoon illustrations that are often mathematically informative, or sometimes just fun.

There are funny "scenes from the life of a mathematician" when he/she is trying to publish a paper, or of the behaviour of students during a math exam, or the adventure of attending a mathematical conference. I quote a paragraph from the latter to illustrate the language used:

In an honourable attempt to reduce the travel costs — there is only so much I can do with that bench fee — I usually have an itinerary involving too many flight legs and not enough armrests. As a result, I am often so sleep deprived by the time I arrive at my destination that I look like a badly drawn version of the person on my passport picture. At least this explains why we are no longer allowed to smile when they take our picture: we all look grumpy upon arrival anyway.

Or this one where he is explaining what a 287-dimensional hypercube means

I think that some people spend less time looking for a partner than for their keys (even when they know they're in their handbag). (...) [A room in 287 dimensions]... already has more corners than electrons in our observable universe. Then again, who needs keys anyway? It is relatively safe to leave the door unlocked in 287 dimensions, since your house has even more walls than corners, so it does take a stubborn burglar to find your door. And although it's quite unlikely that you will catch your children playing soccer indoors, for the simple reason that the size of their ball will shrink into nothingness, I do not recommend you put them in a naughty corner: it might take them more than a few decades to be back for supper.

This attempt to characterize the content should make clear that there is indeed mathematics, but there is also a lot of jokes. In my opinion it is more a fun book for mathematicians than it is a book for non-mathematicians to learn some serious mathematics from. There is indeed much informative mathematics presented, although not really fundamental, but neither the mathematician nor the layman can deny that it is a lot of fun.

**Submitted by Adhemar Bultheel |

**11 / Dec / 2019