Things to Make and Do in the Fourth Dimension: A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More, by Matt Parker

This is such a wonderful book. I started to read this as I wanted some inspiration for how to communicate math to children who are just begin to explore mathematics, long before they move into formal education, to see if I could find a vaccine against boring teachers. What I found was much more.

It is not often you read a book about math that is not oversimplifying interesting areas, while still making you laugh. Too many of the books about math tries so hard to make people interested that it feels as if the book is written by a group of PR people without knowledge or interest in math.

I find it hard to pick any particular favorite areas so I will just leave two examples of the kind of style of writing in two of my favorite areas:

1 “Infinity” for an example of the short and brilliant explanations “People seem to have the idea that if you keep counting up along the number line past bigger and bigger numbers, in the end, the numbers just give up. They can’t be bothered to go on, and there’ll be an infinity sign (∞) there to mark the end of the number line. This is not the case. There is always a bigger number. Infinity is not safely contained at the end of the number line. Infinity is not a big number. Infinity is actually a measure of how many numbers there are. The number line never stops, so we say it is infinitely long. Just like we said before that the number ‘five’ is the size of any set of five things, infinity is the size of a never-ending set of things.”

The whole chapter on infinity is very good. Infinity has been almost a hobby for me for a long time and I think the way Matt captured what infinity is, and what it is not, is a good example of the straight forward language that this book excels in. I’ve been surprised over the years of how many people that does not understand infinity, as they think it is a large - but impossible - number, rather than a description of a certain situation. This is true for some academics as well. The people I had the hardest time explaining infinity to has been philosophers who considered themselves experts on extreme risks and neoclassical economists who consider themselves experts on math. I wonder if “infinity” is extra hard for people who are control freaks and struggle to think outside a very specific box.

2. “Ridiculous shapes” for an example on how complex issues are brought into an everyday situation “I had seen a few knitted Klein bottles online, so I asked my mother if she could knit me the 3D immersion of the 4D Klein bottle so I could wear it as a hat. She just looked at me. We then had a long conversation where I was talking Maths and my mum was speaking fluent Knitting, but because she is quite the dedicated knitter, she eventually got it to work. The first one she knitted for me (the prototype, as I called it; or as she called it, a perfectly good gift) worked well, but it was all the same colour. I asked if she could knit me one that was stripy. Apparently, this is easy enough to do when knitting – you just change colours after a few rows – so I gave her a long list of numbers for the thickness of each stripe in the hat. The photo here is me wearing my Klein hat. The stripes are the digits of pi. Should anyone have a nerdier hat than this, I’d like to hear. ” For me the two texts above represent the core of the book. It is a book written by a passionate person who loves to share his experiments and ideas. If the tone in the book seems off sometimes (it did for me at first) have a look at Matt’s YouTube channel and you will understand how you should read the book. https://www.youtube.com/user/standupmaths

My only frustration with this book was that it was too short. I particularly would have liked one, or a few, chapters about fractals. In the next books it would also be great if Matt could include even more great ideas for making math physical, like the Möbius loop suggestions in the chapter “Ridiculous shapes” and how to make a four-dimensional cube by straws and pipe cleaners in the chapter “the fourth dimension”. Matt has already done a lot in the area of fractals, and I really like the fractal Christmas tree.

I would even like to challenge Matt, or anyone else with a similar skill set, to develop a toolkit for math. Something like the Snatoms, but for different themes in math… I’m sure that would be a successful Kickstarter project.