We asked guest author Elliott Baxby to take a look at John Allen Paulos’ latest book, Who’s Counting.
Mathematics is an increasingly complex subject, and we are often taught it in an abstract manner. John Allen Paulos delves into the hidden mathematics within everyday life, and illustrates how it permeates everything from politics to pop culture – for example, how game show hosts use mathematics for puzzles like the classic Monty Hall problem.
The book is a collection of essays from Paulos’ ABC News column together with some original new content written for the book, on a huge range of topics from card shuffling and the butterfly effect to error correcting codes and COVID, and even the Bible code. As it’s a collection of separate columns, it doesn’t always flow fluently – I did find myself losing focus on some of the topics covered, particularly ones that didn’t interest me as much. This was mainly down to the content though – the writing style is extremely accessible and at times witty.
The book included some interesting puzzles and questions, which were challenging and engaging, and included solutions to each problem – very helpful for a Saturday night maths challenge! I even showed some to my friends, who at times were truly puzzled. I loved the idea of puzzles being a means of sneaking cleverly designed mathematical problems onto TV game shows. It goes to show maths is everywhere!
I enjoyed the sections on probability and logic as these are topics I’m particularly interested in. One chapter also explored the constant $e$, where it came from and where else it pops up – a very interesting read. It does deserve more attention, as π seems to be the main mathematical constant you hear about, and I appreciated seeing $e$ being explored in more depth.
This book would suit anyone who seeks to see a different side of mathematics – which we aren’t often taught in school – and how it manifests itself in politics and the world around us. That said, it would be better for someone with an A-level mathematics background, as some of the topics could be challenging for a less experienced reader.
It’s mostly enjoyable and has a good depth of knowledge, including questions to test your mind. While I didn’t find all of it completely engaging, there are definitely some points made in the book that I’ll refer back to in the future!
Way back at the end of last year I put out a call to mathematicians I know: hop on Skype and chat to me for a while about the work you’re doing at the moment. The first person to answer was David Roberts, a pure mathematician from Adelaide.
We had a fascinating talk about one thread of David’s current work, which involves all sorts of objects I know no more about than their names. I had intended to release this as a podcast, but the quality of my recording was very poor and it turns out I’m terrible at audio editing, so instead here’s a transcription. Assume all mistakes are mine, not David’s.
If you’ve ever wanted to know what it’s like to work in the far reaches of reallyabstract maths, this is an excellent glimpse of it.
DR: I’m David Roberts, I’m a pure mathematician, currently between jobs. I work – as far as research goes – generally on geometry and category theory, and the interplay between those two. And also a little bit of logic stuff, which I thought I’d talk about.
Why should I worry about dying? It’s not going to happen in my lifetime!
Raymond Smullyan, This Book Needs No Title (1986)
This week, the mathematical community has lost not one but two of its most beloved practitioners. Earlier this week, Swedish statistician Hans Rosling passed away aged 68, and today it’s been announced that author and logician Raymond Smullyan has also died, aged 97.
Good news, logic fans! The Open Logic Project is a project to write an open-source textbook on logic. And if you read it, you’ll find tautologies like the last sentence completely thrilling.
The book is aimed at a non-mathematical audience, mainly computer science and philosophy students, so it assumes very little knowledge of the basics. The project was instigated by Richard Zach, who’s Professor of Philosophy at the University of Calgary. The rest of the project team consists of Aldo Antonelli, Andy Arana, Jeremy Avigad, Gillian Russell, Nicole Wyatt, Audrey Yap, and Richard Zach. They’re aiming to cover first-order logic, sequent calculus, soundness and completeness theorems, computability theory, and incompleteness. If things go well, they want to add material about model theory, computability and Turing machines (that’s already in progress), and some stuff on philosophy of language and mathematics.
A high-quality textbook for free would be pretty good on its own, but what’s really nifty is that the source code has been set up so the book is configurable to your tastes: you can say what kind of notation you’d like, and even adapt theorems and lemmas to use different proof systems.
In case you weren’t already excited enough about Matt Parker’s Domino Computer (see: Math/Maths Episode 112, and articles on this website), the Manchester Science Festival blog has posted an official press release about the event, including photos of the domino assembly team lying around on the floor (none of us are professional models, but we did our best for the camera), and quotes from Matt about how important domino computers are.
Top marks go to sometime Aperiodical author Paul, for looking super-bored in the group photo. I’m sure he was thinking about hard maths.