A few months ago a group of us launched a membership club, The Finite Group, which you can join!

A big update is the lineup — your membership now supports the work of and gives you access to content from mathematician and TikTok star Ayliean MacDonald, as well as Chalkdust’s Matthew Scroggs and The Aperiodical’s Katie Steckles and me. Membership gives you access to a chat community and monthly livestreams. For a taste of the livestreams, check out this π minute video!

The big news is that the next livestream will be free to view live online on 27th March from 5-6pm GMT. All four of us will be working through the recent ‘100 Mathematical Conventions Questions’ quiz that’s been dividing (a small subset of) the internet. The stream will be available live, and a recording will be available to members afterwards.

Our own Katie and Peter have collaborated on a new popular maths book, along with friends of the site Alison Kiddle and Sam Hartburn, which is out today. Short Cuts: Maths is an “expert guide to mastering the numbers behind the mysteries of modern mathematics,” and includes a range of topics from infinity and imaginary numbers to mathematical modelling, logic and abstract structures. We spoke to the four authors to see how they found it writing the book and what readers can expect.

How did this project come to be?

Peter: From my point of view, Katie approached me to ask if I’d like to be involved, which was very exciting! She’d worked on a couple of books with the same publisher and was asked to commission authors for this one.

Katie: The publishers wanted to make this book – one of a ‘Short Cuts’ series which needed a maths title – and asked me to be commissioning editor, which meant I could write some of it and ask others to write the rest. I chose some people I’ve worked with before who I thought would have something interesting to say about some topics in maths (in particular, the topics I know less about, so they could help me with those bits!)

Alison: As I was the last of the four of us to come on board, I think everyone had already expressed a preference for their favourite bits to write about, but luckily that left me with the two best topics, logic and probability.

Do any of you have previous experience of working on a project like this?

Alison: I’ve been involved in writing a book before but that one was about maths education, for an audience of mainly teachers, so this was a different sort of challenge, writing for a general audience with different levels of maths prior knowledge and enthusiasm.

Sam: I’ve worked on many books in the same genre as a copyeditor and proofreader, but this was my first time as an author. I enjoyed seeing how the publishing process works from the author’s point of view – it’s definitely had an impact on my editorial work!

Peter: My first time in popular book form, though I felt it used a bunch of skills I’ve developed in other work. And Katie is so great at organising projects that it went really smoothly.

What’s the book like?

Sam: It’s a book you can dip into – you don’t need to read it from front to back. Each page is self-contained and answers a question, and we tried to make the questions as interesting as possible (two of my particular favourites are ‘Is a mountain the same as a molehill?’ and ‘Do Nicholas Cage films cause drownings?’).

Alison: We had quite a strict word limit to write to, which was a bit hard to get used to at first as I have a tendency to use ten words when two will do – but this turned out to be a blessing because it focussed us all on what the really important concepts were, and we found ways to express those concepts in a concise manner.

Katie: I love how the style of the book builds in these gorgeous illustrations – we worked with the illustrator to make sure they fit with the text, but also bring out fun aspects of the ideas we’re talking about.

Who do you think would enjoy reading this book?

Sam: I’d like to think that anyone who has a vague interest in maths would get something out of it. Even though it delves into some deep mathematical topics, we’ve (hopefully!) written it in such a way that it’s understandable to anybody with school-level maths. But I’d hope that experienced mathematicians would also be able to find something new, or at least fun, in there.

Alison: I’m definitely going to be recommending it to the students I work with. The bite-size dipping in and out model is great for them to skim read so they can find out a little bit about the mathematical ideas that appeal to them. Particularly useful for people preparing for university interviews where they want to show off that they know some maths beyond the usual curriculum!

Katie: My mum’s definitely getting a copy for Christmas – and not just because I was involved in writing it: she’s not from a mathematical background but I think she’d enjoy the straightforward explanations and discovering new ideas.

What’s your favourite bit?

Sam: The publisher did commission some lovely illustrations. The bear in the modelling cycle is a particular delight!

Katie: Yes! We love the modelling bear. I also liked being able to share ideas people might not otherwise encounter if they read about mathematics, like how mathematical modelling works, or what topology is, or some of the nitty-gritty of mathematical logic.

Peter: There are loads of quick summaries of areas of maths I know less about, which is really nice to have. The illustrations are great — the baby failing to manage a crocodile always makes me chuckle, and I can’t wait to show my son the game theory dinosaurs!

Short Cuts: Maths is available to buy today from all good bookshops.

“Wouldn’t it be nice if there was a place where maths people could hang out and create cool maths things?” This idea was put to me a couple of years ago, and has stuck with me. It does sound nice.

Fast forward to 2023, and social media is collapsing. Some people have chosen a direction and are marching off towards Mastodon, Bluesky, Threads, or a number of other platforms. Some people are trying to keep up with multiple of these, but feeling spread too thin and wondering if it’s worth the effort (ask me how I know!). But many people are taking the opportunity to step back and think again. People are rethinking whether they want to conduct their online social lives in public. There is a surge in private communities, things like WhatsApp groups, Slack channels and Discord rooms. These have the advantage that you aren’t part of the ‘engagement’-driven content push, but they have disadvantages too – you have to know the right people to get into the group.

Meanwhile, wouldn’t it be nice if there was a place where maths people could hang out and create cool maths things?

So we’re creating it. We’re calling it The Finite Group (who doesn’t love a punny maths name?). “We” is Katie Steckles, Sophie Maclean, Matthew Scroggs and me. It’s going to be a maths community that gets together to share and create cool maths things, that supports creators to do their work within the group and on the wider internet.

I was interviewed by Nira Chamberlain, President of the Mathematical Association. I am the twelfth person to whom he has asked his question “what is the point of mathematics?” Hoping to offer something a little different, I spoke about teaching students the role mathematical modelling can play in sustainability.

In this series of posts, we’ll be featuring mathematical podcasts from all over the internet, by speaking to the creators of the podcast and asking them about what they do.

We spoke to… ourselves, since we run a podcast here and realised we haven’t done one of these posts about it! Katie and Peter are currently in their third season of fortnightly episodes, with plenty more to come.

TL;DR: We’re holding a distributed Wikipedia edit-a-thon on Saturday, May 12th, 2018 from 10am to improve the visibility of women mathematicians on the Wikiquotes Mathematics page. Join in from wherever you are! Details below, and in this Google Doc.

Extension and abstraction without apparent direction or purpose is fundamental to the discipline. Applicability is not the reason we work, and plenty that is not applicable contributes to the beauty and magnificence of our subject.
– Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect of, or care for, applicability.
– Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand.
Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

Now, don’t get me wrong. I have every admiration for Peter and his work; his is a thoughtful voice of reason, and it’s not at all unreasonable for the Wikiquote page on mathematics to cite his writing.

On 31st January 2008, I gave my first lecture. I was passing my PhD supervisor in the corridor and he said “there might be some teaching going if you fancy it, go and talk to Mike”. And that, as innocuous as it sounds, was the spark that lit the flame. I strongly disliked public speaking, having hardly done it (not having had much chance to practice in my education to date – I may have only given one talk in front of people to that point, as part of the assessment of my MSc dissertation), but I recognised that this was something I needed to get over. I had just started working for the IMA, where my job was to travel the country giving talks to undergraduate audiences, and I realised that signing up to a regular lecture slot would get me some much-needed experience. I enjoyed teaching so much that I have pursued it since.

I just noticed that last Wednesday was ten years since that lecture. It was basic maths for forensic science students. I was given a booklet of notes and told to either use it or write my own (I used it), had a short chat about how the module might work with another lecturer, and there I was in front of the students. That was spring in the academic year 2007/8 and this is the 21st teaching semester since then. This one is the 15th semester during which I have taught — the last 12 in a row, during which I got a full-time contract and ended ten years of part-time working.

I have this awful feeling this might lead people to imagine I’m one of the people who knows what they are doing.

P.S. The other thing that I started when I started working for the IMA was blogging – yesterday marks ten years since my first post. So this post represents the start of my second ten years of blogging.