The Aperiodical 

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Topics I taught this year

By Peter Rowlett. Posted May 23, 2025

It’s been quite a year. We introduced a totally new mathematics degree course, redesigned from the previous version. In addition, restructures and people leaving meant there were fewer of us teaching on the maths degree. All this together means I’ve been teaching new topics aplenty this year. Now we’re at the end of teaching, I’m looking back (and definitely not just looking for things to do that aren’t the marking I must be getting on with…) and thought I would write another of those self-indulgent blog posts that are probably only of interest to me.

This year I have taught over 200 hours across level 3, level 4, and level 6. At a high level, I have taught proof and mathematical thinking, mathematical modelling and simulation, methods in various areas, research and project skills, and maths and society. More specifically, I have been covering the following topics (some in greater depth than others!) [those marked * are new topics for me to teach this year]:

Double Maths First Thing: Issue 25

By Colin Beveridge. Posted May 21, 2025

Double Maths First Thing has toothache.

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in figuring things out. And take my mind off of the dental work I had done yesterday. Send ibuprofen and puzzles.

Among several reasons to celebrate the election of Nicușor Dan in Romania is that the chap is an accomplished mathematician: he won two IMO gold medals in the 1980s, and I’m told he was one of only 11 candidates to solve the legendary question 6. Future Fields Medallist Terry Tao scored one point out of six. I’m sure Mr Dan has other qualities relevant to running a country as well. In the words of George III, “good luuuuck!”

Links

If we’re talking about Olympiads, Andrei Ciobanu has a long post about the “trickonometry” of IMO inequalities. (I’m slightly on the fence about whether competitive mathematics is a good thing, but Olympiads certainly generate some good problems.)

Among certain world leaders without maths degrees — and why would you elect one of those? — there seems to be a bit of a failure to understand the economic basics of supply and demand. If you’re in the same boat, Jason Fantl’s series on simulated economies is definitely worth reading.

I enjoyed Ben Orlin’s piece on why the number line freaks him out — it feels like a nice, gentle explanation of the different types of number you’ll find on the number line.

But wait… do numbers even exist? What about unicorns? Antoine Chambert-Loir wonders exactly that, finding evidence for all four possibilities.

I’m a bit of a sucker for tiling patterns and for Islamic-inspired art, so Laura Taalman’s post on Girih tiles was catnip to me.

Currently

It’s Finite Group livestream time — I gather this month’s show is about the Rubik’s Cube, which all right-thinking people know is impossible to solve. It’s on Friday 23rd at 7pm UK time; you can join the Finite Group for free, but only paying subscribers get access to the livestreams.

At the Aperiodical, it seems like Katie Steckles’s series on [one] to watch is back from the dead: interviews with maths/science YouTubers about their background, approach and content. And it wouldn’t be Katie if she didn’t ask who the audience is.

That’s all I’ve got for this week. If you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.

Meanwhile, if there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something you want to tell me.

Until next time,

C

Double Maths First Thing: Issue 24

By Colin Beveridge. Posted May 14, 2025

Double Maths First Thing wishes it could be formatted as a square

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in figuring things out. The 11yo is doing SATs at the moment, which runs exactly counter to that goal.

What runs parallel to the goal is MathsJam, which takes place around the world every month; most places meet on Tuesday 20th, but check to see your local date. If you don’t have a local Jam? You can set up your own, you just need a friendly pub and some people to maths with. The site will tell you more.

I mentioned last week about the horror show that is return periods; I wrote up the problem and my solution. I’d also like to shout out Georgii Bocharov’s excellent pyextremes package, which saved me weeks of doing a worse job with it.

You’ll also be pleased to hear that my Toastmasters talk went well, and that the stone-louse’s mischievous giggle went down a storm.

Links

In things I want to know about but haven’t made time to read, here’s Katie Steckles on representation theory.

Another friend of DMFT, Rob Eastaway, has an article about trying extreme cases to see whether your instinct holds water.

I also enjoyed Sam Rose’s latest post on reservoir sampling — I’ve used the technique frequently, and understand why it works, but this felt like a much clearer explanation than I’ve seen before.

By now you probably know that I’m a sucker for an article that digs unnecessarily deep into a topic I previously didn’t realise existed. For example, what proportion of the US’s exports are blood?

Currently

There a lot of events I want to mention coming up — on top of the Pseudorandom Ensemble‘s show at Warwick Arts Centre in August — so I’ll list them all at once:

• Although it clashes with MathsJam, Ashleigh Ratcliffe is talking at the Pint of Science festival in Leicester on May 20th
• James Arthur is doing a show at the Brighton Fringe from May 24-26. That’s three separate shows, not one really long one.
• Ingrid Daubechies is giving the Bakerian Lecture at the RI on June 2nd.
• Katie Steckles and Ben Sparks are giving maths communication workshops on June 11th in Edinburgh and June 24th online.

That’s all I’ve got for this week. If you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.

Meanwhile, if there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something you want to tell me.

Until next time,

C

Maths events at Cheltenham Science Festival 2025

By Martin Whitworth. Posted May 9, 2025

This is a guest post by Martin Whitworth.



I am the organiser of Cheltenham MathsJam, and I am a fan of our local Cheltenham Festivals. In addition to successful Jazz, Music and Literature Festivals, they have an annual Science Festival with high profile presenters, this year from 3-8 June. The Science Festival always includes some maths content, and that’s particularly strong this year.

Double Maths First Thing: Issue 23

By Colin Beveridge. Posted May 7, 2025

Double Maths First Thing will sign autographs, form an orderly queue

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in mathematical practice.

Last week, the Pseudorandom Ensemble gave our first performance, A Totally Normal Song live at the Clopen Mic Night. At the moment, the video is still up and available to watch. I’m really pleased with how it went, and we’re looking forward to an in-person gig at Warwick Arts Centre in August. Once we’ve learned a few more songs, that is.

Links

I enjoyed this paper by Jacob Siehler about port-and-sweep solitaire — I thought it was neat how a relatively simple game could be modelled with some much more sophisticated maths.

On my to-read list is Perette Barella’s piece on the Collatz conjecture, which looks like it goes a bit deeper than most such pieces.

Aybüke Yılmaz has a lovely piece on square Sufic calligraphy. Also in the art world, I’ve recently come across turtlestitch, which seems like the sort of thing that would steal entire weekends from me if I allowed it to.

I’m giving a talk at my local Toastmasters group tonight, and while this article didn’t exactly tell me anything new, it’s still advice worth sharing.

And if you’re after a Terry Tao-approved challenge, you could always try to decompose 300,000! into the product of 300,000 factors, all of which are larger than 100,000. I especially like this: it’s a simple-to-state problem that would make most non-mathematicians say “why on earth would you want to do that?” but gives some people an itch they have to scratch.

Currently

This month’s Carnival of Mathematics is hosted by Karen Campe. Susan at Beauty of Mathematics is in the hot-seat next time, and you can submit your interesting maths here. (And you should email me about it. I miss a lot of cool things.)

People who are more up on this You Tube thing than I am tell me that Tibees is self-publishing a book about 4D. I’m not watching all that, but it’s exciting to people whose judgement I trust.

Speaking of videos, Grant Sanderson’s Summer of Math(s) Exposition is open again, and April’s TMiP animation challenge is over and rounded up. May’s challenge is to animate a proof of Pythagoras’s Theorem.

That’s all I’ve got for this week. If you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.

Meanwhile, if there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something you want to tell me.

Until next time,

C

Carnival of Maths 239

By Katie Steckles. Posted May 6, 2025

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of April 2025, is now online at Reflections and Tangents.



The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

Double Maths First Thing: Issue 22

By Colin Beveridge. Posted April 30, 2025

Double Maths First Thing is HORRIFIED and you should be too.

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight, so obviously I’m going to start with something awful: I recently learned that a “one-year flood” is not remotely the same thing as a “365-day flood”. In fairness, they don’t usually go down to timespans that short, but it’s important for something I’m modelling. (As I understand it, a one-year flood is certain to happen in a given year. A 365-day flood has a 1/365 chance of occurring on any given day, hence occurs in a given year with probability of about 62%. I don’t like it.)

More pleasingly, I get to offer a gold star to Lew Baxter, who took up the challenge of integrating sec(x) from last time out and coded it up in Prolog. I won’t pretend to follow the code, but I’m assured it found the correct answer in considerably less than 99 years.

Links

We’re coming into the checks notes merry month of May-ing; in England, at least, that means maypole dancing. Dogs are optional, I understand. Dave Richeson has written about the maths thereof. Maypoles, not dogs. (A tip of the hat to Mair in the Finite Group).

From poles to entire planets. I was delighted by the look of the A5 geospatial system, which divides the surface of the globe into (almost) equal-area pentagons. Lovely stuff. Meanwhile, ZenoRogue has some ideas about plotting on spheres, and Matt Zucker combines my loves of truncated icosahedra and Truchet tiles

A thing of beauty: Ismail al-Jazarī’s Mechanical Devices. I certainly owned a translation of this once, but I fear I left it with an ex many years ago.

While I’m a fan of Slay the Spire, I’ve never played Magic: The Gathering. Manon Bischoff in Scientific American outlines how you can develop a Magic deck that goes infinite, but only if the twin primes conjecture is true. (Here’s the much-missed Vicky Neale talking on the subject — Closing The Gap is an excellent read.)

Currently

If you’re near a computer tomorrow night (Thursday May 1st, 8-9pm UK time), you should definitely check out the Clopen Mic Night — a pay-what-you-want variety show that, for one night only, features the Pseudorandom Ensemble. I’ll be singing a verse.

THIS Saturday (don’t get me started), which is May 3rd, Rob Eastaway is talking Shakespeare at the RI in London. That’s a 2pm kick-off, you’ll need tickets in advance.

Some conferences of interest: Bridges is in Eindhoven in July and Talking Maths in Public in in Warwick in August. I’ll definitely be at TMiP. There are rumours of a PRE gig, but I couldn’t possibly let that slip yet.

That’s all I’ve got for this week. If you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.

Meanwhile, if there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something you want to tell me.

Until next time,

C