The Aperiodical 

You're reading: Posts By Colin Beveridge

Double Maths First Thing: Issue 33

By Colin Beveridge. Posted August 27, 2025

Double Maths First Thing is at about 3.5/5 on the ready-to-rock-o-meter

HELLO $CURRENT_LOCATION! Sorry, hang on, the show isn’t until tonight. Let me switch off rock god mode and try again.

Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing maths for its own sake, puzzling things out, and sharing it with friends and strangers. To that end, I’m on my way to the Talking Maths in Public conference at Warwick University – do stop and say hello if you see me there. And, of course, get your Pseudorandom Ensemble tickets before tonight’s performance.

It’s been raining links this week, so I’ll get straight on with it.

Links

For a while back there, everyone was playing 2048, and then people kept saying “but Threes is so much better!”. Alex Fink’s Dive is more mathematical than either, and just as frustrating.

The rest of the links are unusually arty this week. Let’s start with Ana Dodik et al’s amazing work on Meschers, meshes for representing impossible objects.

Also artistic and neat: an anamorphosis simulation by Charles Petzold. What’s that, then? It’s a technique for making art that looks like something (e.g., Mary, Queen of Scots) from one angle and something else (e.g., a skull) from another.

Not really maths-related, but lovely all the same: the cutaway illustrations of Fred Freeman.

But far and away my biggest art rabbit-hole recently: Andrew Taylor is very much at it again, making tools to produce dithered QR codes that (a) scan and (b) look meaningful. (This builds on work by Erik Demaine and I was pointed at it by Dave Richeson.)

Currently

A nice-looking upcoming conference on algorithms in the creative arts: Alpaca 2025, in Sheffield and online from September 12th-14th. (Please join my campaign to call baby alpacas ‘alpacinos’.)

I’m in the hot-seat for this month’s Carnival of mathematics, so use that link to send me anything you’d like to share in the August post.

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

Review: The Mathematician’s Library, by Thomas K. Briggs

By Colin Beveridge. Posted August 25, 2025

Books. Every self-respecting mathematician’s floor has a pile of them, some half-read, others to re-read, some merely providing structural support. In The Mathematician’s Library, Thomas K. Briggs considers an alternative approach to the literature, instead using the books of the last few millennia to tell the story of mathematical development around the world.



When I say “around the world”, I mean it: Briggs takes care to pick out important early texts from India and China; if the southern hemisphere feels a bit hard done-by, I suspect that’s more a shortage of available works than a deliberate snub. As far as possible, he tries to counter the narrative that all mathematicians conform to the traditional old-white-bloke stereotype by providing counterexamples. The tone is light and friendly, a “hey, look at this cool thing!” approach, typified by the last few selections: rather than pure research, the picks move assertively towards popular maths.

It’s a beautiful book – a gorgeous cover and thoughtfully laid-out illustrations, even if the ligatures on the typeface feel like a little much. It follows a largely chronological path, split into six sections – the first 40,000 years (up to Euclid), the origins of mathematics (up to about 600CE), global evolution (up to the Renaissance), scientific revolution (up to Newton’s Principia), modern mathematics (up to Russell and Whitehead’s), and – somewhat eyebrow-raisingly – the future, from 1932 to 2024.

My main criticism of the book is that there’s obviously a concept behind it, but what the concept is isn’t made clear. Is Briggs an enthusiastic librarian showing us around his imaginary collection? Are we travelling through time to visit the floor-piles of mathematicians gone by? Is it just a list of some interesting books and some commentary on them? I believe it’s the first, but the introduction ought to put it beyond doubt.

There’s something for everyone here: enough detail to get you started if you want to burrow into a rabbit-hole, but not so much as to overwhelm; a mix of familiar and unusual book selections; lots of pretty pictures if you don’t feel like digging into the maths right now; and a wide, tall format that will add stability to my personal pile of books.

• Disclosure: Colin received a free review copy of The Mathematician’s Library and hopes the author still considers him a friend after this.
• The Mathematician’s Library will be published by Ivy Press on September 11th, 2025, with a list price of £28.00.

Double Maths First Thing: Issue 32

By Colin Beveridge. Posted August 20, 2025

Double Maths First Thing is looking forward to the cricket

Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing maths, solving puzzles, and feeling really clever about it.

This week, we’re planning to take a trip to Worcester to watch a cricket match. The last time I tried that was when the 11yo was three, and it bucketed down all day. A lot of maths in cricket, you know.

Links

How many ways are there to place two knights on a chessboard so they attack each other? Susam Pal has an answer.

Some things I’ve simply never understood. For example, Why the Metropolis-Hastings algorithm works. Gregory Gundersen knows! But the other question is, why do I always think “but Hastings is a medium-sized seaside town, not a metropolis.”?

I really enjoyed Scott Sexton’s piece about applying vector calculus to topographical data to find out where it makes sense to build things.

This may not be strictly mathematical, but I found it interesting all the same: how to lay out stones in a mosaic to emphasise the edges of what you’re trying to depict.

Karen Campe has important notes on building a network of maths people, and pays tribute to her late friend Shelli. I’m sorry for her loss.

Currently

We’re a week out from TMiP! I’ve been banging on about the Pseudorandom Ensemble show for ages, but I should probably highlight that it’s also a good conference for anyone who enjoys talking maths in public. Or hanging out with the kind of people who do.

If you’ve got posts for the Carnival of Mathematics, use that link to send them my way for this month’s blog post.

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 31

By Colin Beveridge. Posted August 13, 2025

Double Maths First Thing feels like this rubber band is getting longer.

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

This week I’m mainly on childcare duty and watching the calendar until I can pick up a new weather project in September. As always, I’m interested in unusual and quirky maths projects (especially ones that do some good for the planet or the people on it), so hit me up if you feel like a mathematician/developer/writer woud be a good investment.

Links

This week, Ayliean, the Fringe’s hardest-working pretend showhand has a question from her mum (hi, Lorna!) – can a shape be a shape if it’s really three shapes? What we’ve got here are three quornettos – each made of four cones joined together at the base in a loop. The three of them then fit together in a very pleasing way to form a triquornetto that my autistic fingers are LONGING to turn inside out over and over for hours. Ayliean suspects they’re linked to the flexagon family – this I know from nothing, but I wonder if any loyal readers can help?





Tired of the platonic solids? You’ll be wired about the parallelohedra, of which there are also five, but all of which tile Euclidean space in three dimensions. (Via 0xDE on Mathstodon).

A nice problem from reddit: you roll n n-sided dice and tally up how many of each number you roll – so if you rolled six D6s and got 6-4-1-6-6-1, you’d have three 6s, two 1s and a 4 – 6 is the outright winner. What’s the probability of the result being a tie as n gets large? (I have an experimental answer, but not a theoretical one.)

There’s a new season of Sam Hansen and Sadie Witkowski’s Carry the Two podcast, which is focussing on emerging technologies this time – episode 1 is about quantum computing. In related news, this game looks like some people might find it fun.

And in “articles I want to read but likely never will”, here’s an article about using graph theory to write more efficient code.

Currently

Tomorrow (Thursday August 14th, 10am UK time), there’s a Finite Group livestream on space-filling curves. I hope there’ll be a flowsnake!

Tuesday coming (Tuesday August 19th), it’s the traditional day for your local MathsJam – follow that link to find it, or for details on how to start your own.

And if you’re coming to Talking Maths in Public, I hope you’ll be able to join us in the Ensemble Room at Warwick Arts Centre for the Pseudorandom Ensemble show on Wednesday evening. There’ll be a link to reserve a seat in your conference pack, with a suggested contribution of a fiver to help cover costs. It’ll be a blast!

Lastly, I’m hosting this month’s Carnival of Maths – that link is the one to send any interesting and/or important articles to.

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 30

By Colin Beveridge. Posted August 6, 2025

Double Maths First Thing keeps getting bumped to the next room

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

This week, the kids are at a sailing course. I’ve never quite understood how it’s possible to sail into the wind, so I’m looking forward to them explaining this to me.

Links

A nice puzzle via Mair in the Finite Group discord: you have a triangle with an obtuse angle, and need to divide it into triangles with only acute angles. How many triangles do you need?

At the brilliantly-titled Solutions Looking For Problems blog, Bryan Wolf wondered if there’s a ‘most-scrambled’ Rubik’s cube.

Here’s a thing of beauty: an alternative representation of the periodic table. There’s a wonderful collection of similar things at All Periodic Tables.

Also lovely: Christian Lawson-Perfect has implemented a simulation of a glass sudoku, in which cells move between energy states.

I haven’t put any time at all into examining the content of The Journal of Humanistic Mathematics, but at first glance it looks like an excellent project.

Lastly for this week, an overview of some of the things you can do in Lean, including making the maths haunted.

Currently

There’s a new Carnival of Maths, courtesy of Katie at the Aperiodical. I’m hosting the next one, and you can submit links here.

The TMiP animation challenge for July has closed, with a playlist of responses here. August’s challenge is Hilbert curves, which is always a good excuse to mention the flowsnake — and to point out that the next Finite Group livestream is on space-filling curves.

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 2F

By Colin Beveridge. Posted July 30, 2025

Double Maths First Thing says humf! and sort the big list

Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight in doing maths.

Not everyone takes delight in anagrams, but being clever, I do: delightfully, Sarina Wiegman is an anagram of “I win as manager”.

Links

Speaking of jumbling up letters, Tom Snelling has collated all of the books in the Library of Babel, a peculiar and slightly mathematical short story by Jorge Luis Borges.

In somewhat sad, but also “the dude was 97 and got to spend most of his life doing maths” news, Tom Lehrer died last week. He’s very much on the vision board of people I want to be like when I don’t grow up. Here is a lovely story about a reference in his work and I’ll note a degree of gladness that we didn’t all go together after all.

I’m looking forward to reading this, on convolutions, from Eli Bendersky.

Need some puzzles to while away the long summer? I know I do. For an hourly Countdown variant, follow the Hectoc bot, and for a daily “come up with a nice solution to a puzzle from AMS with a known answer” follow Suat Ayöz.

And here’s an article on knots in New Scientist that’s behind a paywall, which I linked to before realising it quotes my dear friend Nicholas Jackson. You definitely shouldn’t go to the archived version, that would be immoral.

Currently

If you’re in Edinburgh this weekend, Coburg House has an open house, where mathematical knitter Madeleine Shepherd will have work for sale.

Time is running out to submit an item to this month’s Carnival of maths and to this month’s TMiP animation challenge.

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 2E

By Colin Beveridge. Posted July 23, 2025

Double Maths First Thing might just let them watch a video

Hello! My name is Colin and I am a mathematician on a mission to spread the love and joy of struggling with a puzzle until it finally breaks up into beautiful bits.

This week, I’ve been looking at methods for how to board a plane. Turns out there’s a lot going on there. Monte Carlo methods, Lorentzian geometry, all sorts of tasty stuff.

Links

I’m not a wordsearch fan. I feel like there’s not much puzzle there. So I was surprised when Cracking the Cryptic suggested a wordsearch was an incredible puzzle, and amazed to find I agreed. (h/t to Tony Mann.)

On the to-read list for the summer holiday is this introduction to Galois fields — I particularly enjoyed (and felt) the grumble:

Many resources assumed either:
* It’s beyond your skill level so let’s oversimplify (“it’s hard, don’t worry about it”), or
* You had prior Pure Math studies in Abstract Algebra (“it’s easy, just use jargon jargon jargon”)

As much for the acronym as anything else, I’m pleased to link to the Database of Original and Non-theoretical Uses of Topology — topological data analysis is also on my list of things I’d like to learn one day.

I enjoyed @zenorogue’s discussion of different map projections.

Also in “problems I didn’t know I needed solved”, why are piano keys the widths they are?

There are many interesting papers from the Bridges conference in Eindhoven, last week, but I think my favourite is this one: Katherine Seaton’s exploration of hitomezashi stitching patterns on an isometric grids.

Currently

A big call-out from Dr Laura Taalman — an instant follow when I realised she was on Mathstodon — for a crochet art project you can join at Granny Life Crochet.

A reminder that you should join the Finite Group if you value off-beat mathematical discussions, and get your tickets for TMiP if you want to (a) learn more about talking maths in public and (b) come to the Pseudorandom Ensemble‘s show on the Wednesday evening.

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