Colin Beveridge

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Double Maths First Thing: Issue 29

By Colin Beveridge. Posted June 18, 2025

Double Maths First Thing is excited about the moon!

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

Annoyingly, immediately after last week’s issue went out, several interesting things popped onto my radar. One of them was Katie and Peter asking why nobody can draw a noughts-and-crosses board properly.

The other was Matt Parker going to the moon — or at least sending code to the moon to estimate pi. The kickstarter is already way beyond its goal, and schools are encouraged to get involved. I keep telling non-mathematicians about it, and they look blank and say “… why?!”. I shake my head at them. IT’S MATHS ON THE MOON! (I seem to be involved in the project. It is great fun working with bizarre restrictions.)

Links

My favourite link of the week is this, from Abigail Pain, in which she hacks into her cybersecurity homework assignment to avoid having to do it. This falls squarely in the mathematician’s remit of going to extreme lengths to avoid doing any proper work. Of course, there’s also a relevant XKCD.

While my lunar coding hasn’t yet involved any bit-twiddling, it may reach a level where that’s required. This means I’m more than usually interested in a radix \( 2^{51} \) trick for adding things up and a leap year check using bitmasks. Smashing stuff.

Walking legend Robin Houston has pointed me at an online version of Stewart T Coffin’s The Puzzling World of Polyhedral Dissections, which I’ve barely had a chance to glance at, because I would vanish into it for a couple of weeks and DMFT wouldn’t go out on time, my work would go unfinished and neither the kids nor Pete would be fed. If you can read it and summarise for me, that would be great, hmmkay?

What else is good here? Oh yeah square theory. I keep flipping between “this is really obvious” and “that’s actually a really nice model for several things I enjoy” — crosswords, jokes, and proofs.

And my most fun fact of the week: Raisa Smetanina won an Olympic gold medal for cross-country skiing a couple of weeks before her sixth birthday.

Currently

There’s a Finite Group livestream taking place a week today (on Wednesday 25th June) at 2pm UK time. It’s Games Time with James Grime, which is a good title because the names rhyme.

The Carnival of Mathematics is coming home this month, being hosted by Katie at the Aperiodical. If you’ve got a blog that could provide a future stopping-point for the Carnival, let Katie know!

Also, Talking Maths in Public is a couple of months away — whether a Pseudorandom Ensemble show is enough to persuade you or not, bursaries for those who wouldn’t otherwise be able to go are available, but the deadline is this Friday, June 20th at noon UK time.

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,

Double Maths First Thing: Issue 28

By Colin Beveridge. Posted June 11, 2025

Double Maths First Thing is bringing the thunder

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in playing with patterns, puzzles, figures and logic.

First up, an apology: in last week’s issue, I mistyped the number of solvable nonograms: rather than 25,000, there are 25,000,000. As of Tuesday evening, humanity has solved about 27% of them. Good work, fellow humans!

Links

One fellow human doing good nonogram work is Lucas Cimon, who has developed code to generate nonogram QR codes. He says it will likely be “difficult to solve manually”.

Since we’re looking at puzzles and logic, all-round good egg Tony Mann has pointed me at a remarkable 4-by-4 sudoku and Cracking the Cryptic’s solution video. Meanwhile, there’s a ferocious argument going on in the group chat about Zp-ordle, the daily puzzle game for people who think Wordle needs more p-adic integers. (Which is everyone, right?)

There’s one question on everyone’s lips: “Will Jesus Christ return in an election year?” Eric Neyman explains why the likelihood given on Polymarket is 3%, considerably higher than most analysts would predict.

Meanwhile, here’s Hannah Fry peeling an orange.

And in mental arithmetic news, Niklas Oberhuber estimates some logarithms. (I particularly liked that 5^10 is about 9.8 million, which I’ll store in the Useful Approximations drawer of my brain.)

Currently

It’s mid-month, which means that your local MathsJam is coming up soon (Tuesday 17th in many locations, including Weymouth). Find yours here, or email Katie to find out how to start your own.

The 240th Carnival of Mathematics now has a link at Beauty of Mathematics. Similarly, the TMiP animation playlist for May is live.

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.

Until next time,

Double Maths First Thing: Issue 27

By Colin Beveridge. Posted June 4, 2025

Double Maths First Thing always takes the weather with it

Hello! My name is Colin and I am a mathematician on a mission to disseminate mathematical joy and the pleasure of figuring things out.

I’m just back from a week in the Peak District, where we discovered that Pete the dog likes neither stepping stones, nor the river that he jumps into to avoid them. Apparently it’s my job to carry wet dogs across rivers, although I don’t remember THAT being in the information pack.

We visited George Green’s windmill in Nottingham, which is unusual in that its science centre doesn’t hide the maths away — Green’s theorem is prominently displayed on banners around the place (although there’s only a limited attempt to explain it.) I’ve just added it to Nerdy Day Trips, which is BACK! (It was very easy to submit, so I recommend adding nerdy day trips you’ve enjoyed.)

I spent the car journey back doing my best to help humanity defeat the evil nonogram: there are about 25,000,000 solvable five-by-five puzzles, and we need to solve them all. After a while, you get into a flow state, it’s quite an experience. [Edited 2025-06-04 to correct number from 25,000]

Links

On to the links! First up, a couple of questions from dear friend Colin Wright: does this theorem have a name in English?, and is there a good ‘why?’ for Marden’s theorem?

In games news, Boggle has been (effectively) solved, and students at Purdue have broken the robot Rubik’s cube world record, with a time of 0.103 seconds. (Incidentally, the 4×4 robot record fell recently — but that’s still significantly slower than the human world record.)

From the Fields medallists doing interesting things beat, Terry Tao has launched a Lean companion to Analysis I — Lean is a “formal verification system” that checks your proofs hold water. Meanwhile, if you’d like a Tim Gowers lecture on why LLMs aren’t better at finding proofs, you should watch one.

Another piece on my to-read-more-carefully list is Aeva’s article on spline fields, for storing and rendering realistic terrains.

Currently

It’s a new month, so there’s a new Carnival of Mathematics: this month’s host hadn’t been posted at press time, but might be before you read this; you’ll be able to find it at Suzza’s Beauty of Mathematics blog.

There’s also a new TMiP Animation Challenge prompt: if you’ve got something to visualise about curves of pursuit, feel free to give it a go. It’s a good excuse to learn a new skill; the Finite Group generators seem to delight in using unconventional approaches like tikZ, but Manim or possibly Lottie appear to me like more reasonable starting points. Last month’s efforts will soon be linked from the same page at TMiP.

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.

Until next time,

Double Maths First Thing: Issue 26

By Colin Beveridge. Posted May 28, 2025

Double Maths First Thing shaves newsletters if and only if they don’t shave themselves

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in puzzles, problem-solving and practicing maths.

I’m currently wading through the combinatorics of meteorology, which is another way of saying “this walk is a bit muddier than I expected”. Coincidentally, I’m also thinking about the maths of rainstorms, which is much more exciting than the practicalities of navigating the dog through them.

Links

You don’t have to be in Aoteroa to appreciate Maths Craft New Zealand’s resources — I love things like step-by-step instructions on meanders — and (for example) @welshpixie’s guide to drawing Celtic knots, which inspired Andrew Taylor’s Celtix.

If you feel like maths games should be less knotty and more numerical, Andrew has you covered there, too: his newest offering is Ophex; I am annoyed that I recently lost my perfect streak, so it’s dead to me now.

For a change of pace, you might want to read Toby Lam’s piece on differentiating inverses graphically. I’ve only skimmed it, because it has diagrams with arrows in that remind me of my Erasmus year in France, where I understood the French perfectly, but the maths was gibberish to me.

I have mixed feelings about this piece in defence of Venn Diagrams by Jack Murtagh. It’s lovely as far as it goes (I was surprised to realise that Venn diagrams are less than 150 years old), but it doesn’t go very far — I suspect this is a function of SciAm’s word count limits.

Back in Issue 21, I mentioned Fractran; Tzerjen Wei has a working interpreter in case you want to try it for yourself.

Currently

This afternoon (Wednesday May 28th, 5pm UK time), Paul Lockhart, author of Lockhart’s Lament, is doing an AMA.

You’ve got a few days left to submit anything interesting to Carnival of Mathematics 240, which will be hosted by Suzza at Beauty of Mathematics.

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.

Until next time,

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.

Until next time,

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.

Until next time,

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.

Until next time,