Me! On Numberphile! Who would’ve thought it?
Earlier this year, Brady Haran visited Newcastle to record a video with some Leverhulme scholars. Luckily for me he had a bit of spare time to record a video with me, so we did one about the Herschel enneahedron, which I first looked at back in 2013.
There were a few common questions among the comments on YouTube. I thought I’d quickly respond to them here.
Double Maths First Thing is the Ultimate Answer.
Hello! My name is Colin and I am a mathematician on a mission to the moon! But I’m also on a mission to spread joy and delight in doing maths anywhere in the cosmos.
Talking of doing maths in strange and hostile environments, I’m going to Bristol this weekend for my Rubik’s cube competition. Going by my current success rate at blindfold, it’s about 60-40 whether I’ll manage to complete a solve.
This week I’ve also been working on a nice combinatorics problem with Zoe Griffiths for her AEOUD talk about finding sets of children’s names with no common letters. I learned that in 2023, at least three families decided to name a child “C”. I don’t like to judge, but that feels even worse than calling them JavaScript.
There’s a breathless, magaziney furore over a link between primes and integer partitions (ArXiv paper here) — it’s not my field, and part of me doesn’t feel very surprised that there’s a link, but having used the method of “Leonhard Euler would have thought of that already” to rebut a “proof” this week, I feel like there’s a corresponding method of “if it was trivial, Ken Ono wouldn’t be publishing it.”
Here’s an old post from David R Hagen about an XKCD cartoon. He wonders “how come the 11th of the month doesn’t show up as often as it should?”
Some curved paper sculptures to make you go oooo! and clap your hands a bit? Yes, please, Erik and Martin Demaine, yes please.
I enjoyed Vanessa Madu’s talk at Big MathsJam about rubber ducks and ocean currents, but I also enjoyed her article about consecutive odd semi-primes, another of those questions that you didn’t know you needed to wonder about, and which then drops out quite neatly. Quack!
It’s a big couple of weeks for the Finite Group, with a livestream today (June 25th, 2pm UK time) and another in a couple of weeks (Friday July 4th, 7pm UK time) — meaning that joining today for £4 will get you access to both. Bargain!
You’ve got a week or so to submit entries for this month’s Carnival — and I imagine Katie would love it if you volunteered to host a future event. (It’s not that much work if you’ve already got a blog.)
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 (not my full name)
In my childhood memories, the lanterns in my hometown always fascinated me – circular palace lanterns, polyhedral colorful lanterns. How did my ancestors achieve the magical transformation from flat to three-dimensional through simple bamboo strips and paper? As a child, I was often confused: was there anything hidden behind these beautiful shapes?
Three decades slipped by, and as I returned to the art of paper folding, that long-forgotten question suddenly became clear. It turns out that the structural principles of those traditional lanterns align with geometric calculations—how a flat sheet of paper can be perfectly transformed into a three-dimensional structure with specific curvature. This process contains profound mathematical essence: straight creases correspond to developable surfaces, while curved folds achieve their shapes. From rectangular paper-based to porcelain like smooth curved surfaces, every fold undergoes intricate geometric transformations.
This perfect fusion of craft and mathematics not only showcases the ingenuity of folk artisans but also remarkably anticipated the evolution of modern computational origami techniques. The craftsmanship behind traditional lantern-making constitutes humanity’s earliest exploration and practice of spatial geometry—a profound legacy that has continuously inspired the development of structural design approaches.
A question lingered unresolved for over three decades—until I encountered modern origami theory and finally grasped its profound mathematical wisdom. This long-delayed revelation compels me to ponder: In our relentless pursuit of so-called progress, have we overlooked something profoundly valuable? As masters worldwide have long pioneered innovations in paper folding, shouldn’t we pause and reflect? This isn’t merely an academic gap; it speaks to the neglect of foundational mathematical research. It’s time we reignite our appreciation for the enduring brilliance of mathematics!
As an archetype of curved-crease origami art, Origami Blue-and-White Porcelain transforms flat paper into exquisite three-dimensional forms through precise calculated creases.
In the art of origami creation, I have always adhered to the concept of “subtractive aesthetics” – shaping forms by accurately hiding excess parts.
This principle is particularly typical in the structure of traditional Chinese circular lanterns: When the lantern ’ s uniformly arranged petal-like segments are unfolded into a planar sheet, the absent portions represent exactly those strategically eliminated excess regions.
This foundational geometric principle can be extended to designing curved vessels (e.g., circular lanterns, porcelain), with its computational workflow comprising three key steps:
Ultimately, the algorithm generates precise crease distribution diagrams, providing scientific mathematical guidelines for vessel fabrication.
Applicable to rotatable vessels, papercraft lamps/lanterns, circular heritage architectures, and pagoda-style structures.
This method overcomes the planar limitations of conventional origami techniques, offering an alternative computational approach for developable surface design with potential applications in industrial design and architectural mechanics.
We observe that exquisite ceramics and traditional circular lanterns alike are formed by rotational assembly of curved crease units. This exemplifies the core principle of origami engineering: a material optimization process where precise folding conceals redundant sections to achieve visually streamlined forms.
This artifact demonstrates uniform curved crease unit distribution in its structure. The waist contour is formed through rotational constriction, showcasing exceptional craftsmanship in curvature control. Notably, its spiral patterning precision surpasses comparable paper-folding implementations.
These gear-like structures represent unanticipated structural outcomes during folding operations. The creative process requires continuous cognitive switching between 2D crease patterns and 3D topological realization, presenting significant neural adaptation challenges. Particularly without physical reference models, the spatial imagination ability of the brain often goes through a debugging stage, and these “wrong” works are considered a good thing from a certain perspective.
This is the mark of my encounter with mathematics. The folding and unfolding of paper is like a pair of hands revealing the science behind it. I returned to the old me, learning to discover the beauty of mathematics, exploring the mysteries of origami, and leaving my own thinking trajectory in this interlaced field.
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.)
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.
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,
C
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of May 2025, is now online at Beauty of Mathematics.
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 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!
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.)
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.
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 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]
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.
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.
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