We are, I am reliably informed, near to that arbitrary point in our planet's
orbit at which much of humanity habitually mark the end of one and the
beginning of another. I'm usually neither sentimental nor self-obsessed enough
to write something to mark the occasion with a blog post, but looking back on
the last eleven months and thirty days I'm struggling more than usual to
convince myself that nothing much has happened. Aside from being one internal
organ down on the complement I started 2025 with fifty-two-and-seven-fiftieths
weeks ago[1], a handful of things happened that I consider (in an entirely
self-indulgent sense) to be noteworthy.
Seeing my own book for sale in the British Library's bookshop was pretty cool.
I might even get away with describing some of them as:
Hello and welcome to December 2025's Carnival of Mathematics!
We've reached Carnival number $246 = 2 \times 3 \times 41$, and that's special for
a variety of reasons, not least of which is that its digits are, in order, the
first three terms in one of the first sequences most of us were introduced to;
the chicken soup of all integer progressions that is the two times table.
$246$ is also the current best-known upper-bound for the minimum size of gap
that exists between an infinite number of pairs of consecutive primes. It's
palindromic in (e.g.) bases 5, 9, and 40; it is
untouchable (which means that it is not expressible as the sum of
the proper factors of any other number); and if you had a bit of string and
seven of each of two colours of bead, you could make one of $246$
different necklaces (using every bead).
And in maths history, Indiana House
Bill No. $246$ was an 1897 foray into proof by legislation: it proposed
to
square the circle using a method that, among other things, implied that $ \pi =3.2 $.
You've taken your seats and loaded up on popcorn, so let's get started on the
Carnival's...
Here's Dr Christoph Bartneck of Canterbury University talking about charts and
data visualisation. The video is the very first one hosted on Mathateca's
new YouTube Channel, and the talk was the public keynote at the Oceania MathsJam Gathering 2025.
Mathateca is an Ōtautahi Christchurch, NZ based charity working towards
creating a public space to celebrate mathematics, and who among us isn't well up for some more of that?
In serious business, Skewray Research isn't clowning around with the basics of
probability in their exploration of that 'mysterious gremlin of chaos:
Randomness is an Inverse Stochastic Process.
... and a mystery! Robin Whitty (of Theorem of the Day) wonders what's going on: 'A Plus magazine email said "Take part in our pilot study". The link was to a rather anonymous Cambridge University questionnaire. Frustratingly, nothing on Plus's website that I could see, nor on that of its host, the Millennium Mathematics Project.' The survey at the link he included has since been deactivated. Can you shed any light on this mystery study? Answers on a postcard direct to Robin, or written in lemon juice and left at the usual dead-drop.
Less mysteriously, Robin also submitted a post on Factoring Carmichael Numbers, in which Lance Fortnow discusses how the Miller-Rabin algorithm can (unbeknownst to the AI models he asked) find non-trivial factors as well as determining the compositeness of Carmichael numbers (which are, as I had to look up, composite numbers that can be mistaken for primes because they satisfy $ a^{n-1} \equiv 1\pmod{n} $ for all integers $a$ that are relatively prime to $n$). Robin has also enjoyed Gil Kalai's blog post on Computational Complexity and Explanations in Physics, which discusses their thoughts on some of the ideas raised by Scott Aaronson in a talk of the same name.
Act II
November also saw the release of Chalkdust's 22nd issue which includes, in addition to its usual features, an interview with the creator of legendary vigilante number-hero El Nombre. Printed copies are available for nothing more than the cost of P&P, or you can read it as a PDF for nowt. Donovan Young submitted his own article, A tale of $n$ cities, to the Carnival, so check that out while you're there, even if it's not the Dickens novel that I, personally, would think of first at this time of year. There's also a blink-and-you'll-miss-it moment on page 60: second-from-bottom, on the left.
Jencel Panic wants you to know about the online book about category theory that they're writing. They've submitted it here because in the last month they've finished an important chapter: Natural Transformations.
Arguably too early for December's Carnival, it was also too late for November's, so Robin thought it was worth including and I agree: Fractal Kitty's Mathtober 2025 Sketches are a case-in-point that mathematics and art do not exist in isolation from each other. They're also a bit lovely, and fairly soothing to browse.
John D Cook explores the 'intellectually and visually satisfying' Japanese Polygon Thereom, complete with some Python code for exploring the theorem more deeply, and generating your own related images.
That rounds up this months submissions, but feel free to explore some of the...
Sideshows
Or: Things I Stumbled Upon or Did Last Month That I Thought Might Be Worth Sharing
2025's MathsJam UK Gathering took place over the weekend of 22-23 November. This year it was held in my own stomping ground of Milton Keynes, and you can find out what you missed on the MathsJam Gathering 2025 archive. I particularly enjoyed dusting off my guitar and taking part in the MathsJam Jam for the first time in years!
Maths Week England took place from 15-23 November, with a launch event at the new MathsWorld discovery centre in London. Go to mathsweekengland.co.uk to find resources and read about this year's events, and sign up to make sure you don't miss out on next year's activities! If you represent a museum or primary school you might be interested in this.
I've recently been made aware of the AgRoMa project, based at Newcastle University, which is studying the Roman practical mathematics tradition. I'm particularly excited by their intention to create educational materials to encourage and support teaching that bridges mathematics and humanities. Fun fact: AgRoMa is a contraction of Agrimensores and Roman Mathematics, and a groma was an instrument used by ancient Roman surveyors!
Next time...
Thanks for joining me for this month's Carnival of Mathematics! The show's over, the curtains have closed. You don't have to go home but you can't stay here: if you're still buzzing from the experience why not head over to the Aperiodical's Carnival of Mathematics page and see where it's appearing next month, and maybe get involved: there's a form to submit any mathematical tidbits you feel might be worth featuring over the next month, and if you have a maths-themed blog they're always looking for future hosts.
As you go, do have a look around the gift shop: The Mathematicians' Library would make an excellent gift for anyone in your life with a slightly nerdy disposition.
I recently took time out for a quick weekend away in South Wales. The
itinerary involved, as is only right, castles[1]. I was struck by the geometric shapes of the keeps - particularly one with a
circular cross-section at Tretower castle, and a larger one with a hexagonal
base that forms part of Raglan castle.
Goodrich Castle, a ten-minute drive from the Welsh border in Herefordshire,
England, has to be one of my favourites[1]. It's a Norman medieval ruin that
played host to an English Civil War siege by Parliamentary forces upon the
Royalist forces stationed there. Despite not having its defences updated to
17th-century standards, the medieval castle stood up well to direct attacks
and artillery was introduced to the conflict, with Parliamentary Army Colonel
John Birch commissioning the casting of a mortar called Roaring Meg.
For years I have been periodically prompted to think "ah yes, must go there
one day" by signs for Bolsover Castle as I pass through the vicinity of
Junction 29A on the M1. That day, as all things must surely do, finally came
to pass on Monday 11th August, 2025[1].
As with all posts in the
Maths in Museums series, it is not for me to tell you how or when to visit, how much
it costs, or even much about the history of the site (though some will
surely creep in). All of that can be left to
English Heritage, who are its current custodians. Our purpose here is to uncover some of
the opportunities for mathematical exploration that I spotted during my
visit[2]. As with most museums and galleries, there's no interpretation at the site that will help you to structure any exploration of these ideas.
Will There be a Pink Moon in April?
-
*I've seen a number of **posts promising a pink full Moon** on 4th April
2015. This is one of those recurring internet shares that crops up around
this tim...
