Goodbye 2025...

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:

Carnival of Mathematics #246

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...