Carnival of Mathematics #237
Welcome to Carnival of Mathematics #237! It’s traditional to start the post with a few interesting facts about the number… only 237 is one of the dullest numbers in existence. It’s not prime. It has no entry in David Wells’s Penguin Dictionary of Curious and Interesting Numbers. It’s not even the sum of two squares, and I honestly think nobody would miss it if it were removed from the natural numbers.
Unless, of course, you’re especially invested in triangle-free simple labelled graphs with five vertices, of which there are 237; it is also a lucky number (although it’s a long way down the list) and involved in Calabi’s triangle1. There are 237 four-digit numbers where the mode and mean of the digits are equal, and there are 237 basis orbits of 6-dimensional hypercubes. Also, 237 litres is approximately the volume of a barrel with height 93cm, top radius of 30cm and mid-radius of 35cm, the bottom of which I am currently scraping.
Roll up!
Let’s get the Carnival rolling with a blog by a relative newbie, Michał Dobranowski: voting systems are dear to my heart, and May’s theorem says FPTP is fine… as long as there are exactly two candidates.
Fractal Kitty is (for my money) one of the undersung stars of maths communication – she’s responsible for the Mathober challenge among other things. This month, I’ve been told about her Stream of Me journalling experiment and a gorgeous haiku visualisation.
More absurdly, but also beautifully, Filip Hráček has a lovely dive into a nonsense book – Filip calls it graphical poetry – titled Math Minus Math.
“Claude may not be able to think but it can definitely talk and this puts it on the level of most politicians”
More absurdly, but less delightfully, Mark Dominus asks Claude about graph theory with predictably poor results.
Continuity
It’s worth following up several posts in Carnival #236.
Rather than focus on Thony Christie’s ongoing diatribe against The Secret Lives of Numbers: A Global History of Mathematics & Its Unsung Trailblazers by Kate Kitagawa & Timothy Revell, I think it’s probably more in line with spreading joy to point to some books Thony does recommend.
There’s also a part two to Brian Clegg’s series on infinity, looking at googols and myriads – not to mention a part three looking at Achilles and the Tortoise.
Karen Campe has also extended a series: she’s up to episode three of her tools for dynamic geometry suite.
Jim Propp probably makes this a serious series of series; his is interested in the work of Richard Dedekind and rigorously defining real numbers.
Miscellany
I enjoyed John D Cook’s note on using matrices to link complex, dual and double numbers, and a couple of posts from Lance Fortnow and Bill Gasarch at Computational Complexity: Does Lance dislike Ramsay Theory because he’s colour-blind? and a Big Breakthrough in the exciting world of sum-free sets.
In Serious Maths News, Quanta Magazine has the scoop on a new proof that Hilbert’s 10th problem2 is undecidable in any ring of integers.
I’ve also been pointed at the British Society for the History of Mathematics’s schedule for a recent seminar on research in progress, in case you’re interested in what the historical movers and shakers are up to at the moment.
Peter Woit’s Not Even Wrong wonders – as do I, even as someone with pretty much a full house on the privilege bingo card – about the viability of travelling to the US over the next few years, and asks whether it’s worth considering an alternative venue for the 2026 ICM.
Thanks to everyone who submitted articles, especially Robin Whitty, who’s put in a proper shift this month. If monthly links to interesting maths posts are just too infrequent for you, you might want to sign up for Double Maths First Thing or read the archive at the Aperiodical. This week’s issue will mark its half-birthday!
I swear I wrote the bit being nice about Fractal Kitty before realising that she’ll be hosting Carnival #238. I hope that’s a more interesting number!