A conversation about mathematics inspired by a 3D wooden puzzle. Presented by Katie Steckles and Peter Rowlett, with special guest Grant Sanderson.
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I’m trying something a bit different. Here’s a ten-minute video about a sequence I found on the OEIS.
Here’s a round-up of maths news stories from this month we haven’t otherwise covered on the Aperiodical (not including, of course, the important enneahedron news Christian just posted about).
We’ve gone crashing into October and that means it’s also #Mathober, an annual maths/art celebration taking place on the internet. If you’re into maths or art, or both, and would like to try producing something creative this month, on an informal schedule, #mathober provides a structure for you to do that.
The number one component of music that really gets my attention is Brian May plays guitar, but a very close second is clever lyrics. The first morning of 2025’s Talking Maths in Public (TMiP) conference, from waking up, through carving myself a slice of scrambled egg at the breakfast buffet, up until the blessed relief of Jon Chase’s fabulous keynote talk, was soundtracked by a repeating refrain that only I could hear:
‘I like the Pope / The Pope’s got notes on polytopes’.
Books. Every self-respecting mathematician’s floor has a pile of them, some half-read, others to re-read, some merely providing structural support. In The Mathematician’s Library, Thomas K. Briggs considers an alternative approach to the literature, instead using the books of the last few millennia to tell the story of mathematical development around the world.
When I say “around the world”, I mean it: Briggs takes care to pick out important early texts from India and China; if the southern hemisphere feels a bit hard done-by, I suspect that’s more a shortage of available works than a deliberate snub. As far as possible, he tries to counter the narrative that all mathematicians conform to the traditional old-white-bloke stereotype by providing counterexamples. The tone is light and friendly, a “hey, look at this cool thing!” approach, typified by the last few selections: rather than pure research, the picks move assertively towards popular maths.
It’s a beautiful book – a gorgeous cover and thoughtfully laid-out illustrations, even if the ligatures on the typeface feel like a little much. It follows a largely chronological path, split into six sections – the first 40,000 years (up to Euclid), the origins of mathematics (up to about 600CE), global evolution (up to the Renaissance), scientific revolution (up to Newton’s Principia), modern mathematics (up to Russell and Whitehead’s), and – somewhat eyebrow-raisingly – the future, from 1932 to 2024.
My main criticism of the book is that there’s obviously a concept behind it, but what the concept is isn’t made clear. Is Briggs an enthusiastic librarian showing us around his imaginary collection? Are we travelling through time to visit the floor-piles of mathematicians gone by? Is it just a list of some interesting books and some commentary on them? I believe it’s the first, but the introduction ought to put it beyond doubt.
There’s something for everyone here: enough detail to get you started if you want to burrow into a rabbit-hole, but not so much as to overwhelm; a mix of familiar and unusual book selections; lots of pretty pictures if you don’t feel like digging into the maths right now; and a wide, tall format that will add stability to my personal pile of books.
Here’s a round-up of mathematical news stories that happened in the last couple of months, that we didn’t otherwise cover on the site.
A newly discovered shape (ArXiV paper), described as a monostable tetrahedron, always lands the same way up – whatever orientation you place it in, gravity pulls it to the same place. There’s a write up in Quanta Magazine about it with some lovely videos. The write up mentions a lost physical model built in the 1980s, but it turns out Colin Wright has the model! Colin shares the story and some pictures in a blog post MonostableTetrahedron.
In other things-landing-on-particular-sides news, a new method for identifying stationary points of solids and the probabilities of resting at them has enabled the design of dice with target, non-uniform probabilities – and has been used to generate dice shaped like dragons, of course.
It’s now been confirmed that all the Mersenne numbers below M49 (three largest known Mersenne primes ago) have been checked and confirmed as being non-prime, so M49 is now definitely the 49th Mersenne prime.
The sixth Busy Beaver number, previously known to be greater than \(^{15}10\), has had its bounds improved – it’s really extremely big.
Up-and-coming mathematician Hanna Cairo has discovered a counterexample to Mizohata-Takeuchi conjecture, a problem in harmonic analysis – here’s the ArXiV paper if you’d like to read it.
Quanta magazine also reports some new developments in sphere packing, on how to get increasingly dense packings in higher-dimensional space.
MathsWorldUK has announced in its latest newsletter (PDF) plans to launch a second maths discovery centre location, in London. Located in the heart of Southwark (not far from the Tate Modern), the new site MathsWorld promises to be “a vibrant playground for mathematical exploration”.
The five UK maths teaching associations are to merge – the The Association of Mathematics Education Teachers (AMET), the Association of Teachers of Mathematics (ATM), The Mathematical Association (MA), the National Association of Mathematics Advisers (NAMA) and the National Association for Numeracy and Mathematics in Colleges (NANAMIC) will henceforth be known as AMiE (the Association for Mathematics in Education).
Soccer team MK Dons are paying tribute to Bletchley Park Codebreakers with a new Enigma-themed away shirt, with a design of Enigma machine key caps (circles with letters in) in recognition of the work of codebreakers at the former stately home, close to their home ground.
Google’s Gemini Deep Think AI model has achieved gold-medal level performance at the International Mathematical Olympiad, having solved five out of the six IMO problems perfectly, and within the 4.5-hour time limit. Previous attempts have taken two to three days of computation, and this represents a significant improvement.
And finally, a piece of sad news: mathematician and musical satirist Tom Lehrer has died. We’d like to share our favourite Tom Lehrer quote: “Some of you may have had occasion to run into mathematicians and to wonder therefore how they got that way.”