The Simons Foundation just dropped a massive batch of lecture videos on YouTube: https://www.youtube.com/@SimonsFoundation/videos

Numerologists take note: tomorrow, 27th September 2025, is a square date in both US and Everywhere Else notation. 5205² = 27092025 and 3045² = 9272025 This is the last time this will happen for a thousand years! (from @EdPeggJr on math-fun)

I didn't know about Charles Howard Hinton. Interesting chap! I just discovered him via researching the etymology and origin of the word tesseract. (Turns out it was coined by Hinton, combining Greek words meaning ‘four’ and ‘ray’.) He married George Boole's daughter Mary Ellen Boole, with whom […]

https://travisdoesmath.github.io/s6/ funky visualisation of the nontrivial element in Out(S_6)

In Stephen Wolfram's recent blog post _The Ruliology of Lambdas_, he mentions in passing the traditional way, in the English-speaking world, to pronounce ‘de Bruijn’: > we can write this in the “de Bruijn index” (pronounced “de broin”) form Since learning a little Dutch, I've become quite […]

I never knew that Pete Waterman had such a deep interest in railways. https://en.wikipedia.org/wiki/Pete_Waterman

I missed the news that the bbchallenge collaboration have released a preprint on the determination of BB(5): https://arxiv.org/abs/2509.12337

I tire of box-shaped boxes

Who would win in a game of chess between a dinosaur and a rhombic dodecahedron?

Proof Equivalence in Linear Logic is Undecidable: https://www.irif.fr/~diguardia/papers/note_indecidability_proof_equivalence.pdf I don't find the result surprising, but I love how simple the proof is!

Fun puzzle, well made, mathematically interesting, absurdly cheap. I endorse this product and/or service. https://mathsgear.co.uk/products/dodecaplex-puzzle

This is fun, if you have a 3D printer and like regular dodecahedra. https://www.printables.com/model/194566-cracked-platos-egg-puzzle

“Unlike a typical mesh, which stores per-vertex 3D positions, a mescher stores per-vertex 2D screen-space positions and a per-edge depth difference. Whereas differences in depth across edges must sum up to zero as we travel around a standard mesh, this is not […] [Original post on mathstodon.xyz]

I’m building a Segerman Grabber. I think this is going to be fun. https://www.youtube.com/watch?v=vy7SJuhkGMY

This is the greatest age of mechanical puzzles that there ever was, and perhaps that there ever will be. What a time to be alive! (This particular puzzle may be acquired from https://www.etsy.com/uk/listing/4348768821/)

@CarlMuckenhoupt Is your profile image a Bilinski dodecahedron, or an ordinary rhombic dodecahedron? I had always assumed it was the latter, and I just noticed that it arguably more closely resembles the former, and now I'm curious.

2swap is about to go live on YouTube discussing “the game Connect 4 and the emergent combinatoric structures that arise when analysing its strategy”. This is like the World Cup for me. https://www.youtube.com/watch?v=klm9-3xds2k

One of the authors of the Noperthedron paper has joined Mastodon! Welcome @sergeyvogo (Or possibly, but less likely, there is a Sergey Yurkevich impersonator in the house.)

The man behind the iconic sculpture/toy/linkage Tangle, via @codinghorror: https://youtube.com/watch?v=WVnYejHWoso

Fun puzzle based on the Penrose tiling, by Oskar van Deventer based on ideas from @csk https://youtu.be/eNXUAQaWKjw

This is a very natural question about the Noperthedron, from @JosephORourke: can it pass through a hole in (another copy of) itself if you're allowed to twist it as you go? https://mathoverflow.net/questions/499720/twisted-rupert-property

Does anyone recognise the spiky boi in the middle? Is it stellated, or merely augmented?

Via @david, new shape just dropped. The authors claim to have proved that this polyhedron lacks Rupert's property. I haven't read the proof yet, but the claim itself doesn't seem outrageous.

I have been given what must surely be the largest model yet made of my dodecahedron whose adjacent faces meet at right angles, except on one edge where they meet at 45°. (Yes, I do need to find a better name for it.)

If you haven’t seen it, there’s a very nice new Numberphile video in which @richardelwes explains subcubic graph numbers – heavily featuring the work of my friend and sometime collaborator Adam P Goucher. https://www.youtube.com/watch?v=4-eXjTH6Mq4

What's the plural of Pentagramma Mirificum?

I wonder if there's a nice way to characterise the n-tuples of natural numbers that can be written as the row sums (or equivalently column sums) of some symmetric n × n zero-one matrix. Clearly all n numbers must be between 0 and n, inclusive. Example: for n=2, seven of the nine elements of {0 […]

I'm catching up on the history of rickrolling, and I've just learnt that Rick Astley grew up in Newton-le-Willows. When I was young, I went to school in Newton-le-Willows. But it turns out there are at least two different places called Newton-le-Willows, and […] [Original post on mathstodon.xyz]

A very interesting geometric model that Jeannine Mosely presented at MOVES. Sadly I can't find anything about it online. It's a hinged chain, alternating between 12 pentahedra and 12 tetrahedra, that can be folded into either a regular dodecahedron or a rhombic dodecahedron.

Amazingly, this very unusual-looking QR code can be scanned just fine.

Thomas Hales at MOVES is showing @gregegan's animation of Reinhardt's smoothed octagon from @johncbaez's blog.

I spent hours yesterday (on a long plane journey) failing to solve Stewart Coffin's Four Fit puzzle. I tried everything I could think of, and nothing worked. If you know the solution please don't tell me.

This was a massive amount of effort for a throwaway joke reply, so please appreciate it. https://mathstodon.xyz/@robinhouston/114965068360546637

Recently I’ve been getting more interested in mechanical puzzles, and I’ve been resisting the temptation to post too much about them here, because there are plenty of places on the internet (and elsewhere) where one can talk to puzzle enthusiasts without […] [Original post on mathstodon.xyz]

I’ve just stumbled upon the information that Chris Patuzzo has written a software implementation of Lee Sallows’ legendary Pangram Machine Mark II. https://github.com/tuzz/pangram-machine (I wonder if Lee Sallows knows about it. I’ve emailed him in case he doesn’t.)

This Mastodon post has four a’s, one b, one c, three d’s, thirty-one e’s, four f’s, one g, nine h’s, nine i’s, one j, one k, one l, two m’s, twenty-three n’s, seventeen o’s, two p’s, one q, nine r’s, twenty-six s’s, twenty t’s, three u’s, three v’s, six w’s, three x’s, five y’s and one z.

An interesting MO question from @noamzoam, that someone here might know the answer to. https://mathoverflow.net/questions/498407/on-joyals-definition-of-a-category-of-plane-trees

I’m hoping that it’s actually possible to physically assemble three of *these* into a cube. https://skfb.ly/pzCW9 I don’t currently have the means to physically test this, but it looks plausible in the animation I made, which I’ll attempt to share in a followup post.

I love it when mathematically interesting objects unexpectedly become commercially successful. I suppose Rubik's Cube is the most famous example, but there are other less famous instances. I am remembering this delightful toy that my now-adult daughter had as an infant […]

‘Math is a great career. It’s fun. It’s interesting. It keeps the mind curious. It’s good for making friends. It’s very good for your health.’ -—Fan Chung, in https://www.quantamagazine.org/why-the-key-to-a-mathematical-life-is-collaboration-20250728/

I think it’s at least mildly surprising that three of these can be combined into a cube. https://skfb.ly/pzByn

My experience so far with LLMs when coding is that they don't write great code, and trying to get them to write working code is a massive time sink which I quickly learnt not to get caught in. But their suggestions often use libraries, APIs and techniques that I was previously unaware of. They […]

New video: slide rule chopsticks! youtu.be/xIMwnBZe4Xw

Admire my CMY cube.

It's interesting that this sculpture, which clearly represents some internecine squabble in the Free Software world, was made so long ago

Oskar van Deventer has a new video where he demonstrates his ‘Bolts Cube’ puzzle: an evolution of the Bolts Loop that we have been talking about, but this time based on an 8-bar linkage. https://youtu.be/M4xVaBqg-8U