My cartoon for this week’s @newscientist.com

Speaking of Hoffman’s packing puzzle (as I recently was), I just found out about Oskar van Deventer’s witty mashup of Hoffman’s packing puzzle with Piet Hein’s Soma Cube: https://www.puzzlemaster.ca/browse/3dprinted/16775-hoffman-soma

how diffie hellman key exchange works (with as little math as possible)

This is mildly interesting: It looks as though current LLMs are becoming at least competitive with expert humans at solving Diophantine equations. Here a new MO contributor has used GPT 5.4 to find solutions to a couple of Diophantine equations that were posted by Bogdan Grechuk in 2023, and […]

Clever.

Does this really work? I wish I had known when I were younger.

“The puzzle in the photograph is now in the collection of HRH Prince Charles.” https://puzzleworld.org/PuzzleWorld/puz/holey_squares_cube.htm Apparently the King collects geometric puzzles!

I just stumbled across this. I haven’t tried it yet. (It’s printing now.) I had not heard about this interesting discovery! https://www.printables.com/model/221119-knuths-packing-puzzle “In 1978 Hoffman proposed that a if you take cuboids with size A×B×C, you can always pack 27 into a cube […]

The Wikipedia page ‘Union Jack’ includes an unexpected mathematical digression: “It is one of two national flags with two-fold rotational symmetry, symmetry group C₂, the other being the flag of Trinidad and Tobago.”

RE: https://mathstodon.xyz/@JosephORourke/115741946729136640 I totally missed the news of this book at the time, but I recently saw it mentioned on @chalkdustmag, and got a copy today. I've already learnt of this remarkable folding wooden table, designed by […] [Original post on mathstodon.xyz]

RE: https://mathstodon.xyz/@liuyao/116227619091892470 This (the Observable link in the quoted post) is a very nice visualisation, which complements the 3b1b video with a different perspective.

What are the chances that two different people would make videos for π day about estimating the value of π from a sequence of random bits, and that they would use COMPLETELY different methods? https://youtu.be/kahGSss6SsU https://youtu.be/WUCm18WFuCE

I don't normally like jigsaws, but when I saw this in the window of a charity shop for £2.95 I couldn't resist.

RE: https://mathstodon.xyz/@robinhouston/116210620815721477 I don't understand why this should be, but it seems possible that you can actually tile space with just this shape and the cubes, *without* the mirror image. As I say, I don't understand this yet […] [Original post on mathstodon.xyz]

@robinhouston that is, of course, a mere summary of that other Thing, the Needle Tower by Kenneth Snelson. In the garden of the Kröller-Müller Museum.

Here’s something I made yesterday afternoon, instead of doing what I had been planning to do. A pentomino tray-packing puzzle with a twist. https://makerworld.com/en/models/2512317-pentomino-tray-packing-puzzle

TIL. In April 1974, in the middle of the night, a small group of conspirators secretly installed a large tensegrity icosahedron made from discarded telephone poles on the campus of Twente University in the Netherlands. It’s still there. People call it Het […] [Original post on mathstodon.xyz]

Has the Mystery of Angzarr finally been solved? ⍼ https://ionathan.ch/2026/02/16/angzarr.html

An unusual polyhedron whose dihedral angles are all right angles. https://sketchfab.com/3d-models/orthogonalized-tetrahedron-c26dd2789da3406bbb00e5df769ade6d

New integer sequence just dropped https://oeis.org/A392894

RE: https://hachyderm.io/@ruuddotorg/116150427971106885 Ok, this is kind of cool. Can you find an elegant proof?

A four-dimensional version of the classic game Lights Out, from @nanma80: https://www.nan.ma/lights_out_4d/

“In this paper we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2,423,206 dodecahedra and 16,096,166 icosahedra.” https://arxiv.org/abs/2602.20425

RE: https://hachyderm.io/@simontatham/116124772439377225 If anyone was confused about how it's possible for a polyhedron to have a self-duality of order > 2, this is an excellent explanation:

I just keep thinking that Golden Gate Claude – may his weights rest in peace – would love it here.

Some of the ZomeTool crowd made a large sculpture of a projection of a tesseract and, in the tradition of Drop Art from which zometool was born, installed it guerilla-style in a nearby park.

Peter Kagey has made the slides for his talk interactive, so you can rotate the polyhedron models, and included a QR code on the first few slides so the audience can play with them during the talk. Nice idea. https://peterkagey.com/talks/2026-02-22/

New Scott Kim ambigram. Look at it upside down as well as the right way up.

A fitting tribute!

Very interesting, and characteristically careful and hype-free, from Daniel Litt on how good current AI models really are or aren't at mathematical research. (He cautiously decides that they're probably a bit better than he thought.) […]

A fun thing from the G4G gift exchange: there's no three-piece dissection between a square and an equilateral triangle – but there IS one between a square and an equilateral triangle with an equilateral-triangular hole in the middle!

The new version of Keynote seems to have dropped the most vital feature: not crashing during a presentation.

My house puzzle was in the December MathsJam Shout, thanks to @stecks, and Robert Webb from Melbourne MathsJam found a *third* way to do it with three pieces that we didn't know about. Can you find any more?

I know this is short notice, and very geographically specific, but one of our party can't make it so I have a spare ticket for @standupmaths in Shrewsbury this evening, if anyone wants to come.

All the native iOS mastodon clients I've tried are unsatisfactory – either missing features, or slow and glitchy. I'm giving up on native clients and using the web app. I think that will be generally better.

Achievement unlocked! Feature in an OskarPuzzle video. https://www.youtube.com/watch?v=Uzc1u2VPNyc (We actually have a rather more general theory of caltrops than this video describes. We’ve written a paper on it, which we have submitted to a conference. Maybe we’ll publish a preprint soon.)

Can you guess which well known mathematician DJs under the name DJ Moonstein? https://soundcloud.com/moonstein

The Simons Foundation have published a playlist of video interviews with Szemerédi (interviewed by Avi Widgerson). https://www.youtube.com/watch?v=L82nG5JbiAM&list=PLWAzLum_3a1_1fUgQGsDp8EpkdoW9wELE There’s a particularly amusing part in this video https://youtu.be/OzYUJFcCJhs, where he laments […]

I’ve only just seen this nice 2024 article from George Hart on “Math/Art”. https://www.ams.org/journals/notices/202404/noti2920/noti2920.html It’s nice to see someone explicitly making the point that this stuff mostly isn’t really art (and that’s okay).

Vi Hart has a new video out. It's not about maths. https://vimeo.com/1159438271

Is there a name for the family of convex polyhedra of which this is an exemplar?

This is a delightful contraption! I imagine it's a bore to print if you don't have a dual-nozzle printer, and it's a bit of a journey to assemble. (It requires M3 machine screws of sundry non-standard lengths, so you'll need to get long ones and cut them to size.) But the end result is lovely […]

i finally found this picture again. it has infected me memetically a long time ago > **Never touch the terminals.** Please don't. Cause of failure. > > This may be the cause. > > It is not possible to use multiple computers at the same time. **It is not possible.**

A tangent from my main thread: here is a surprising fact about polyhedral self-duality. It’s possible for a polyhedron to be self-dual, but only in such a way that applying the duality map twice DOESN’T return the polyhedron to its starting position. Here’s the paper (from 1989), but because […]

We hear so much about symmetrical polyhedra. What about their asymmetrical cousins? Here are the two simplest – I think – convex polyhedra that have no symmetry at all, even combinatorially. In other words, they have no non-trivial automorphisms as graphs. Both of them have 7 vertices and 7 […]

Here's a mathematical fact which I find amazingly counter-intuitive: There exists a polytope (=the convex hull of a finite set) in ℝ⁴ which is not combinatorially equivalent to one with rational vertex coordinates (=the convex hull of a finite subset of ℚ⁴)! 🤯 •1/4

An inverted tensegrity structure with magnets. I've never seen one of those before! https://www.grand-illusions.com/products/tensegrity-floating-loop

The following is much more personal than I usually choose to be on this account, but I am sure some of you would like to know it, sad as it is. My friend and colleague @mhl20 died last night after a short illness. Characteristically he announced the news of his illness on his blog, illustrated […]

I can see why you might be reluctant to watch a more than four hour video about the symmetries of higher-dimensional polytopes, but you'd be missing out. https://youtu.be/AbFAWNb0U3k

Imagine reading this if you didn't know what a reflection was. (This is not a criticism, just a thought that amused me.)