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• Post #4217635

  Surely someone is missing something here: the woven artefact is clearly a cuboctahedron, and I don't think any wasps make cuboctahedral nests.

• Post #4217634

  RE: https://mastoxiv.page/@arXiv_csLO_bot/116911516892048971 It looks as though one of my favourite problems has been solved! It's related to both Petri nets and linear logic. BVAS are more general than VAS – which are more or less the same as Petri nets. The reachability problem for VAS was previously known to be decidable, but with outrageous complexity (Ackermann-complete), so the reachability problem for BVAS must be at least as hard as that. But this work doesn't answer t...

• Post #4071649

  Very nice YouTube short summarising @Ayliean@mathstodon.xyz’s record-breaking 14-disk Towers of Hanoi solve at #emfcamp. https://youtube.com/shorts/3waVV7Fjct0

• Post #2330256

  User cachecrab on Twitter noticed that Google has a rather unusual interpretation of the query “20% of £1k”.

• Post #2175406

  I want to know the relative popularity of the Platonic solids, but a Mathstodon poll can have at most four options.

• Post #1916393

  RE: https://mathstodon.xyz/@henryseg/116437443825536011 This is now my favourite physical object.

• Post #1625839

  I thought Peter Selinger was on here, but I can't find him. Has he left us? Just looking at this interesting new paper https://arxiv.org/abs/2604.20964 which does cite Mathstodon posts by @pieter. (@christianp first citation of Mathstodon in a paper, or have there been others?)

• Post #1540141

  Spotted in The American Mathematical Monthly, Vol. 99, No. 2 (Feb., 1992)

• Post #1278206

  I guess we’re all getting a little tired of talking about this sort of thing, but I think this is the most impressive example yet of an LLM-generated solution to a long-open mathematical problem: https://www.erdosproblems.com/forum/thread/1196 Jared Lichtman, a mathematician who has spent (in his words) “many years” working on the problem himself, describes the proof as “a remarkable artifact […] from The Book”. (See also https://x.com/jdlichtman/status/2044298382852927894 if you do 𝕏.)

• Post #1278205

  There’s a fun paper showing that you can define all elementary functions using just two primitive operations: the constant 1, and the binary function eml(x, y) := e^x - log(y). https://arxiv.org/abs/2603.21852 That’s a neat little result, which makes for some fun games. What’s the simplest expression you can find that evaluates to your favourite constant? The best I have found for 2 is: eml(1, eml(eml(eml(1, eml(eml(1, eml(1, eml(1, 1))), 1)), eml(1, 1)), 1))

• Post #1278204

  I didn’t realise this article was out already! Featuring some computations and diagrams by me (which, to my great excitement, Don Knuth emailed me about when he heard of them). _On Max Bill’s gelbes feld_ by Barry Cipra. https://www.ams.org/journals/notices/202605/noti3334/noti3334.html I can’t find a PDF of just that article. Maybe the Notices don’t do that any more? But here is the whole issue, if you want it formatted more nicely: https://www.ams.org/journals/notices/202605/202605FullIssue...

• Post #1237878

  “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

• Post #1209968

  Fun fact (via otaliptus on Twitter): the president-elect of Romania was one of the 11 students to solve the famous Vieta jumping problem at the 1988 IMO: https://en.wikipedia.org/wiki/Vieta_jumping#History

• Post #1209964

  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

• Post #1209960

  Need to pack a lot of identical regular tetrahedra together efficiently? This may help! From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao

• Post #1157524

  I don't remember coming across the Heptagon Numbers before. Very nice!

• Post #1157522

  Unfortunately there is no way I can persuade you to watch this by quoting a particularly amusing moment, because there are so many particularly amusing moments that I can’t possibly choose one. https://youtu.be/M1si1y5lvkk Here’s the paper, in case you’re more of a reader than a viewer: https://tom7.org/httpv/httpv.pdf

• Post #1157491

  2025 was the first squared-triangled-squared-triangle number for 2024 years, and I spent the whole year not knowing that! https://youtu.be/aulrY8Y4VW8 And it won’t happen again till the year 3△▢△▢ = 443556, which, barring unexpectedly rapid and impressive progress in medical science, I am unlikely to see.

• Post #1099009

  Is math big or small? https://chessapig.github.io/talks/Big-Small

• Post #853423

  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 had been unsolved since. https://mathoverflow.net/a/509413/8217 https://mathoverflow.net/a/509415/8217

• Post #853422

  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

• Post #708861

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

• Post #691359

  “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! *Edit*: … has collected at least one geometric puzzle

• Post #677042

  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.

• Post #677041

  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

• Post #677040

  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.

• Post #677039

  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 Brian Ignaut, who was the lead solar array designer at SpaceX before creating the product design studio Degrees of Freedom (https://enjoydof.com/). https://enjoydof.com/products/solid-african-mahogany-loop-table-1 https://www.inst...

• Post #677038

  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.”

• Post #677037

  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 that has edges of length A+B+C. In 2003 Knuth showed that for a special subset you can fit 28 cuboids into a cube.”

• Post #676534

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