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  For my birthday, my brother-in-law gave me a 4992-digit hex number that, when used as a seed for Python’s random number generator, makes it so that printing a sequence of “random” ASCII characters actually prints a birthday greeting. I find it rather amazing that this is possible! This is the program he sent with the seed: with open("seed.txt", encoding="ascii") as handle: seed = int(handle.read().strip(), 0) r = random.Random(seed) pending = "" while True:...

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

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  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...

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

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

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  @johncarlosbaez@mathstodon.xyz I have a counter-clockwise clock in my kitchen, which I was given a few years ago. It's very rare for anyone to notice that there's anything unusual about it.

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

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

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  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?)

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  @christianp @lmidgey If you tire of the regular dodecahedron, why not try https://skfb.ly/owspv ?

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

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  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.)

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  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))

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  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...

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  “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

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  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

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  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

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  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

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

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  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

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

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  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

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  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

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

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  “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

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  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.

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  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

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  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.”

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  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.”

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  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.