robinhouston

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-optimized.pdf

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))

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.)

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

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.

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

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

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

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

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!

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

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.”

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: @JosephORourke@mathstodon.xyz

I totally missed the news of this book at the time, but I recently saw it mentioned on @chalkdustmag@mathstodon.xyz, 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.instagram.com/p/BqdBh2Gg-NP/?img_index=1

RE: @liuyao@mathstodon.xyz

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.

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 Ding (“the thing”).

https://www.utwente.nl/en/alumni/inspiring-alumni/ut-canon/stories/het-ding/