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Exciting new maths of 2024

By Peter Rowlett. Posted December 17, 2024

Over at the Finite Group, members (including me and Katie) have been discussing what in maths news has excited us this year. Here’s a summary.

Brayden Casella and fellow authors claimed that there exists a non-terminating game of Beggar-My-Neighbour, solving one of John H. Conway’s anti-Hilbert problems. Beggar-My-Neighbour is a card game similar to War in which two players deal cards onto a shared pile, aiming to win all the cards into their hand. Matthew Scroggs made a bot: Beggar-my-neighbour forever. In other game theory news, Othello is solved.

a sofa with 18 curve sections, each taking a smooth analytic form — Gerver’s sofa, image from Wikimedia.

Jineon Baek claims a resolution to the moving sofa problem. This considers a 2D version of turning a sofa around an L-shaped corner, attempting to find a shape of largest area. (There are some nice animations at Wolfram MathWorld.) Baek offers a proof that the shape above, created by Joseph L. Gerver in 1992, is optimal.

The Great Internet Mersenne Prime Search (GIMPS) announced a new Mersenne prime: \(2^{136,279,841}-1\). You can get maximum excitement about this news from Ayliean on TikTok, and join in the fun by signing up to record yourself saying a chunk of the prime for the Say The Prime project.

One thing that’s new, apart from the prime itself, is that the work was done on a network of GPUs, ending “the 28-year reign of ordinary personal computers finding these huge prime numbers”. Also this was the first GIMPS prime discovered using a probable prime test, so the project chose to use the date the prime was verified by the Lucas-Lehmer primality test as the discovery date. In other computation news, the fifth Busy Beaver number has been found, as well as 202 trillion digits of pi.

A new elliptic curve was discovered, breaking a record set in 2006 and pushing at the limits of current methods for finding them. Here’s some background on the curves and some of the characters involved.

This year also saw a proof of the geometric Langlands conjecture, and this article explains why this is such a big deal.

We’re all still excited about the discovery of the aperiodic monotiles, and the result passed peer review and was published this year.

And finally, it may not be top research news, but 2024 was also the year that Colin Beveridge started his Double Maths First Thing newsletter. Subscribe to the newsletter here, and check out the archive of past issues here at The Aperiodical.

Finite Group is a friendly online mathematical discussion group which is free to join, and members can also pay to access monthly livestreams (next one Friday 20th December 2024 at 8pm GMT and recorded for viewing later). The content isn’t at the level of the research mathematics in this post, but we try to have a fun time chatting about interesting maths. Join us!

Double Maths First Thing: Issue 9

By Colin Beveridge. Posted November 6, 2024

Double Maths First Thing is like a diet MathsJam, some of the flavour but only a hint of the joy.

Hello! My name is Colin and I am a mathematician on a mission to spread delight in my beloved subject.

I spent the weekend at Big MathsJam in Staffordshire and gorged myself full of puzzles, surprises and fascination — my personal highlights were Mats Vermeeren’s talk about why the start lines on athletics tracks are curved the way they are, Vincent van Pelt’s MathsJam Jam song (Mnemonic to the tune of Blondie’s Atomic) and the colouring-in in the quiet room. Now I’m sad that I don’t get to do it for another year.

From around the internet

It’s always cool to see ancient technology in action. Slide rules may not be ancient ancient, but they were no longer in common use by the time I was at school. (I remember we had some Napier’s bones, but nobody knew how to use them. I wish they had, I’d have lapped it up.)

As everyone knows, the Mathematical Villain goes through your spreadsheets turning data into dates. Here are some more times that Excel users failed to, well, excel. (Aside: it’s all so avoidable! A halfway-competent programmer can set up a script that checks for this sort of thing. And if you need one of those, you should let me know.)

In “everything is interesting if you look at it closely enough” news, the horrors of implementing daylight saving rules around the world are fascinating.

I also loved this bit of code golf for finding Fibonacci numbers. The explanation is much more interesting than the code.

I couldn’t explain why, but I’m averse to calculator notebooks. Not my cup of tea. Don’t like Jupyter. I may have had a bad experience with Maple as a student. That doesn’t mean you can’t experiment and enjoy, though!

Lastly, to file under “ridiculous but brilliant projects”, several generators of the Finite Group are challenging humankind to say the new record Mersenne Prime before the next one is discovered. Join the race!

Books!

Apparently some people celebrate Actual Christmas rather than (or as well as!) MathsJam. That’s OK, all are welcome. If you’re looking for maths-related books to buy someone so they can add them to the unread pile on the floor, here is a selection of books I’ve either read and enjoyed or have had recommended to me:

(Note: these links don’t necessarily go to the cheapest place to order from. I recommend asking your local independent bookshop — if you don’t have one of those, Gulliver’s in Wimborne deliver across the UK and are lovely people too.)

In the meantime, if you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.

That’s all for this week! If there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something I should be aware of.

Until next time,