Welcome to the 241st Carnival of Mathematics, hosted here at the home of the Carnival, The Aperiodical. The Aperiodical is a shared blog written and curated by Katie Steckles (me), Christian Lawson-Perfect and Peter Rowlett, where we share interesting maths news and content, aimed at people who already know they like maths and would like to know more. The Carnival of Maths is administered by the Aperiodical, and if you’d like to host one on your own blog or see previous editions, you can visit the Carnival of Maths page.
Here’s a round-up of some news stories from the last two months of 2024, (mostly) not otherwise covered here on the Aperiodical.
Maths Research
At the start of December, John Carlos Baez shared on Mathstodon that the moving sofa problem may have been solved – the question of the largest possible shape you can fit around a 2D corner. For many years, a shape called Gerver’s sofa has been thought to be optimal, but an ArXiV paper from 29th November claims to have proved it is. More context in this blog post by Dan Romnik.
And depending on what you consider to be good news, Terry Tao has also announced the creation of Renaissance Philanthropy and XTX Markets’ AI for Math fund, supporting projects that apply AI and machine learning to mathematics, with a focus on automated theorem proving. The deadline for initial expressions of interest is Jan 10, 2025.
The other big news from last December was Hannah Fry’s appointment as Cambridge’s new Professor of the Public Understanding of Mathematics. She joined the Department of Applied Mathematics and Theoretical Physics (DAMTP) on 1st January, and the role will involve communicating to diverse audiences, including with people not previously interested in maths. Fry follows in the footsteps of the late John Barrow, who informally took on the same role for much of his distinguished career.
“Communication is not an optional extra: if you are creating something that is used by, or interacts with members of the public or the world in general, then I think it’s genuinely your moral duty to engage the people affected by it. I’d love to build and grow a community around excellence in mathematical communication at Cambridge – so that we’re really researching the best possible methods to communicate with people.”
– Hannah Fry
Other news
From now until 11th February, Young Researcher applications for the Heidelberg Laureate Forum 2025 are open to any undergraduate/pre-master, PhD or PostDoc researchers who would like to join the highest level of mathematical laureates alongside hundreds of other researchers in maths and computer science for a week of talks, workshops and networking in the beautiful city of Heidelberg in September.
Double Maths First Thing is the biscotti to your Wednesday morning coffee
Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in maths.
This week’s links
I have a difficult relationship with AI. I wrote about it here. tl;dr: it doesn’t fill me with joy and delight, although it can sometimes be useful. However, an interesting use case is in the ongoing and enormous project to formalise mathematics — using machine verification to find mistakes and gaps in proofs (or to say “yep, that’s legit!” when things do work). Via Harlan Carlens, here’s a piece about the use of AI in tackling the IMO. Something that strikes me as slightly more useful is formalising the proof of Fermat’s Last Theorem. Possibly, but not closely, related: an article about playing chess with God; I’m mainly disappointed about the lack of a “… moves in mysterious ways” joke.
In MathsJam-adjacent news, my esteemed friend Barney Maunder-Taylor took the puzzle “what is the smallest number n such that the digit sums of both n and n+1 are multiples of 7?” and turned it into an OEIS entry. I’ve done some proving around it, but have a play yourself. It’s nice!
Lastly, there’s a live-stream about regexes for paid-up Finite Group members on Friday 20th, 8pm UK time. The Discord group is a lovely space (and I believe you can hang out there on the free tier). For me, it’s a Patreon worth supporting.
That’s all I’ve got this week! 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.
Meanwhile, 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 you want to tell me.
AI research company DeepMind said that their AlphaTensor system has discovered a new way to multiply matrices, citing this as the first such advance since the Strassen algorithm was proposed in 1969. AlphaTensor found thousands of algorithms for multiplying matrices of different sizes, but most were not better than the state of the art. Specifically, it found an algorithm for multiplying \(5 \times 5\) matrices in \(\mathbb{Z}_2\) in just 96 operations. There’s a paper in Nature describing how the algorithm was found.
What Can Mathematicians Do?is a series of free online public maths presentations organised by Newcastle University’s School of Mathematics, Statistics and Physics, covering a wide range of topics such as how colours mix, how to make a mint on the stock market, and how to pick your next Netflix binge. Aimed at students in school years 10 to 13, the talks are all given by disabled presenters: to show that anyone can be a mathematician, and mathematicians can do anything.
And finally: last weekend, a group of maths communicators (including several Aperiodical editors and regulars) put together a live online 24-hour Mathematical Game Show, featuring mathematical games, games with a mathematical twist, the maths of games and games about maths. The show has raised nearly £5000 for a collection of excellent charities, and the whole show is available to watch back in half-hour or 1-hour segments.
And finally
Nick Berry of the Data Genetics blog has died. The site ran for over a decade, and was described by Alex Bellos as ‘one of best examples of maths outreach on the web […] A brilliant cabinet of curiosities’. Nick passed away peacefully at home on Saturday October 8th after a long battle with cancer. (via Alex Bellos on Twitter)
Phil Goldstein, aka magician Max Maven, has died. Max Maven popularised the Gilbreath principle, which underlies a host of astonishing mathematical card tricks. (via Colm Mulcahy on Twitter)
DALL·E is an Artificial Intelligence (AI) system that has been designed to generate new images given a text prompt. It’s very much like doing a Google image search with one very important difference: DALL·E doesn’t try to find existing images to match your query, but creates a handful of new ones that it hopes will fit the bill.
You may have seen DALL·E mini posts appearing on social media for a little while now – it’s been viral for a couple of weeks, according to Know Your Meme. It’s an artificial intelligence model for producing images, operating as an open-source project mimicking the DALL·E system from company OpenAI but trained on a smaller dataset. Actually, since I had a play with this yesterday it’s renamed itself at the request of OpenAI and is now called craiyon. Since the requests all take between 1-3 mins to generate, I’m not going to re-generate all the images in this post using craiyon so that’s why they have the old ‘DALL·E mini’ branding.
AI image generation is a massively impressive technical achievement, of course. craiyon doesn’t create as stunning images as DALL·E 2, but still it can create some ‘wow’s.
What’s interesting, sometimes, is how it interprets a prompt. The data craiyon is trained on is “unfiltered data from the Internet, limited to pictures with English descriptions” according to the project’s statement on bias, and this can lead to problems including that the images may “reinforce or exacerbate societal biases”.
To see that in action, we can take a look at how the model manifests cultural expression around mathematics. When I gave it the simple prompt ‘mathematics’, it produced this.
New research looks at how language is used to convey information in context, something which is, according to its abstract “one of the most astonishing features of human language”. Apparently there have been “many” theories providing “informal accounts of communicative inference” but few have succeeded in making “precise, quantitative predictions about pragmatic reasoning”.
