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Double Maths First Thing: Issue F

By Colin Beveridge. Posted December 18, 2024

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!

In a rare concession to Christmas, here is a video about making cut-and-paste Christmas trees — there are PDFs linked, but the author asks that they not be distributed directly.

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.

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.

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.

Until next time,

C

Aperiodical News Roundup – October 2022

By Katie Steckles. Posted November 4, 2022

Research

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.

It’s not all over for us humans just yet, though: the DeepMind announcement prompted two algebraists at Linz University, Jakob Moosbauer and Manuel Kauers, to see if they could do even better. After a few days of thought, they published The FBHHRBNRSSSHK-Algorithm for Multiplication in $\mathbb{Z}_2^{5\times5}$ is still not the end of the story on the arXiv, giving an algorithm which does the multiplication in only 95 steps.

Meanwhile, in other computers-helping-humans news, the Lean 3 library mathlib has made it to 100,000 theorems, none of which have been left as an exercise for the reader.

Events

The IMA and LMS have joined forces to offer a new university access programme called Levelling Up: Maths, which aims to address the difficulties that young people of Black heritage face in STEM. A-level students can join the programme, and will be able to access teaching and mentoring in virtual tutorial groups with Black heritage undergraduates, as well as events with Black guest speakers. The programme is also supported by the RAEng, BCS, IOP RSC, MEI and STEM Learning, as well as the Association for Black & Minority Ethnic Engineers (AFBE-UK) and Black British Professionals in STEM (BBSTEM).

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)

What does DALL·E ‘think’ mathematics and a mathematician looks like?

By Tom Briggs. Posted August 10, 2022

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.

What does craiyon/DALL·E mini ‘think’ mathematics and mathematicians look like?

By Peter Rowlett. Posted June 20, 2022

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.

Model for processing language in context

By Peter Rowlett. Posted June 6, 2012

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”.

Loebner tires of Loebner Prize, discusses future of thinking machines

By Peter Rowlett. Posted June 3, 2012

TechRepublic have published an interview with Hugh Loebner, originator of the Loebner Prize competition, in which he discusses the prize and the future of thinking machines.

Math/Maths 87: Faulty Cables, Ridiculous Buses & Intergalactic Steroids

By Peter Rowlett. Posted February 27, 2012

A new episode of the Math/Maths Podcast has been released.

A conversation about mathematics between the UK and USA from Pulse-Project.org. This week Samuel and Peter spoke about: Samuel’s ridiculous bus trip; Computer programmes with IQ 150; IBM’s Watson and data analytics; Extracting Dynamical Equations from Experimental Data is NP-Hard; OPERA faster-than-light neutrinos experiment UPDATE 23 February 2012; ‘Invisibility’ cloak could protect buildings from earthquakes; How Bots Seized Control of Carlos Bueno’s Pricing Strategy; Calculus: The Musical!; Who says ‘maths curriculum failing to meet the needs of the 21st century’?; Turing Stamp; & more, and Peter spoke to some of the team behind Maths in the City on the occasion of their inaugural London walking tour. Oh, and Samuel forgot to mention Science Sparring Society’s second fight, but the link is in the show notes anyway.

Get this episode: Math/Maths 87: Faulty Cables, Ridiculous Buses & Intergalactic Steroids