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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

Open Season – The Perfect Cuboid

By Katie Steckles. Posted March 4, 2013

In this short series of articles, I’m writing about mathematical questions we don’t know the answer to – which haven’t yet been proven or disproven. This is the second article in the series, and considers a less well-known variant on an extremely well-known problem.

Ask anyone to name a theorem, and they’ll probably come up with one of the really famous ones, like Pythagoras’ theorem. This super-handy hypotenuse fact states that for a triangle with sides A, B and C, where the angle between A and B is a right angle, we have $C^2 = A^2 + B^2$. This leads us on to a nice bit of stamp-collecting – there are infinitely many triples of integers, A, B and C, which fit this equation, called Pythagorean Triples.

One well-known generalisation of this is to change the value $2$ to larger values, and go looking for triples satisfying $C^n = A^n + B^n$. But don’t – Andrew Wiles spent a good chunk of his life on proving that you can’t, for any value of $n>2$, find any such triples. The statement was originally made by Pierre De Fermat, and while Fermat famously didn’t write down a proof, it was the last of his mathematical statements to be gifted one – hence the name ‘Fermat’s Last Theorem’ – and proving it took over 350 years.