If you’ve got a mathematical friend you need to buy a Christmas gift for but have left it too late, here’s some suggestions for what you could get them, drawn from things our friends are doing (that don’t need you to wait for something to arrive in the post).
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.
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
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.
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 is what the internet used to be like before billionaires bought it.
Hello! My name is Colin and I am a mathematician on a mission to share joy and delight in maths.
I’m writing this in a rush, so it’s just a list of links this week. Soz like. I’m rushed because I’ve just got back from my local MathsJam, where we had an unprecedented 11 people. Decimal, although we often struggle to reach that in binary. We had to use several tables and there were arguments over the scissors.
There’s a bit in Surely You’re Joking, Mr Feynman where he talks about a technique for differentiating under the integral sign. For all that Feynman is a… problematic character, there’s some neat maths there — and Leo Goldmakher has a lovely paper explaining it
Talking of lovely things, a redditor pointed out that you can approximate the Gaussian integral by \( \sin(\sin(x))\) for quite a decent range of \(x\) values.
Also via reddit, I’ve been introduced to sinh-tanh quadrature, a numerical integration technique with really nice properties (endpoints can be ridiculous! you can reuse your previous work if you find you need a better approximation! it’s just neat!)
From the glorious to the horrifying: here’s Matt Parker explaining a regex that finds primes. Now I have infinitely many problems.
And somewhere in between is an article from 1985 about the elegant maths of the double-entry book-keeping method.
Lastly, there’s a Finite Group livestream on Friday lunchtime about combinatoric games — you’ll need to be a paid member if you want to watch it, but being part of the community is easily worth the price of a fancy coffee a month.
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
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.
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!
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,
C
Double Maths First Thing is Colin’s refuge from the kids’ obsession with Odd Squad.
Hello, and welcome to Double Maths First Thing! My name is Colin and I am a mathematician on a mission to spread joy and delight in my subject.
It’s half-term week, so this is necessarily rushed, brief, and poorly formatted — but it’s Big MathsJam at the weekend, so I expect to more than make up for the brevity next week.
On my list of things to contemplate on the long journey northwards:
If you’re going to be at Big MathsJam, I hope I’ll see you there! I’ll be talking about HyperRogue, but you risk accidental spoilers if you click through.
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,
C
Double Maths First Thing is part of Colin’s fight against the forces of tedium.
Hello, and welcome to Double Maths First Thing! My name is Colin and I am a mathematician, on a mission to spread joy and delight in maths.
I promise not to make this whole thing about me, but if I’ve got a blog post about something I find delightful, it would be rude not to share it. Here’s a link that took me a long time to make about the relationship between the binomial expansion and the binomial distribution. The clue’s in the name, right?
I am decidedly ambivalent about finding larger and larger Mersenne primes. I feel like some of those involved in the hunt are in it for the money, the mersennaries. Even if it’s been six years since the last one, the announcement that there’s a new one is not one that thrills me. I think throwing more compute at the same problem is of limited use. However, it has reminded me about the Lucas-Lehmer test, which is a very nice piece of maths that happens to coincide with the structure of computers, making it efficient (although still lengthy) to calculate.
Some people who are less cynical than me:
Somewhere deep in the list of tabs that seemed like a good idea to open, I found instructions for making a giant windball. It uses some sort of construction kit called makedo, but I’d be surprised if you couldn’t find some butterfly pins and spare cardboard.
I was surprised by a result, which is always a nice feeling: if you’re thinking about balls (settle down back there), you’d expect to see \( \pi \) show up. Finding \( e \) was not on my bingo card.
I was also surprised to find that the word dodecicosacron in FractalKitty’s Mathober challenge was not a typo, but the sort of spiky shape you would avoid in a video game.
Stretching the theme still further, I hadn’t heard of Pappus’s centroid theorem(s), which you could use to work out the volume of a sphere (see! There is a link!) — they’re reasonably obvious once you think about them a little, but it’s still a nice way to approach surfaces and volumes of revolution.
From Reddit, probably to be filed under “absurd but also very impressive”: a computer cuber broke a world record. Not just any world record, but the record for a 121-by-121-by-121 cube. By 69 hours. My understanding is that a 121-cube is just like a 5-cube, only more so — but still, the concentration and dedication you’d need to do that… chapeau! Oh, and they say this is the fifth-largest cube ever solved by a human.
Over on the platform-still-referred-to-as-Twitter-by-everyone-sensible, David K Butler has an interesting way to look at addition and multiplication using parallel and intersecting lines (respectively). I’m always up for a new thing to add to my mental models!
In podcast news, I am given to believe that Sam Hansen is at it again. I’m not sure they ever stopped, honestly; Sam and Sadie Witkowski now co-host Carry The Two, recently with a theme of elections and representation. It’s almost enough to get me to the gym so I can listen to it in peace. Almost.
And — if you’re quick about it — you might be able to subscribe to the Finite Group in time for their first anniversary livestream.
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 right here 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,
C