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Double Maths First Thing: Issue B

By Colin Beveridge. Posted November 20, 2024

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.

Links

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,

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,

Double Maths First Thing: Issue 8

By Colin Beveridge. Posted October 30, 2024

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:

Miles Gould has pointed me at the Capstan Equation, not to be confused with Captain Caveman. Wrapping a line around a cylinder makes it possible to hold much heavier loads than one would naively expect.
Devine Lu Linvega has a zine about rewriting rules, which appeals to me.
The train wifi is unable to allow me to watch Sophie Maclean talk about voting paradoxes on Numberphile, much as I would love to.
The Finite Group’s birthday livestream included Peter Rowlett talking about Carnelli, a game which involves running film titles together — the canonical example is The Empire Strikes Back To The Future. I’m enjoying subverting it (Run Lola Run Lola Run, or On the Waterfronthe Waterfront, or somehow making Zero Dark Thirty and 300 into a loop). What interesting things can you do with it?
There is a lot of discussion currently about the number of holes in a straw (which is obviously and unambiguously one). If you join the ends together to make a loop, how many holes are there now? If you sew up the top of a sock, how many holes does that contain?

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.

Until next time,

Double Maths First Thing: Issue 7

By Colin Beveridge. Posted October 23, 2024

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.

More from me

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?

New Largest Known Prime!(?)

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:

Ayliean
Matt

A load of balls

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.

Other nice things!

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.

Until next time,

Double Maths First Thing: Issue 6

By Colin Beveridge. Posted October 16, 2024

Double Maths First Thing is to maths news what the noticeboard outside the coffee shop is to theorems

Hello! My name is Colin and I am a mathematician on a mission to spread delight and joy while making people think.

More from me!

I almost forgot (so strongly do I dislike the academic publishing process) that I had a paper published recently about Heron’s formula. One of the reasons I dislike it is that T&F want to charge you £45 of those sterling pounds to read a four-page paper, which is patently ridiculous. I can send you a copy if you want one. You definitely shouldn’t paste the DOI reference, 10.1080/0025570X.2024.2376510, into SciHub, or else the whole publishing system might collapse! (In fact, you can read the proof and the story behind it here).

I’ve also done my stint volunteering for Dorset Coding Day at a couple of local schools. The best questions I was asked were “how many pages were in your books?” and “what’s your favourite Netflix movie?”. Not a single more-of-a-comment, ten-year-olds are brilliant.

And in an email that made me grin from ear, a Tudor living historian emailed me to say he’d read my piece about Henslowe’s trick and is now performing it at events. How amazing is that?

Links from everywhere!

Sometimes, people use the word “intuitive” for something that doesn’t line up with my intuition at all — but that’s ok, it’s good to see how other people’s minds work. For example, Gregory Gundersen’s piece on the Black-Scholes equation doesn’t match with how I’d explain it, but it’s still a lovely piece!

I haven’t yet got around to reading this article on the Kelly Criterion, but it’s a topic that always makes me prick up my ears. From my recollection, it turns out that “maximising expected returns” means roughly “small chance of an enormous jackpot, otherwise ruin”, but it’s a fascinating thing to play with.

Another item on my to-read list is this guide to transforming colours with matrices. This feels all sorts of wrong, but at first glance, it seems to work nicely!

Lastly, from memory lane, one of my favourite pieces of mathematical writing: Tim Gowers on deducing the cubic formula. A Fields Medallist explaining how to think about something? Clearly and lucidly? Sign me right up.

I’m also midway through Grant Sanderson explaining Manim to Ben Sparks and now I want to make videos just so I have an excuse to play with it.

Community!

In a move closely aligned with my key themes, the Finite Group have opened up their Discord to free-tier members. Among other things, it’s a great source of memes and somewhere you can suffer an endless stream of bad jokes, not all of which are from me. (The amazing live-streams — the next of which is on Wednesday 23rd October at 2pm UK time — are paid content, and worth every penny.)

Gathering4Gardner, best-known for their biennial gatherings that inspired Big MathsJam, but who do all sorts of amazing work, have a fundraising auction starting next week. I refuse to look at it because I have to dispose my income on fixing my laptop, but there might be something there that tickles your fancy!

Speaking of Big MathsJam, Tuesday coming is Little MathsJam Day — find your local Jam here or, failing that, start your own! It’s simple enough that I can do it. Instructions are on that page.

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.

Until next time,

Double Maths First Thing: Issue 1

By Colin Beveridge. Posted September 11, 2024

Double Maths First Thing is Colin’s weekly news summary. Or autumnal, if you’re reading this after the equinox. You can sign up to receive it in your inbox on a Wednesday morning here.

Hello! My name is Colin and I am a mathematician. It’s Wednesday morning, and it’s Double Maths First Thing.

Shape-ology

Over on the Talking Maths In Public WhatsApp group, we’ve been looking at collapsible polyhedra, which Barney Maunder-Taylor calls Flatonic Solids. He’s not the only one, though: here’s a satisfying Instagram reel and an article by Liz Meenan in case you want to make your own.

It also reminded me that you can do cool things with pop-ups, whether or not you have the book.

Speaking of books

Tom Briggs has been compiling suggestions of maths books that aren’t about teaching. I’m given to believe he might be making his own addition to the list in due course.

Peter Rowlett and his son have been reading Gulliver’s Travels, and found an interesting early description of something computery. A biased generator of randomness that produces plausible English? I bet the venture capitalists would be all over that.

Sudoku

I recently had cause to revisit the Miracle Sudoku video — memorably described at the time by Ben Orlin:

You’re about to spend the next 25 minutes watching a guy solve a sudoku.
Not only that, but it’s going to be the highlight of your day.

The highlight of my day recently was coming across Phistomephel’s ring, which is a neat consequence of standard sudoku rules.

Tony Mann pointed me at another Cracking the Cryptic video with the same energy — the frustrations and feelings of stupidity that come with not having the answer yet, followed by the sheer joy of having worked out something clever.

Another (and significantly shorter) video plausibly worth your time is Alyssa Williams and Christian Scott at G4G discussing how to set variant sudoku.

Joy in maths

Back to taking pleasure in maths, here’s a short interview with Talithia Williams, PhD: I loved the bit about maths appreciation, and trying to change the mindset that maths is about doing calculations to pass a test.

Another article that caught my eye this week was about climbing. Or rather, spotting an error on the climbing wall and getting it fixed. It’s interesting for several reasons, but what grabbed my attention was what I think of as x-ray vision: the power to see that something looks off, and the insistence that it be put right. That strikes me as a very mathematical thing. (And, speaking for myself, possibly an autistic thing. Drives me MAD when people don’t care about breaking the rules, I tell you.)

For your listening pleasure

This week, I have mostly been listening to:

Tim Harford’s Cautionary Tales
Bec Hill and Matt Parker’s A Problem Squared
Evelyn J Lamb and Kevin Knudson’s My Favorite Theorem
Katie Steckles and Peter Rowlett’s Mathematical Objects — I understand that series 8 is imminent.

I’ve not yet picked up the TMiP podcast, but we all should. And Sam Hansen would give me endless, deserved grief if I didn’t mention Relatively Prime.

The week ahead

Thanks to September ending on a Monday, the monthly MathsJam meet-up is coming around distressingly quickly — those that meet on the traditional penultimate Tuesday will do so on September 17th. You can find your local MathsJam here — I’ll be at the Weymouth one.

Also, if you’re planning to go to Big MathsJam in November, early-bird pricing ends on Sunday.

There’s a Finite Group livestream on Friday, September 13th at 9pm BST — Katie and Ayliean are putting the ‘fun’ into ‘fundamental theorems’, it says here.

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.

Until next time,

Double Maths First Thing: Issue 0

By Colin Beveridge. Posted September 4, 2024

Double Maths First Thing is Colin’s weekly news round-up. Or round-down, if the fractional part is smaller than a half. You can sign up to receive it in your inbox on a Wednesday morning here.

Hello! My name is Colin and I am a mathematician. Welcome to issue 0 of Double Maths First Thing, in which I highlight some of the mathematical things that have caught my eye this week.

Let’s talk about \( \pi \) and powers

First up, a nod to physicists Arnab Priya Saha and Aninda Sinha for doing something with no real application: they “accidentally discovered a new formula for pi”. There’s a bit about it in Scientific American, a Numberphile video, and a paper in Physical Review Letters (open access). I’ve not worked through it in detail, but it’s got a Pochhammer symbol in it, so it must be good.

I promise this isn’t always going to be about pi, but I also stumbled on a proof that pi is irrational — again, I’ve not worked through the details, but it looks like it would be accessible to a good A-level class with a bit of hand-holding.

Via reddit, a surprisingly tricky problem with a lovely twist in the tail: show that \( 3^k + 5^k = n^3 \) has no solutions for \( k > 1 \). (There’s a hint and a spoiler over on mathstodon.)

Somewhere to visit: W5, Belfast

I’ve recently been on holiday in Northern Ireland. We visited W5 in Belfast, which is a pretty cool science museum — lots of hands-on stuff, including a build-your-own Scalextric-style car, bottle rockets and a green-screen bit where you can present the news about the alien invasion. On the minus side… there are lots of missed opportunities for highlighting the maths that underpins it all. Still, it’s a fun half-day if you’re all Titanic-ed out.

Maths in the news

In the proper news, the Guardian had a long read about Field’s Medallist Alexander Grothendieck; although it too is a bit maths-light, it’s understandable given quite how heavy Grothendieck’s maths is. Katie Steckles also pointed me at the devastating news that UK railcard discounts are dropping from 34% to 33.4%, which strikes me as the sort of thing that probably costs more to implement than it could possibly save the train operators.

Upcoming maths

If you’re in the market for more maths, I can heartily recommend both the Finite Group, whose next livestream is on Friday September 13th, and Big MathsJam, which is a gathering of amazing geeks the first weekend of November. Early-bird tickets are (just about) still available; I have mine already. There’s also a day of recreational maths lectures in memory of David Singmaster on Saturday September 21st in London or online, and a New Scientist event about how maths explains the world the following Saturday, also in London.

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.

Until next time,