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Double Maths First Thing: Issue 40

By Colin Beveridge. Posted November 26, 2025

DMFT reckons it must be downhill from here

Hello! My name is Colin and I am a mathematician on a mission to find and disseminate the joy in doing maths, solving puzzles and getting to the root of things in general.

I’m back from an excellent weekend at Big MathsJam, and now rather sad that I have to make my own breakfast and nobody’s saying “have you seen this cool thing?” Bah. (I’m still recovering. I’ll write up my highlights in the next issue).

Links

I had some small involvement with the maths trail at MathsWorld, despite having no background other than following town trails with the kids. I wish I’d known about this paper by Mary L Dalton and Jennifer Yantz, or this helpful gloss from Mykyta Kliapets.

Firmly in the “to read one day” pile is an article by Kenneth E Iverson (who created APL) about how notation shapes how you think.

A delightful thing: the Steinhaus longimeter, a grid on a transparency for measuring the length of a curve by counting how many times it crosses a grid line. Chris Staecker has a page describing a whole batch of “antique” calculating devices.

Also delightful, an interview with Andrew Wiles in Plus, from nearly a decade ago – with the quote “this is what we live for, these moments that create illumination and excitement”. Spot on!

My mental arithmetic is rustier than it was – it’s still good enough to make people swear at me when I get trig questions right in my head – but here’s a technique I didn’t know about for mental division by Daniel Timms.

Currently

Tomorrow, Thursday November 27th, there’s a Finite Group live stream about the maths of robots. I always enjoy catching up on these with young Bill.

We’re almost at the end of the month, which means a Carnival is imminent. Tom Briggs is in the hot-seat, and you can still send him things via the Carnival submission page.

That’s all I’ve got for this week. 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,

Not mentioned on The Aperiodical, March 2016

By Christian Lawson-Perfect. Posted March 30, 2016

There’s been a lot of maths news this month, but we’ve all been too busy to keep up with it. So, in case you missed anything, here’s a summary of the biggest stories this month. We’ve got two new facts about primes, the best way of packing spheres in lots of dimensions, and the ongoing debate about the place of maths in society, as well as the place of society in maths.

A surprisingly simple pattern in the primes

Kannan Soundararajan and Robert Lemke Oliver have noticed that the last digits of adjacent prime numbers aren’t uniformly distributed – if one prime ends in a 1, for example, the next prime number is less likely to end in a 1 than another odd digit. Top maths journos Evelyn Lamb and Erica Klarreich have both written very accessible pieces about this, in the Nature blog and Quanta magazine, respectively.

Oliver and Soundararajan’s paper on the discovery is titled “Unexpected biases in the distribution of consecutive primes”.

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.