Goodbye 2025...

We are, I am reliably informed, near to that arbitrary point in our planet's orbit at which much of humanity habitually mark the end of one and the beginning of another. I'm usually neither sentimental nor self-obsessed enough to write something to mark the occasion with a blog post, but looking back on the last eleven months and thirty days I'm struggling more than usual to convince myself that nothing much has happened. Aside from being one internal organ down on the complement I started 2025 with fifty-two-and-seven-fiftieths weeks ago^[1], a handful of things happened that I consider (in an entirely self-indulgent sense) to be noteworthy.

Seeing my own book for sale in the British Library's bookshop was pretty cool.

I might even get away with describing some of them as:

Carnival of Mathematics #246

Hello and welcome to December 2025's Carnival of Mathematics!

We've reached Carnival number $246 = 2 \times 3 \times 41$, and that's special for a variety of reasons, not least of which is that its digits are, in order, the first three terms in one of the first sequences most of us were introduced to; the chicken soup of all integer progressions that is the two times table.

$246$ is also the current best-known upper-bound for the minimum size of gap that exists between an infinite number of pairs of consecutive primes. It's palindromic in (e.g.) bases 5, 9, and 40; it is untouchable (which means that it is not expressible as the sum of the proper factors of any other number); and if you had a bit of string and seven of each of two colours of bead, you could make one of  $246$ different necklaces (using every bead).

And in maths history, Indiana House Bill No. $246$ was an 1897 foray into proof by legislation: it proposed to square the circle using a method that, among other things, implied that $ \pi =3.2 $.

You've taken your seats and loaded up on popcorn, so let's get started on the Carnival's...

Maths in Museums: The Geometry of Castle Keeps (and Why Shapes are Important to Architecture)

Castle keeps come in many shapes - circles, squares, rectangles, and other polygons - and these choices were not accidental. In this post, I explore the geometry of castle keeps, how mathematical considerations influenced medieval military architecture, and what you can still see today when visiting historic sites and museums.

I'm no square

I recently took time out for a quick weekend away in South Wales. The itinerary involved, as is only right, castles^[1]. I was struck by the geometric shapes of the keeps - particularly one with a circular cross-section at Tretower castle, and a larger one with a hexagonal base that forms part of Raglan castle.

The Circular Keep at Tretower © 2025 by T. Briggs is licensed under CC BY-NC-SA 4.0

Maths in Museums: Roaring Meg at Goodrich Castle

In this post I explore how a Civil War mortar at Goodrich Castle illustrates mathematical ideas about angles and projectile motion - part of a broader “Maths in Museums” series.

Introduction: Roaring Meg at Goodrich Castle

A found some maths at Goodrich Castle: a ten-minute drive from the Welsh border in Herefordshire, England, it has to be one of my favourites^[1]. It's a Norman medieval ruin (now looked after by English Heritage) that played host to an English Civil War siege by Parliamentary forces upon the Royalist forces stationed there. Despite not having its defences updated to 17th-century standards the medieval castle stood up well to direct attacks and artillery was introduced, with Parliamentary Army Colonel John Birch commissioning the casting of a Civil War mortar called Roaring Meg.

Roaring Meg at Goodrich Castle © 2025 by Thomas K. Briggs is licensed under CC BY-NC-SA 4.0

Maths in Museums: Bolsover Castle

For years I have been periodically prompted to think "ah yes, must go there one day" by signs for Bolsover Castle as I pass through the vicinity of Junction 29A on the M1. That day, as all things must surely do, finally came to pass on Monday 11th August, 2025^[1].

Bolsover Castle © 2025 by Tom Briggs is licensed under CC BY-NC-SA 4.0

As with all posts in the Maths in Museums series, it is not for me to tell you how or when to visit, how much it costs, or even much about the history of the site (though some will surely creep in). All of that can be left to English Heritage, who are its current custodians. Our purpose here is to uncover some of the opportunities for mathematical exploration that I spotted during my visit^[2]. As with most museums and galleries, there's no interpretation at the site that will help you to structure any exploration of these ideas.

Book Review: Love Triangle by Matt Parker

Full disclosure: I received a free copy of the book on the promise that I would write this review, but you have my word that what follows is my honest appraisal! I need to take this opportunity to apologise profusely to Matt^[1]. Love Triangle is Matt Parker’s playful and deeply mathematical exploration of why triangles - and trigonometry, geometry, and other mathematical themes - matter in the real world.

Love Triangle, The Life Changing Magic of Trigonometry^[2] is Matt Parker's n^th offering to the pop-sci shelves in your bookshop of choice, where n is a number that's a little bigger every time I look it up. He's one of the more well-known current writers of books destined for that section that have an explicit focus on maths, mathematical applications, and real-world examples of maths; and his trademark informal style of unashamed explicit nerdity carried along by a current of comic sarcasm might not be for everyone, but it does seem to do the job for more people than it doesn't.

My copy of the book starts with a note...

Maths Trails at Cultural and Heritage Sites

Many museums, galleries, and other heritage sector sites offer trails for visitors (including booked school groups and members of the public). Trails are a great way to help visitors of all stripes to structure a visit in an engaging way, and can be used to provide additional - or different - context, and to draw attention to particular themes.

One possible use of a trail activity is to encourage the use of mathematical skills to analyse whatever the trail guides them towards, or to highlight the role of mathematics in the objects and stories encountered where the exhibitions themselves may not have been designed with this in mind.

Prompted by a post in a TMiP chat group and a similar conversation on a GEM discussion list I thought I'd collate some of the examples and supporting resources in one place: I know that users of museums and galleries often seek out maths-related activities and events; and an increasing number of sector organisations are looking to develop their own, so I hope that this compilation might be useful for people in either camp.

Maths trails in action

These are maths trails out in the real world that I'm currently aware of, listed in alphabetical order of the organisation that offers them:

Edinburgh: The University of Edinburgh's Maths Outreach team created this digital interactive Discover Edinburgh's Mathematical History trail: browse from the comfort of your own home, or fire up your phone (assuming you've got a good data plan) and march across the streets of Edinburgh. (Google Maps link)

Museum on the Mound (Edinburgh): I'm told that The Money Maths at the Museum trail is popular with school groups, and that they occasionally bring it out for public use, e.g. during Maths Week Scotland. If you'd like them to offer a maths trail for general visitors, it wouldn't hurt to let them know. (Google Maps link)

National Museum of Scotland (Edinburgh): The A World of Maths Trail is downloadable as a .pdf. It's targeted at teachers to use to print for their students and bring to enrich a school trip to the site, but there's absolutely nothing to stop anyone else using it, and the teachers notes available from that page are useful outside that demographic too. (Google Maps link)

The Science Museum (London): Their Maths Activity Trail is a downloadable .pdf that aims to support visitors as they work their way through the Winton Mathematics Gallery and Science City 1550 – 1800: The Linbury Gallery. It's aimed at teachers, but as its offered as a free public download there's nothing to stop anyone making the most of it. (Google Maps Link)

Scotland (various locations plus location-independent resources): Each year an increasing number of museums and galleries offer mathematical activities including trails for Maths Week Scotland, which usually takes place towards the end of September. The Maths Week Scotland website lists activity packs and learning resources for schools (freely and openly accessible regardless of whether you represent a school or not); a community learning resource; family activities to do at home; and events offered by a host of museums, galleries, and other organisations across Scotland. Many of the events listed are exclusively offered during Maths Week Scotland, so do make sure you get in touch with your local sites and let them know that you'd like the option to experience maths in museums during the other 51 weeks of the year too!

York Minster: Their Maths Quest trail is available either as a .pdf downloaded from their website, or their Learning Resources page (which lists this along with trails on other themes) says that you can 'collect them at the Welcome Desk when you arrive.' (Google Maps link)

Your local museum or gallery: If your favourite local site isn't listed here and you'd like it to be, then get in touch with them and let them know that you want their help to explore the maths in their stories, objects and exhibitions. When I ask people who work for a museum or gallery why they don't offer resources to help visitors engage with the mathematics that's just out of site, they usually tell me it's because nobody asks them to...

So ask them to!

• Does your organisation offer a maths trail that you think should be featured here? 
• Is anything listed here out of date (e.g. a link is broken or a site no longer offers a listed trail)?

If so, post a comment or get in touch.

Resources for people interested in creating their own maths trails

University of Bath Cryptography Challenge case study (from Maths Engagement Case Studies): https://katiesteckles.co.uk/casestudies/CS_Bath-Crypto-Competition.html

Math in the City: Designing a Math Trail for High School Students (chapter 4 of Handbook of Mathematical Science Communication): https://ionicasmeets.com/Publicaties/1887_3567511-2023-Bossema-Zwetsloot-Smeets_Book_chapter_Math_trail.pdf

• Do you know about an excellent resource aimed at helping people to create maths trails that isn't listed here?
• Are any of these resources no longer available (e.g. a link is broken)?

If so, post a comment or get in touch.