The obvious starting point for any mathematical gift quest is our friends over at Maths Gear, who have their usual excellent selection of gifts, toys, games and household goods. Personal favourites include the squared square coasters (inspired by a set James Grime originally got made up as a gift for my wedding), James’ lovely Drinkulator mug, and these fab mug/donut earrings (which I had a pair of but sadly lost one, not sure which).

On the subject of jewellery, if you’re in the US it’s worth checking out Hanusa Design, who have a great range of 3D printed jewellery (in coloured nylon, and gold/silver). They do ship worldwide but it’s a bit pricey (£35 shipping!), and some of the products take a few weeks to prep if they’re not in stock already – but there’s some gorgeous stuff on there, including these Forbidden Subgraph Earrings which I love.

Present Indicative, an excellently-named gift shop which sells ‘beautiful, practical and intelligent gifts for thinking people’ has an entire collection of mathematical gifts, including these lovely pudding bowls with mathematical proofs on, a few good popular maths books and some nice mugs and accessories. Particularly loving the ‘outlier’ badge.

I was recently reminded of the excellent Pseudorhombicuboctahedron tshirt, which was created as a mashup of a very time-specific meme and as far as I’m aware, partly to troll me (I love it so much), but is available along with a selection of other great maths items on the Aperiodical Teemill shop, and also the Aperiodical RedBubble shop which can also print onto homewares like mugs and cushions. There’s also a wealth of goodies on other print-on-demand sites like RedBubble, including the classic ‘I (red circle) topology’ tshirt.

Given it’s the new mathematical craze of the year, I’d be remiss not to include some ways to get more aperiodic monotiles in your life – check out these amazing earrings by Rob Simmons; Jamie Gallagher’s fantastic aperiodic pride pin (which launched at the TMiP conference this year, but his shop is currently under a deluge of orders thanks to a celebrity wearing one of his pins on TV, so there might be a delay in shipping); or some of the lovely aperiodic tile products available from the Etsy shop for Qwirkshop, laser cutter to the (maths YouTube) stars.

And finally, also on Etsy, there’s the lovely Mathysphere who produce mathematical and sciencey cross-stitch patterns, including this incredible maths sampler.

If you’ve seen any good mathematical gifts this year, add them to the comments!

]]>At this year’s MathsJam UK Gathering, I had the pleasure of running one of the Saturday Night Tables – a chance to invite attendees at the Gathering to drop by and play with something. Together with fellow Manchester MathsJam regular Andrew Taylor, I ran a table of **Mathematical Drawing Hacks** – ways to make drawing complex mathematical objects and shapes easier.

I thought it’d be nice to share some of the ‘hacks’ we brought, and those others contributed – so I’ve included photos of each below, in case any of them are useful to you. Enjoy!

Andrew’s contribution (which slightly inspired the whole idea for the table). We all agree it’s a little bit ‘draw the rest of the owl‘, but I think it’s lovely.

This was my contribution – one of my students showed me this and it’s changed my life (intersection with the times when I have to draw a set bracket).

Thanks, Ash!

Scroggs just walked up and drew a Cool S and then left. Legend.

Do you know of any cool drawing hacks you can share? Add them in the comments!

]]>A while ago we announced a competition to win a copy of algebraic blackjack game 21X, which was recently successful on Kickstarter, smashing its funding target by an order of magnitude. If you’d like to pre-order a copy of the game, you can sign up to be notified when that’s possible.

We had over 30 entries in the competition, of which 20 achieved correct answers, and have picked a random set of winners to pass on to Naylor Games, who should be in touch with them by email in the next few days.

For anyone interested in seeing the answers, here’s what they were. As a reminder, the challenge here is to find a value for \(x\), given that \(n\) represents the number of cards, to get the total of all the card values closest to 21.

Like many turns in the game of 21X, this one turns out to be not as difficult as it might initially look. Given that there are two cards and therefore \(n=2\), this resolved to simply \(2x – x = x\). So for this one, the correct answer is 21, which almost everyone got right!

The middle term here is just \(2^3 = 8\), so overall we have \(\frac{24}{x} + 8 – 2x\). Solving this for \(x\), it turns out \(x=-8\) will work here – possibly slowing down anyone who’d intuitively start with positive values for \(x\). Some entrants spotted that if you’re also prepared to take non-integer answers, you can use \(x=1.5\).

This one was slightly trickier – it’s not possible to make exactly 21 with these cards, but there are two solutions for non-integer values of \(x\), around \(x=0.4\) and one around \(x=10.1\). The closest you can get to 21 with integer values of \(x\) is when \(x=10\), giving a value of 20.8. Exploiting the other root, one entrant spotted that using \(x=0.39588\) will get you a value as close as \(20.9999\) – although I’m not sure you could work that out in your head!

]]>The main premise of 21X should be familiar to anyone who’s played a game of Blackjack: the aim is to have a set of cards in your hand which total 21. Sounds simple – but the cards aren’t regular playing cards. Each contains an algebraic expression, and players must assign a value to the variable(s) on the cards, and then evaluate the total, which is the value they’re trying to get to 21.

So, if you were holding a $3X$ card and a $4X$ card, you could decide that $X=3$ to give yourself the desired total of 21. The same value of X must apply across all your cards, but you can change it each time you add more cards to your hand.

Within the game, there are several difficulty levels depending on which cards you use – the simplest (triangle) has linear expressions which are mainly sums or multiples of X; the next level (square) also includes exponents, fractions and bracketed terms; and at the highest level (pentagon) there’s even more complex expressions. Each set includes some cards which, in addition to X, also use the variable N – which represents the number of cards you’re holding, so your decision to ‘twist’ and grab an extra card will change this value.

We played a few rounds at Manchester MathsJam (a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like, including fun games they’ve been sent a copy of).

One thing we noticed quite quickly (apart from the fact that the card backs are absolutely GORGEOUS – click the image here to enlarge) was that it isn’t nearly as difficult as you might imagine – facing down a set of cards like the one I faced (below) there were several ways to simplify it. In this case, I kept taking an extra card up to the maximum of 5, since the first four cards I had frustratingly wouldn’t let me make an odd number, and I was really determined to get 21.

But despite having a huge hand of cards, I could immediately see that the left three cards, which contain a 2X and a -2X, cancel out and will always be worth a total of 16; then I just needed to pick a value of X that worked with N=5 to make the rest of the cards add up to 5…

There are definitely some hands you can be dealt which make it easy to pick a value for X (especially if several of them cancel out!) but the competitive aspect means that if you’re the first one to realise this, you can make 21, or close to it, before anyone else, and the time pressure adds a bit of challenge.

We had fun playing this, and it’d also be a great way to develop arithmetic skills and understanding of algebra (or while away some hours in the pub!) We also enjoyed the care that’s obviously gone into it – rather than standard card suit symbols, there’s a lovely pattern in the design that reflects the card’s value, using the suits to cleverly represent positive and negative variables.

Naylor also sent along some 21X-based puzzles – example ‘hands’ that present the challenge of determining if there’s a value of X that’ll give you a total of 21. We set some of these up to play with, and I’ve included pics below (no spoilers in the comments).

In addition to the base set of cards, Naylor Games plan to add **extra cards** to the game through collaboration with mathematical stars – Professor Marcus du Sautoy has contributed an idea for a special bonus card to add to the game, which unsurprisingly involves prime numbers. They’ve also spoken to several other prominent maths communicators, and *cough* I’ve also thrown some ideas at them, so if the Kickstarter is successful, the final version of the game will potentially include several special celebrity rule cards, one of which is mine. I couldn’t possibly hint at what my card will be – you’ll have to grab a copy to find out. Here’s a quote from Marcus himself, if you were still on the fence:

Professor Marcus du Sautoy OBE

“A clever take on a classic game. As a lover of games and maths, 21X pushes all my buttons. I was excited to be able to contribute my own twist to the game by authoring one of the cards. A game to get the brain cells buzzing.”

As if all this weren’t exciting enough, Naylor have offered us a couple of copies of the game to give away – so we’re running a little competition using the **puzzles from the photos above**. In each case, work out the value of \(x\) that gets you a total of 21 (if an exact score of 21 is not possible, get as close as you can!) and fill them in below. Again, no spoilers in the comments, but if you complete this form, once the game is ready to ship we’ll pick a winner or two randomly from the correct entries and contact you about sending your game.

If you have small mathematicians in your life and enjoy #tmwyk (talking maths with your kids), or are yourself a mathematician of any size continuing to marvel at the mathematical nature of the universe, you might enjoy checking in each day to notice and wonder, or try a puzzle, or find some hidden maths in a thing. The first prompt, which was posted on 1st August, is below.

Here are the first three stages of a pattern made out of Lego.

What do you notice?

What do you wonder?

What questions might a mathematician ask?

Can you work out how many yellow bricks and how many red bricks you’d need to make the tenth pattern in the sequence?

Or the 100th pattern?

Or the nth pattern?

Some responses already shared on social media can be found in the replies to this tweet.

The prompts will be posted daily on Alison’s blog, and you can join in the conversation by finding the corresponding posts they’re putting out on their Mastodon and Twitter and adding your thoughts.

]]>*We spoke to friend of the site, award-winning maths communicator and past math-off competitor Kyle Evans about his Edinburgh Fringe show for 2023, which is about maths. *

**Who are you (as if we don’t already know)?**

I’m Kyle D Evans, I’m a teacher by day and entertainer/performer/presenter of all things mathematical by… well, also by day. But different days. I have children, so I really don’t do anything by night any more.

**Is it true you’re doing a maths show at the Edinburgh Fringe?**

It is true! It’s called ‘Maths at the Museum‘ because I really wanted the title to double as an elevator pitch. (‘Elevator pitch’ is one of those terms where the American version really works better, doesn’t it? ‘Lift pitch’ just sounds dreadful. That occurred to me while I was walking down the sidewalk with my aluminum fanny pack on). It’s an hour of comedy, poetry and stacks of audience participation, running at the National Museum of Scotland from 4-15 August. It’s a family show, aimed at kids aged 7+ and their parents. Tickets are available now!

**What’s the show about?**

I’ve been to the Fringe four times now, and I also tour accessible, interactive maths shows around the country throughout the rest of the year. So because I have such a special venue this year, I’ve put together a greatest hits set of all my favourite family maths bits I’ve devised over recent years. This includes the infamous ‘T-shirts of Hanoi’, a maths trick in two/three different languages (time dependent) and some paradoxical poems.

**How do audiences tend to react to a show about maths?**

For the most part, I find that having ‘maths’ in the title of my shows really makes sure people come in knowing what to expect! But the biggest excitement for me is winning round the parents and older brothers/sisters who have been brought along under duress and think that they hate maths or are too cool for it. I take great pleasure in winning these people round, and hopefully showing the most hardened maths-philes at least one cool new bit of maths too.

**Summarise, in one sentence, why people should come and see your show.**

It’s inclusive, it’s accessible, it entertains, educates and informs. And hopefully it’s funny too (sorry, two sentences.)

**Are there any other maths/science shows happening at the Fringe you’d recommend?**

I’m proud to say I’m the only show with ‘maths’ in the title, but there are several maths/science-adjacent shows I recommend. Foxdog Studios make robots do utterly absurd things and I can’t wait to see what their ‘Robo Bingo’ entails. Tom Crosbie is the most talented Rubik’s Cube wrangler you’ll ever see, and for the younger viewer there’s a charming climate change musical called ‘Chrissie and the Skiddle Witch‘ which I highly recommend.

*You can find details of Kyle’s show on the Edinburgh Fringe website. From a quick browse of the programme, some other potentially mathematical shows you could catch while you’re there include: Nick Mohammed presents The Very Best and Worst of Mr Swallow, which promises *‘*noise, maths, magic and the whole of Les Mis*‘*; there are also more generally sciencey shows like Stand Up Science and Comedy For The Curious; on a similar climate change theme, there’s Ted Hill Tries and Fails to Fix Climate Change; and for a bit of arty dance performance with a maths word in the title, At The Intersection might be worth a try.*

In *The Spirit of Mathematics: Algebra And All That*, David has pulled together a collection of what he refers to as ‘elegant mathematics using only simple materials’ – neat, short algebraic proofs and definitions, models of physical systems and mathematical tricks and curiosities.

He includes all the classics, from proof by induction to Fibonacci numbers to hitting a snooker ball, and each is presented with enthusiasm, alongside stories of mathematicians – and fearlessly including all the equations and derivations (if every equation really did halve your readership, as Stephen Hawking believed, this would be a very brave book to publish). But the maths is well-explained and very approachable, and it’s refreshing to see it featured so prominently outside of a textbook.

The book is also filled with helpful diagrams and illustrations, as well as humorous asides, cartoons and pictures of many mathematicians (sadly, only one female mathematician is featured, and she’s included only for her joke about how hard she’s found it to get a proof…) – but the book is well-produced and clearly laid out, with well-defined, short chapters each with a clearly defined topic.

The result is a compendium of intriguing ideas which would fascinate and compel a keen mathematician wanting to learn more, and provide hours of intrigue and jumping-off points for further investigation. Most topics are only covered briefly, so a deeper understanding would need research elsewhere, but for an enthusiastic reader this would happen naturally. Each discovery is motivated by a real-world example, or an interesting puzzle or curiosity, and all the key topics from algebra are touched on in one way or another.

However, this book wouldn’t suit an inexperienced mathematician – given which steps in the calculations are described as ‘simple’, a reasonable level of maths is assumed, and I’d imagine a strong GCSE or A-level student, particularly one already keen to learn more, would get much more out of it than a younger student. It’d also suit an adult wishing to refresh their mathematical knowledge from school and pick up some new ideas. But despite the blurb on the back claiming ‘for those who dread the subject, this book may be an eye-opener’, I suspect that such a reader might struggle in places.

Overall, this is a well-presented celebration of the best parts of mathematics, and showcases just how powerful maths can be.

]]>As part of the 24 Hour Maths Game Show which took place at the end of October 2022, our own Christian Lawson-Perfect designed a maths/games crossover gameshow format to end them all – a mashup of hexagon-fighting TV quiz Blockbusters, and his own personal obsession: interesting mathematical factoids. Welcome to Blockbusters of Interesting Maths!

The premise of Blockbusters of Interesting Maths is simple. Start by collecting three maths communicators – in this case, me (**Katie Steckles**), Sheffield Hallam Uni maths lecturer and recreational maths fan **Alex Corner**, and mathematician and juggler **Colin Wright**. Colin is a self-described “torturer of adults and confuser of children”, but to clarify, he mostly does that using interesting maths. Alex teaches on the SHU Game Theory and Recreational Maths module with our own Peter Rowlett, and was prepared to have a good go at coming up with some interesting facts. I, on the other hand, have come across far too many interesting maths facts in my time, and can definitely half-remember most of them.

Between us, we’re pitted against Christian’s board of randomly chosen words – from Ogden’s Basic English, a collection of 850 common English words, from which he’s deliberately removed a chunk of the mathematical and scientific terminology. To make our way across the board, we pick a letter and find the word hiding behind, and are then charged with coming up with some kind of interesting maths fact relating to that word.

Christian’s judgement on whether our maths fact was interesting enough is final, and we’ve got to make an unbroken line from one edge of the board to another. If we fail to come up with a sufficiently interesting fact, or our fact is deemed too tangential to the word in question, that tile is blocked off.

Since we could never do anything the easy/conventional way, instead of a tessellation of hexagons, CLP’s gone for the Cairo pentagonal tiling, so each cell is only adjacent to five others instead of six. His web gadget, a version of which can still be found online for anyone to use (BYO interesting mathematicians), was deployed live on the Game Show to challenge the three of us, and the below is a blow-by-blow of what went down, with links to some of the things we talked about.

We’ve also included some additional facts from Christian, who is also a font of interesting maths facts and is making up for the fact that he didn’t get to play himself. Next time!

My initial instinct was to pass over to Colin, as he’s got a whole bit about calculating the distance to the moon using a pendulum, but instead he gave some interesting facts: the distance to the moon is pretty much exactly about 10 earth circumferences (~40 megametres), and it creates tides on opposite sides of the earth at the same time.

**Christian**: I can’t remember if anyone talked about all the different ways of counting a lunar month… I like the word sidereal and have no idea how many syllables it has.

We failed to come up with sufficient interesting maths for this – a bit of discussion about publishing results before someone else who’s working on them was deemed to be too depressing.

Alex talked about the work of Alan Turing on abiogenesis – mathematical models that can be used to describe patterns found on animal fur, including leopard spots and zebra stripes. Christian confirmed this was to do with reaction-diffusion models.

**Christian**: Back in 2008, a Simon Scarle published a paper connecting Turing’s work on reaction-diffusion to his other work on computability, through simulations of cardiac arrhythmia on the Xbox 360. I’ve never known what to do with this information. If you want to play with reaction-diffusion models yourself, there’s a good simulator called Ready, which we wrote about it in 2012.

I waffled briefly about the history of counting and the Ishango bone, which is an interesting historical artefact linked to early mathematical activity, and which it turns out I’d got mixed up with the Lebombo bone, which is an even older one.

Colin took this as a verb, and talked about predator-prey dynamics, particularly related to pursuit predation, including ambush and persistence behaviour in hunting. For each type of hunting, the animal has to weigh the probability of a successful catch against the amount of energy expended on the chase.

After a brief digression about which direction the real line points in (since we’d missed the opportunity to connect the board top-to-bottom, which most of us hadn’t realised was a thing), Alex couldn’t think of anything to say, so we lost this one.

After mentioning the mathematical use of the word, I managed to just about describe a particular maths problem this reminded me of that involved chasing something that’s swimming in a river (Christian mentioned this was covered in Dara Ó Briain’s School of Hard Sums, and it turns out there’s a writeup on Marcus Du Sautoy’s blog), and we then went on to another puzzle about a cat in a pond, which Ben Sparks has done a great video about.

**Christian**: Talking of interception reminded me of this fun paper describing a strategy for avoiding being intercepted while mapping an unfriendly subway system.

Colin covered a couple of topics – starting with control theory, which Colin compared to riding a unicycle. The trick is to keep the wheel under you, by (e.g) pedalling faster if you’re falling forwards, which can be understood by solving fairly straightforward differential equations – as unicycling robots often do.

He also talked about controlling a dog’s behaviour, and how rewarding good behaviour every time means the effect of training wears off more quickly, whereas rewarding it randomly some of the time means the effect lasts longer – this is related to spaced repetition as a learning technique.

Back over to Alex, who took electrical inspiration and used it as a chance to talk about capacitor laws. There were lots of nice relationships between different physical laws and it all got a bit physics, and as a result was rejected by Christian, so we lost this one.

I took the opportunity to talk about mathematical crystal structures, bond angles and 3D lattices (and got in a Kathleen Ollerenshaw mention). Christian also connected it to the structures of viruses, and mentioned Hamish Todd’s lovely videos.

Colin riffed on ratios in mixtures, from concrete to cake recipes, and then moved on to mixed techniques. Combinatorics, for example, uses a variety of different techniques you have to try in different combinations in order to solve a problem, and Colin explained how maths research, particularly in applied contexts, a mixture of techniques can be most powerful. Von Neumann showed that mixed strategies are always more effective in game theory!

After a brief digression about profit-loss models in economics, I jumped in with a mention of the version of internet protocols used in communication with objects in space, which Colin then ran with – talking about comms in trading (which relies on the speed of light to make sure transactions are instantaneous). A client-server model can be used, and in some contexts, equations from fluid mechanics are even used to describe how packets of information are moved around.

With that, we finally managed to satisfy Christian’s mathematical interestingness quotient and successfully connected the opposite sides of the board.

If you’d like to rewatch this or any other part of the 24 Hour Maths Game Show, you can find links to each segment on the website, and you can still donate to our charities by visiting 24hourmaths.com/donate.

]]>*We spoke to Coralie Colmez, mathematician and author of Math on Trial, about her genre-busting new Young Adult novel for mathematically minded teenagers: The Irrational Diary of Clara Valentine.*

*The Irrational Diary of Clara Valentine* is a fun novel aimed at readers aged 15-19. It’s got all the good things in it: a mystery, a sharp-witted narrator, an idiosyncratic best friend, a couple of charming potential boyfriends, a mostly-loveable family, and some maths!

I first had the idea for the book around 10 years ago. My mother (a mathematician) and I had just written a popular maths book called *Math on Trial*, which was really fun to do, but it made me realise that I wanted to find a way to write about maths which was closer to the things I like to read myself, and I mostly read fiction. Following the release of *Math on Trial*, I got the chance to talk about it at events for students, which I really enjoyed, so I decided to write for that age group.

I found it easy to decide which maths topics I wanted to cover – they are all my own favourites, and the things that made me love maths when I was a teenager! The topics are quite abstract and high-level, like countable infinity and logic – things that would normally only be introduced at university, even though they don’t require much prior knowledge and I think high-school students would really enjoy learning about them.

I was also interested in writing YA because I felt that, while there is a lot of great YA literature, none of it looked like my own experience of teenagerhood. Characters are either off dealing with a fantasy world, with major emotional trauma, living an extreme life (Euphoria-style), or on the contrary behaving in a totally PG way. There is a space and a need for all of these types of characters, but I wanted to try and write ones that felt more real, and could have been my friends and me.

Thank you, and I am glad you think so! Because the topics I wanted to cover are quite high-level, I had to find some creative ways to include them. I got a lot of well-meaning publishing professionals suggesting that I have Clara solve problems involving measuring angles, calculating the length of a rope and that kind of thing, but I was really set on sticking with more abstract concepts.

I definitely wanted to make sure there were a few different ways that the maths became part of the story: some of it happens via the characters in the book that know maths at a high level, but we also see moments like Clara teaching her little sister something, or Clara’s best friend learning a bit of mathematical history in her philosophy class. That’s what it’s like in my family (which is made up of 50% mathematicians, so not entirely representative): maths is just a part of normal life.

I also wanted to include what it’s like to think about maths, so I really liked getting in Clara’s mind when she is solving a question: how she approaches problems from different angles – how some of these angles sometimes don’t work at all – and how amazing it feels to crack a problem.

I really think that anyone could enjoy the book. As a novel, it’s a pretty exciting read, it’s funny, and hopefully I’ve managed to capture a bit of today’s really exciting generation of young people, who are so sharp, aware and witty.

When it comes to the maths, it’s written so that readers of different levels can take what they want. Someone who has quite a high level of maths might even try to solve some of the problems along with Clara, whereas someone who only has a basic interest in maths might simply enjoy the overall concepts that are introduced, like realising how different ‘Infinity’ is to just ‘A really big number’. In terms of the level of the maths, I would say that an 18-year-old reader who already has an interest in maths might already have heard of 2 or 3 of the 8 topics covered, but hopefully they’ll see even the ones they already know in a fresh way, with some new anecdotes attached! A couple of the topics are included in the A Level syllabus, though most aren’t.

The book is aimed at readers all of all genders, but as a woman maths graduate – the only one in my year at my college – with a mathematician mother, it’s really important to me to encourage more girls into maths and science. I hope that having an awesome (if I do say so myself) female narrator like Clara can help with that.

Finally, age-wise, I wouldn’t recommend the book to younger readers, because there are some themes that might be too old for them, and there is some sex (which is entirely age-appropriate, at least if you are French, and also very positive for ages 15+) I’ve had some very lovely comments from older readers though, so I’m going to say that there is no maximum age to enjoy the book!

When I finished my first draft of the book, I actually found an agent very quickly, and there was immediate interest from publishers when she sent out the manuscript. I’ll be honest, at the point when I was talking to three big publishers at once, I thought I was about to be famous! But in the end, none of them wanted to publish exactly the book I wanted to write. One wanted it for a younger audience, another wanted me to focus just on the mystery, the third wanted me to first write a novel with no maths, as they were nervous about Clara being a debut. There was a lot of talk about which ‘shelf’ my novel would fit in, and I realised I didn’t want to write a book that just fitted on one shelf, because that’s not what life looks like! Clara cares about maths, about her relationships, about solving a mystery, about politics, about doing well at school… just like we all do (well, apart from the mystery maybe).

You can get a copy on pretty much any online retailer, like Amazon – or if you are avoiding Amazon, it’s on Waterstones if you are in the UK and Bookshop.org if you’re in the US, for example. I’ve also put the PDF on my website, so anyone can read it for free. The book is pretty though, and I’m quite proud because I designed the cover myself, so I’d recommend getting a copy!

]]>Friends of the site Maths Gear have their usual selection of excellent gifts, including a new range of Maths Icons earrings (£14.99) including the Mandelbrot set, and a set of nested polygons. They also have a range of other jewellery and cufflinks which includes the wonderful mug/donut earrings (£17.89) and π cufflinks (£6.91).

There’s also some great Impossible Shape jewellery (from £3) – including Borromean Rings and Necker cubes – available from Earth Symbols, and there’s of course the classic Cofactor Pythagorean theorem earrings ($15 in 3D printed nylon).

Maths Gear also have a wide collection of different types of dice, as do scholastic suppliers Tarquin (including class sets and some individual items). We particularly like Maths Gear’s set of polyhedral dice in shapes they don’t usually come in (£10.97), and Tarquin’s set of blank rewriteable dice (£5.99), for when you want to make your own rules.

More generally, Tabletop Supply are a good go-to for many different types of dice, as well as replacement (or upgrade!) pieces for existing games, or games you’ve invented yourself.

Plenty of mathematically interesting board games come in travel versions which can fit into a small space – some of our favourites include number-based favourites Red 7, 6 Nimmt! and The Game, and if shapes is more your think we can also recommend travel Blokus and travel Qwirkle.

Oink Games also do some visually stunning and simple games with a mathsy vibe, and our favourites include Troika, Deep Sea Adventure and The Pyramid’s Deadline. We also love OK Play which is very compact.

Simple classic board games with a mathematical twist include Shut The Box, and you can’t go wrong with a deck of cards (this Math Stack variant (£10.49) from Maths Gear is pretty, but any will do!)

Site editor Christian recommends what he calls a Nobbly Wobbly, but tends to be sold under the name ‘woven bouncy ball’ or ‘rainbow spaghetti ball‘ (£5.95 for 5) depending on who you ask. The underlying geometry of the shape makes it mathematically interesting, but dogs and small children alike will have fun with it.

Happy Puzzle Co have IQ Minis which fit in your hand, and a range of other pocket puzzles. We also love Edmund Harriss’ Curvahedra (£11.93), which are available from Maths Gear. Paper-folding puzzle Manifold was a big hit with us a few years ago, and it looks like Manifold 2 is now available.

There’s also Rush Hour (£16.49), and we’ve had a recommendation for the STAX games from Huch’s range of puzzles, which comes in Cat, Dog and Sea versions. Don’t forget about the Rubik’s cube and other twisty puzzles too!

For a more refined mathematical palate, you can pick up some elegant vintage maths gifts from Present and Correct, including a 1970s desk abacus (£19.50), gorgeous metal protractors (£4), this ruler sticker tape (£3) and a classic geometry puzzle (£12). Or why not pick up a Golden Mean Compass (£14.99) from Grand Illusions?

If you have any suggestions of your own, feel free to include them in the comments below!

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