Talking Maths in Public Podcast - Series 2 Episode 5

Katie Steckles: Welcome to the Talking Maths in Public Podcast, a community podcast for members of the Talking Maths in Public network, which is a UK organisation bringing together maths communicators of all kinds. My name's Katie Steckles, and I'm a maths communicator and member of the Talking Maths in Public team.

In this podcast, we'll be hearing from the TMiP community, sharing their maths communication projects, recommending their favourite bits of maths comm, and discussing how we can communicate maths engagingly and effectively. In this episode, we'll be hearing from Christian Lawson-Perfect, the winner of the 2025 Mega Grant, and Clare Wallace, who helped him make the Beach Spectres project a reality. We'll also have a chat with Ayliean MacDonald and Hana Ayoob about maths art, what it is, and why it's important in engaging people with maths. And finally, we'll hear from Hazel Lewis about what's involved in designing mathematical puzzle trails to help turn the city of Leeds into the City of Maths.

To see links to the things discussed in this episode and find more episodes, you can visit talkingmathsinpublic.uk/podcast.

First up, I talk to the team behind this year's Talking Maths in Public MEGA Grant project about how they made use of the grant to engage people on a large scale.

I'm talking to Christian Lawson-Perfect and Clare Wallace, who have been the organisers of the Beach Spectres project, and this has been the Mega Grant maths outreach project for the year 2026. So the Mega Grant is administered by Talking Maths in Public in partnership with Matt Parker and his Stand-up Maths YouTube channel, and the Mega Grant basically is a funding pot that is available to people who want to do a large-scale public engagement event. And previously on this podcast we've had a chat with Hana Ayoob, who was doing the Number City project two years ago. Beach Spectres is now the, the kind of the following project in that series, and the Mega Grant essentially takes submissions during odd-numbered years, and then in even-numbered years we... Uh, well, in, in the same odd-numbered year we announce at the TMiP conference who's won it, and then in the even-numbered year we run the project. So this was announced at the last TMiP in 2025 that this year's Mega Grant winner with the, the most well-reviewed proposal by our panel of maths communicators was Christian's project, which is Beach Spectres. So Christian, do you wanna tell us a bit about Beach Spectres and where the idea came from?

Christian Lawson-Perfect: Yeah. So I got really excited about the aperiodic mono tile when it was discovered when they were discovered really. So I think a couple of TMiPs ago we had a big build for the hat tiles. Matt had some foam hat tiles made, and we collectively put them together and laid them out on a floor. After the hat, the spectre was found, which is a proper aperiodic mono tile, which I got really excited about. But this thing that,the problem that comes up when you are trying to assemble the tiling, that you're limited by the number of tiles you have bothered me. I live at the seaside, and I thought, "Well, if we could just make... imprint the shape on the sand, then you could just keep going forever." So I had a little play with that just before the Mega Grant's call for proposals came out. I 3D-printed a little thing and went out myself on the beach and thought, "Oh, this works." So I thought this would be a really good big public maths project to get lots of people all on the beach together trying to produce this tiling.

Katie Steckles: Yeah. And, I mean, I'm part of the committee that does the deciding, but I think one of the things that we were really excited about when we were discussing this was the fact that it is very public, right? So people will just be walking down the beach, they'll see this happening, they'll go, "Oh, what's this?" And it's quite visual as well. It's sort of a, you know, almost an art thing in some ways. Uh, it's got this sort of geometry aspect to it, but it is, you know, a making a pretty pattern on the beach in some sense. And yeah, it's, it's fun and it's, it's celebrating a new discovery, which we liked as well, and- Yeah. It, I think one of the things that we also found fun was the sort of ephemeral-ness of it, 'cause obviously the tide comes in and washes the whole thing away. And, we sort of kind of made that part of it, right? 

Christian Lawson-Perfect: Yeah. I really loved that. I, I feel like it reduced the stress level so much knowing that if we made a mistake, it wouldn't really matter anyway. We weren't gonna make something that was gonna hang on a wall for decades. So just we could have a go, we could do it, and it could be a little bit messy but we'd put it together. You said the beach was a really good public place. I really think that's worth repeating because it's sort of ideal really, because everybody at the beach is just there to spend some time. They're not... Like when you- if you do something even in a shopping centre, people are there for a reason to do something. But people come to the beach to just sort of chill out. 

Katie Steckles: Yeah. And I got a sense on the day that, that there were people who were not, absolutely not expecting to see this. Like, we'd done a bit of advertising beforehand. We had some banners up and things like that, but there were people who were just like, "Oh, what's this?" And when we said, "Oh, we're doing a maths thing," and there were some really nice conversations we had with people on the day. 

Christian Lawson-Perfect: Yeah, it was, it was amazing the number of people that came up. And I mean, people who weren't interested, I suppose, would just walk past. The amount of people that came up and looked interested or maybe asked us a question and had a really positive attitude to what we were doing they were intrigued by the maths, the monotile, but then really positive about obviously the nice thing you're doing on the beach, making a nice pattern.

Katie Steckles: Yeah. And we had a huge team of volunteers for this that were absolutely fantastic. But there, there was a good... I think we managed to develop between ourselves a good range of levels of explanation for this. So some people would come along and we'd say, "Oh, we're doing a tiling. You can stamp on the sand, and they'll all fit together, and they'll fill the whole space." And that was enough for some people, and they would go down, and we'd tell them where to tile, and they would go and do it. And then other people who were literally asking, "Can we see the research paper?" You know? Like every level in between as well. 

Christian Lawson-Perfect: Yeah. It was good. And it didn't really correlate with age how much detail people wanted. Yeah. We had some, some school kids who got very into it, and then some, some adults who were just happy with the broad explanation. A surprising number of people with like a proper maths background just wandering along the beach. Mm. I never would've guessed so many mathematicians were loose in the public.

Katie Steckles: Yeah. Well,they are part of the public, I guess. This is what, what talking maths in public involves. So Clare's been sitting here very patiently while we've been chatting about all of this. So as part of the, the MEGA Grant we have the idea that comes from whoever submitted it, and you know, a lot of the logistics of kind of the maths of it, I guess has come from Christian but the more of the logistics side, the kind of the actual admin of this, the project management, I guess, has been Clare. So Clare, you know, how has that gone? What have you done, and how have you done it? 

Clare Wallace: Yeah. It's been great. There have been a lot of logistics involved with it particularly sort of getting permission from the council to use the space and submitting the risk assessment. There was an awful lot of paperwork involved there that we didn't necessarily- know about as we went into it. But that was really good. We got St. John Ambulance along to make sure that we were all safe and looked after, and they were actually... Our St. John Ambulance people were really, really interested in the maths as well.

It turned out they were really engaged. We did a lot of recruiting volunteers, so we used the Ridiculous Public Maths mailing list to get loads of the sort of familiar faces, and it was lovely to see people that we've crossed paths with before at things like this. But we also had loads and loads of staff and students from Newcastle University and Durham University getting involved, and I think for a lot of them, it was their first ever Ridiculous Public Maths thing. And that was also really lovely to see, colleagues who wouldn't necessarily do a lot of outreach in their day-to-day jobs getting involved and talking to members of the public. 

Katie Steckles: So has part of your role been in managing kind of budgets and things as well? 

Clare Wallace: Yeah, we we had a budget from Standup Maths, and we've been able to keep incredibly close to our budget. At the end of it, we've just added it all up, and I think we've come within about £20 of the final amount. We spent quite a lot of that on free ice cream vouchers for participants, so anyone who came along and joined in could have a free ice cream. That was very important to us, and we found the space for that in the budget. Yeah, it's been great to work really closely with lots of local businesses and local vendors as well to get the gazebo that we were sat under, the ice creams, the lunches. Finding people who were local to Whitley Bay to help us out with that has been really, really great. 

Katie Steckles: Yeah, and it, it kind of did feel like a community thing. Like, there were a lot of people out, and a lot of our team was there, but, you know, we had our T-shirts on so people could tell who was there with us. But there were so many people out on the beach. And I guess we... So there, there will be a YouTube video about this. The whole thing was filmed for the Standup Maths channel. And I think Matt's planning to make a video that combines this and the hat tiling project that Christian mentioned from a couple of TMiPs ago so that it will all be one video about aperiodic tilings and about the, the different ways that you can do that. But yeah, if you watch the footage in the video, you can really see there's a huge number of different people, and as Christian said, from all ages, all different, you know, different levels just getting involved. And I also think there was a minimum of people who were saying, "What do I need to do just to get the free ice cream?" There were a couple of people who said, "Have I done enough to earn an ice cream yet?" But mostly people were just quite happy, and a lot of them came back, right? A lot of them did some stamping and then came back and did some more.

Christian Lawson-Perfect: Yeah. It was it was amazing really. I put in the proposal that we could do this on any beach, but I pr- prefer my beach. I'm really glad that we did. I think for that community thing we advertised it around local schools and I talked to my kids' school. So it had quite a few kids from there came down. So it was, it was really nice to see a lot of people I know actually just coming up who I would never talk with about maths, talked with before about maths, to find them engaging with it really well. 

Katie Steckles: Fantastic. So in terms of the maths of this, obviously it's an aperiodic tiling. You know, you can't just start stamping and hope that you're not gonna kind of work yourself into a corner. So this, it was, I think, one of the challenges of this, 'cause there is a sort of substitution tiling method that lets you build the whole thing. So Christian, do you wanna say a bit about how, how we worked that out? 

Christian Lawson-Perfect: Yeah, that was really hard. I mean, that, that was the first really hard thing to do in the planning stage, was to work out how to coordinate making that tiling. It's very easy to get a computer- well, not very easy- it's fairly straightforward to get a computer to produce the tiling because it's got incredible memory. But for an unknown number of people who have an unknown level of expertise to all coordinate together to produce it is quite difficult. We needed a good system. So I..., in the original paper, there's a substitution system where you start with one tile and you say expand that into a collection of nine tiles, and then each of those tiles stands in for... Like, you replace it with another copy of that thing. So you, you build up bigger and bigger collections of copies of the previous level down of tile. It's a recursive thing.

So the initial plan was to sort of follow that exactly as it was and do that work on the beach to say, "Let's put a tile down and work it out, and then work out where the next things go." I had a couple of practice goes on my own. Then we, we had a team practice. Some of the volunteers came up, and everything just sort of ground to a halt as we all got confused about talking about directions. So that didn't really work. And then I don't... I think someone suggested it would be nice to have a map, a printed map, and I thought, "Well, yeah, we could do that." So I printed out on sort of A0 size, massive a very large patch of the aperiodic tiling. It was a level four meta tile, which means that the replacement had happened four times. It had just under 5,000 tiles on it.

So we had this map which we could use to check against where we were. We'd still... On the beach, we went down, we took the stampers and set down the first tile and had a little reference for the first level of the substitution and did that. But then whenever someone finished a group of nine tiles, a level one meta tile, they went back to the map and ticked it off and signed it. And then we... Or we also used a version on our phones and a tablet to sort of work out what to do next-

Katie Steckles: Navigate.

Christian Lawson-Perfect: To navigate. Yeah. Yeah, exactly. A lot of the photos I think show, so one person looking at a phone and another person kneeling down next to them with a stamper poised "Tell me where to put it."

So that's the way it worked, and it worked incredibly well. I was so impressed by how we didn't really encounter any problems. A couple of problems with things not quite matching up. I think that was... the other big worry was would we be able to do this accurately enough that when you have tiles coming at each other from a couple of different directions, they'll meet up nicely? And largely it worked. We got a lot put down that sort of fitted together. 

Katie Steckles: Yeah, I think we sort of built outwards rather than trying to join anything up. Like, yeah, there was discussion about could we start in two places and spread and join together. We just thought absolutely no. Not a chance.

Christian Lawson-Perfect: It's just in sand, and nothing actually really has to line up other than visually. You can sort of fudge it a bit when you're putting things down. So there was a little bit of self-correcting going on. So yeah, that worked really well. The thing with the map was, was I'm so pleased that we did this. The very first meta tile a couple of kids had been waiting for us to start, and I said, "Oh, you can do that." So they did it, and then I took them over to the map to check where we need to go next, and I thought, "Why don't you just put your initials on that? 'Cause you did that, and we'll record it." So then we did that with everybody that came down and stamped some tiles, so that the final finished maps from both days are just covered in initials of people, like a record of who did it, and that is such a nice thing to look at. 

Katie Steckles: Yeah, and I think people could see that map and they could see what we were trying to achieve as well. It gave them a real sense of the scale of it. And we kind of, we maybe filled a third of the map on each of the days, maybe a bit more. I think we calculated on the second day we'd done over 100 meta tiles. That was a nice moment when we had the sort of triumphant 100 meta tile barrier has been smashed. Yeah. Well, I think overall it was, it was a really nice project to run over a couple of days. It was good to have a couple of days 'cause the weather wasn't amazing on the first day, so it meant we had the second day with a clearer run to be able to do more. And I think we learned a lot from the first day that we put into practice on the second day in terms of the logistics of it and everything. I was gonna say, Clare, is this the first time you've done a project of this scale, and what have you learned from doing it? 

Clare Wallace: Yeah, absolutely. I think this is the biggest thing I've ever organized, apart from my own wedding. I was quite nervous about it, actually. In the end, we had 54 volunteers in total. We had hundreds of members of the public involved. And thinking at the start about organizing something of that scale was quite intimidating. I think the thing that really made it possible was how willing everyone was to pitch in and get involved. You know, I went to pick up the lunches and realised it was more than I could carry, even if the guy with the lunches helped me, and just sent a text to everyone, "Can anyone come and help me carry things?" And, you know, four people immediately appeared. Everyone's willingness to just get stuck in was really, really helpful. I think I learned a lot about the organization and sort of keeping track of everything, the spreadsheets, the documents, that sort of thing, was new for me. But it was really helpful actually that we got some notes and advice from Hana who organized the previous MEGA Grant project. That was incredibly helpful just for getting a sense of, "I should expect to be looking at...". 

Katie Steckles: Yeah, and hopefully we can pass on some notes from this to whoever ends up running the next MEGA Grant project in two years, that they can take on some of that learning as well and expand on it and do something else. Yeah. 

Clare Wallace: Yeah. We've definitely found some friendly people that we'd love to work with again, and passing that on would be really good. 

Katie Steckles: Yeah. And I guess everyone who was involved in this can get onto the Ridiculous Projects mailing list so we can contact them about the next one. Well, thank you to both of you. This has been nice to chat about this. If people wanna find out more about the Beach Spectres project or about the MEGA Grant or any of the things we've mentioned, we'll put some links in the show notes so you can find out more about that. And hopefully we'll see some great submissions coming in for the next MEGA Grant so we can do something even more cool next time.

Thanks very much to Christian and Clare for their incredible work on the project and for telling us all about it.

Up next on the Talking Maths in Public podcast, what is mathematical art? I spoke to science artist Hana Ayoob and arty mathematician, Ayliean MacDonald, about how we define maths art and why it's a great way to engage people. So should we start off just by getting an introduction to both of you and what your kind of experience is with maths art? So if we go to you first, Hana. 

Hana Ayoob: Yeah. So I was doing maths art for a lot long... I was doing maths art for a long time without realising it was maths art. So I have considered myself an artist pretty much since I was able to pick up a crayon. Like, I never really stopped drawing. And when I was about 12, I started doing henna art which is a traditional form of body art across South Asia sort of North Africa, and lots of other regions in the world. And a lot of the traditional patterns I was drawing from had a lot of symmetry in them. It was mandalas. It was repetitive patterns, and that sort of formed the basis of my art style for the following decades. But it wasn't until I started sort of comparing notes with you, Katie and talking a bit more about symmetry and circles and patterns that I realised that what I'd been doing all along was maths art.

Katie Steckles: Yeah, I think that potentially that there'll be good, some good discussion to be had about what is maths art and what mean- what makes something maths and what makes something art, I guess. Yeah, let's go to Ayliean. 

Ayliean MacDonald: So I approached it from the other side from Hana, which is wonderful. So I loved maths. I have always loved both maths and art, but I did my degree in maths. And throughout that whole time, I was just kind of really just looking at the pictures, if I'm very honest. The thing that drove me to find a piece of maths interesting would be when I found a certain way to look at it that I found aesthetically pleasing. And one of the wonderful things about maths is you can view it from loads of different angles, from loads of different ways. So I really enjoyed basically finding maths concepts that I liked and then finding a way to be visually creative with them. And a lot of the maths art that I do involves time-lapsing sequences. I feel like when you add that element of time in there, and you can show the maths moving and growing, you get this sort of understanding that you might not otherwise got from a still image. So there is a good question as to is what I do actually art, or is it just a way of showing maths? Which, you know, clearly we're going to get into what is art? What is maths? But really for me, if it makes you think about the world in a different way, then it's art. Like, good art makes you think about the world in a different way. And I get that from maths, and then I'm just trying to take, you know, that feeling that maths gives me and express myself via visual sometimes, sometimes audio as well, but usually via visual media. I'm trying to express that feeling that I get from the maths and kind of instill it in someone else so that we can have this shared experience of like, "Whoa, maths is so cool and beautiful, and I've gained this new insight into the world." 

Katie Steckles: Yeah, I think that is often the way with a lot of art, that it's about kind of saying something in a way that isn't kind of just directly saying it, but in the way that you're expressing something. And yeah, I get... I sort of see how that works with maths as well, that it's a way of thinking about the world. And that's a lovely connection between the two things. So a member of the TMiP community has recently had this experience where they were showing somebody some maths art, and the person said, "This isn't maths. None of this is maths. This is just art." Which must have been a really interesting thing and a kind of good question to sort of try and answer. So what would you say in that situation? Let's go to Hana first. 

Hana Ayoob: So I would say the maths in maths art can be both deliberate or sort of incidental/accidental. I think that it feels natural that I'd say that given that I, you know, have already said that I was doing maths art for a long time without realising. But I think whether deliberate or sort of incidental, the maths is something which can be either seen without sort of prompting, and that might be something that those who are, who are more confident and more knowledgeable in maths themselves might immediately spot something.

But also, the maths can be something that can be discussed, that can be brought out, can be another layer to be enjoyed within that art. So if I was to show someone a mandala that I've created, you know, them being able to talk about, say, the different forms of symmetry within it, that there is you know, that you can see reflections, but there's also rotation within it, and that, I think, can add an extra layer to that discussion and another way to talk about the art, but a way to discuss the maths that's within it as well 

Ayliean MacDonald: Yeah, very much to add to what Hana's talking about there. So the maths does come from the discussion that you have. I have a, a little stock answer that I do use for this, so feel free to steal this. But often when people are discussing art or beauty, they'll say something like, "Beauty is in the eye of the beholder." Very much for maths, the maths is in the mind of the beholder. So yeah, if you're looking at this maths art and you're not thinking mathematically or discussing mathematically, then yeah, it's just a piece of art or not. Like, art's very subjective. So you do need to have that sort of mathematical engagement. And you'd like to think that good maths art with people who are engaging in good faith with an open mind will give that, it's, that stimulus. So you can either have art as a stimulus for a maths conversation like Hana's saying. Some art it's impossible to look at and not feel this symmetry and want to talk about the symmetry. Or you can have maths, which is a stimulus for art. So good example for that is Marjorie Rice's pentagons.

So when she discovered -- amateur mathematician who discovered, I think, four new types of pentagons which tessellate, irregular pentagons, the first thing that she did with that was then create these beautiful artworks to show off her  new tessellation. So yeah. Then, very much when you're saying, "Where is the maths?" I think that we all know that there is a lot of maths in creating this, and what you're trying to do is entice people into saying "Look, there's something really tasty here. Go on, take a bite. Can you engage with it mathematically?" But if you're gonna refuse to engage with it mathematically, exactly the same as if you're in a literal maths class, then no, you're not doing any maths.

Katie Steckles: Yeah. I think that there is kind of different ways of combining maths and art, I guess, that we've sort of touched on, that you could maybe just look at the way that an artist would create an image or a design or whatever, and think about what maths they would need in order to do that, sort of geometrical constructions and the, you know, the symmetries and the patterns that are in there, and how they can use mathematical ideas to make the actual artwork happen. And then yeah, as you say, also taking an idea from maths and being inspired by that to create something beautiful. And that's not necessarily gonna create something that doesn't look like any other piece of art. But it's got kind of a mathematical idea that you want to sort of express in some way.

Hana Ayoob: I think there's, there's parallels to this in science art as well, which is my sort of other area. I recently had a painting that was in an exhibition and it's based on astrocytes, a type of neuron in the brain. And, you know, most people just look at it and see something pretty and colorful with sort of patterns and branching, you know, within it. And, you know, during one of my stewarding shifts, I also saw someone walk past and go, "Oh my God, there's neurons!"  And I think as Ayliean said, you know, people can engage with art without seeing that, the maths behind it or the science behind it, or they can also see it instantly or talk about it. 

Katie Steckles: Yeah. And I guess this may lead into my next question, I guess, which is why is it important? Why do we need maths and art to cross over in this way? Shall we go to Ayliean first? 

Ayliean MacDonald: We're huuuuumans. We need that creativity. Maths is done by people. So the interesting thing about maths is that it does exist separate to, you know, whether someone is doing the maths or not, but we do need to kind of like pluck it out of the ether almost. We need to interpret it. Like, there is a Chinese art form where essentially you take slabs of stone and you take fine slithers of them, and it creates these sort of images, and these are considered artworks. And so there's a good question there where it's like, okay, well, that's an artwork without an artist. People buy these for, you know, hundreds of thousands. They are very much considered an art form. And I wonder that sometimes with maths art because, say, the dragon curve fractal, it exists whether I show it to you or not. Whether someone found it or not, it existed there. So it is this sort of found artwork, and then obviously there's the way that we interpret it.

But there are so many different ways to view art as being important with maths. Because being artistic in any field, I believe, is important. If you love two things, merge them together, see what happens. So whatever you can think of, what would happen if you merged it with art? So sports and art, what would happen? Computing and art, you get a lot of generative art things which are really wonderful, like if you liked woodworking and art. Food and art, all of these things can be merged together, and I think it just brings out the human element in what's going on. You can also, you can change the world with art and I think that's a good aim for any artist.

I'll give an example, which is Dundee University was recently facing 432 compulsory job losses. And as a kind of guerrilla art piece, me and a couple of other people got together and we put chalk stick figures all the way around the edge of the university to show people what 432 people actually looks like. Kind of building in that element of time where people would have to walk past 432 stick figures and think, "Oh my gosh, this is, this is gonna have such an impact." So that is a piece of street art, you know, it's just chalked onto the pavement which is helping people understand a number. It's real world representation. You can argue whether it's a particularly good piece of art or not, because it is just stick figures drawn out of chalk. But it did change the way that people see the world. And that, along with a very strong campaign by the unions, led the Scottish government to then say "No, you cannot have these 432 compulsory job losses. Think of something different." So, I mean, whatever it is that you want, if you want the sort of wellbeing, wholesome side of things, or if you want real-world impact, art is a vehicle for that to happen through both maths or any other interdisciplinary thing. 

Katie Steckles: Yeah. I mean, that's not only maths art in the sense that it's data visualisation but it's also kind of making, making a point about scale, right? About, about how art can help us to visualise things in a different way. Yeah, I mean, I think a lot of art is about kind of presenting something to people, right, in a way that they haven't previously seen it. I think what you were saying before about the slices of stone, and is this actually art or are you just showing us something that already exists I'm reminded of the artist Yves Klein, who one of the first kind of art pieces that I saw in an art gallery, and actually was really impressed by. And he's got this series of paintings that are a particular shade of blue, which he's christened International Klein Blue, and he just paints the whole canvas in this one shade of blue. And it's quite a nice shade of blue. You know, as a colour it's quite enjoyable. But when you look at the sign next to it, you're like, "Oh, they forgot to put a painting here. It's just, you know, the blue screen," or whatever. You know, they've not turned the projector on. But actually the the art is, "This colour is my colour now. I've patented this colour," or whatever he'd done. And I found that really powerful 'cause he's not just, you know, he's not creating a drawing using it, but he's literally just saying, "This colour I think is beautiful in its own right and I want you to see it." And I feel like that's to some extent the way that some of the maths art works, that it's like I'm just demonstrating this idea that has its own inherent beauty and I want this to be shared with people. But yeah, so Hana, to go to you on this one, why is maths art important? 

Hana Ayoob: So I'll second pretty much everything that Ayliean has already said. But to add to that, I think speaking to we are human, if you look at traditional art forms, almost all of them have symmetry and pattern and repetition in them. And clearly humans have been drawn to representing mathematical concepts visually for almost as long as humans have been around. So I think it is a really core part of who we are. Stick figures have also been around for almost as long as humans have been making images. But I think continuing on with sort of how maths art and being human connects, I think it can showcase how broad both maths and art can be as disciplines, and how porous any boundaries we try and set, or any definitions we try and set for what those two things are. I mean, that speaks to sort of an entirely blue canvas as well. When people are like -- I know we've already talked about what is mass art -- but when people are like, "What is art?" I'm like, it feels like a futile thing. Like, let's just go create some rather than spending time talking about what it is.

And I think, yeah, they're just both so expansive. And I know we're gonna talk about this a little bit more, but I think that there's also roots here in that there's a lot of people who are anxious about maths or who think maths isn't for them, and actually there's, I would say, as many people who see art, especially creating art, as not for them. And I think bringing the two together doesn't inevitably mean that it's more engaging, but I think it does have the potential to be more engaging. 

Katie Steckles: Yeah. I feel like having done various projects where we get people to do drawing in a maths context, so for example, the Mirror Pillar project that I did a few years ago I'll put a link in the show notes if people wanna find out more about it. But yeah, literally the two things that people are quite happy to say, "Oh, I'm terrible at that," are maths and drawing. We were like, "Hey, come and do some maths drawing." They're like, "Oh, yeah, no, you're right. I'm fine, thanks." Yeah. So speaking of which, I guess this is the Talking Maths in Public podcast. We probably should talk about, you know, engaging people with maths at some point in this. So how is maths art important in that? Like, what does it give us as a tool to be able to engage people with maths, I guess, or with art, I suppose, potentially? Hana? 

Hana Ayoob: I think, as you've just said, like it is possible to sort of scare people off by bringing together things that they are already nervous about or don't see as for them. But I think if we boil things down to their very essence, we can also create incredibly sort of welcoming spaces. And so I think some of the work that you and me have done, Katie, where, you know, we've essentially built workshops from a single sort of ruler and compass construction that, you know, gives people a template on which to create a piece of mathematical art. And one of my favourite quotes about those workshops is that it's like one of the most wholesome spaces that people had ever been part of. And I think there's something there about using this framework, using maths to develop a template, which means that people aren't looking at a blank page when it comes to creating something.

But then also giving that space for expression and creativity and agency that means that you're not sort of stuck to sort of following rules or to a template, and I think that really does have the power to create these very welcoming and wholesome spaces. I think sort of in a very different way something like the Number City project, which we also both worked on, which was creating sort of this big cardboard box city based around sort of prime numbers, had the opposite thing of people making a small component to something which then grew into this big demonstration of mathematical principles. Including... Like, I hadn't thought about prime numbers anywhere near that much until we worked on that project, and it was such a wonderful way to see a visual representation of mathematical concepts that everyone involved had been part of making. And in different ways, both those examples, and I think this is true of so many other sort of mathematical art projects that involve the public, there is this real opportunity for sort of contribution and interaction and collaboration and agency, which is, I think actually a lack of agency is often what can put people off certain subjects, including the ones we're talking about. So I think that can be really powerful. 

Katie Steckles: Yeah, and I guess there's, there's almost an inherent tension that some people might think is there between art, which is this creative subject where people can produce whatever they want, and maths, which is this subject full of logic and rules. But actually, if you talk to most mathematicians, they'll tell you that maths is inherently quite creative, and I guess there'll be a lot of artists who have particular rules that they follow when they're doing what they do. So those are, are probably both slightly inaccurate descriptions of those things. But yeah, that tension potentially will be there, and it's about finding a way to, to cut through that and to not make people feel too constrained or too kind of lost in the possibilities, I guess. What do you think, Ayliean?

Ayliean MacDonald: Yeah, very much. Like, having been in some of your workshops before, the sort of experience is coming away thinking, well, you don't have to be good at something to enjoy it. And that is something which I think should be applied to both maths and art. And I think people understand that there is a joy in art and a lot less we have the reputation of there being a joy in maths.

So I think combining those lets people see oh, okay. I think also, as well as the tension that you mentioned with the "I need to get the answer right for maths, but art could be everywhere" there is a tension between art, which has an intrinsic value, and then maths, where we're often trying to justify its value in terms of this will get you a job, and you know, this is really important, and the... I do dislike the hierarchy that we have between subjects where people are like, "Oh, you better do well in your maths exam otherwise, you know, your life's gonna fall apart," which is not true. But I think it would be, it would be really fun to see people start saying like, "You better do well in your art exam, otherwise your life is gonna fall apart."

But yeah, I do think that kind of breaking down the barriers and merging together the idea that both maths and art have this intrinsic value, and if you wanted to look at it the opposite way, you know, art can be, if you want to get a job in creative industries, art is a very good way to go. But yeah, so just kind of showing people that there are more similarities than differences. And like you said, Hana, with the agency, giving people that ownership, saying, you know, "You could do art in any number of ways, whatever way is right for you. You can do maths in any number of ways," which I think is something that people often don't get to experience through, you know, various reasons - probably because we do have such packed curriculums and really intense exams, people don't get to explore and do maths in the way that works for them or the way that they would like. So yeah, very much if you ever get a chance to go to any of Hana or Katie's workshops or visit something like Maths World and just experience maths in a more creative way it is a wonderful, very welcoming atmosphere. 

Katie Steckles: Yeah. Talking about kind of ways to find, you know, engage with maths that are not the way you normally would, I guess via art is as good a way as any. And, you know, there's lots of ways people can do that even just on their own at home. If people look online, there's lots of examples of maths art. There's also things like the Bridges Conference, which I know Ayliean was at this year where people celebrate all this brilliant art and maths that they, they've brought together. But yeah hopefully via wonderful maths communication projects put together by members of the TMiP Community inspired by this excellent podcast segment. So thank you to both of you for chatting about this. Hopefully, people wanna find out more about what you do, and we'll put some links in the show notes to let people find stuff that you're doing elsewhere online. But otherwise, thank you very much. 

Ayliean: Woo, maths art.

Hana: Thanks so much for having us.

Katie Steckles: Thanks again to Hana and Ayliean. To finish off this episode, I chatted to Hazel Lewis about her work on a set of mathematical puzzle trails. So earlier we heard about the City of Maths project taking place across the city of Leeds from 2026 to 2027, and I'm joined by Hazel Lewis, who's working for the City of Maths project as a freelance resource creator.

And one of the things that Hazel's worked on that I'm really interested to hear about are maths puzzle trails. So Hazel, tell us about these maths puzzle trails.

Hazel Lewis: Yeah. So the maths puzzle trails are all themed around a story called The Great Jewel Heist. So this is where 10 of the world's most expensive jewels have been stolen. So the idea is that the thief has left a trail of clues hidden round Leeds city centre, and that you need to solve these clues to rescue the jewels. So there are three maths trails for different age ranges. So there's one for ages four to seven, one for seven to 11, and then the final one is for ages 11 to 14. So each trail has got 10 clues, and it's free to download from the Leeds City of Maths website. There are also paper copies you can pick up in MathsCity, which is the Maths Discovery Center in Leeds.

Katie Steckles: Fantastic. And I just love it when thieves do this, like they steal something and then they just leave a dastardly set of clues that are maths problems somehow for you to solve. They could just not do that, and then no one would ever find the treasure. But yeah, so this sounds like a really great thing to kind of give people something to do and, and kind of get involved. I guess they can do it in their own time you know, at, as part of this City of Maths thing. So how do you start planning something like this?

Hazel Lewis: Yeah. So actually I thought of the story of the great jewel heist first. So I love playing board games. I've done a few escape room type games, and so I always wanted the puzzle trails to have a backstory which would catch people's imaginations. It also allowed our designer to create some fantastic illustrations, which have really brought the trails alive. So having a theme isn't essential, but it can be a really fun element. And then setting the maths trails around the great jewel heist theme also naturally led to the possibility of people opening an actual physical safe at the end of the trail inside MathsCity. So for those not able to get to MathsCity, there's also a digital safe that people can enter the code into online, along with a monthly prize draw 

Katie Steckles: Fab. So kind of you, you do the fun thing, you go around, you spend a bit of time on it, and then you get if you want to go to MathsCity, you can get this actual physical safe you can crack at the end which is fantastic. And I guess the prize draw is just sort of like an extra incentive for people to finish you know, get their entry in. So that's absolutely great. And yeah, I think it's the sort of thing I would love to do. I love setting puzzles and all that, that kind of thing, but thinking about how to actually build it into a trail, I guess is a lot more work than just, just coming up with a few maths puzzles. So how do you plan a maths trail like this?

Hazel Lewis: So the first thing I think to think about is your target audience and the context that they're going to be doing the trail in, and then this should be driving everything about your trail. So a trail for families is going to be really different to a trail for adult puzzle enthusiasts, for example. 

Katie Steckles: Yeah, I can imagine. And I've seen some of these kind of- I think there's a website called Treasure Trails that just does these sort of for fun that you can just, you know, download a PDF or whatever, or do it on an app on your phone. And some of the ones for kids are very much just like, can you count how many times this word appears on this sign or something like that. And I guess, you know, the pitching things at that level, I guess you don't want anything too involved, but if you've also got you know, things for older people or for older kids, there's a different thing you're looking for there, I suppose, yeah. Fantastic. So in your trail, do all the questions have a specific answer that you're looking for, is there a definite correct answer to each puzzle?

Hazel Lewis: Yeah, they do, and I think this is a really important decision you need to make before you start writing the trail. So do you want your trail to be a puzzle-style trail with clues, or do you want to create a more exploratory maths trail? So in an exploratory maths trail there are opportunities for pupils to sketch things, maybe do data collection, estimation, often without specific right or wrong answers. And this type of exploratory maths trail can lead to really rich discussion back in the classroom for example, if it's aimed at school groups. And then some maths trails blend exploratory questions with questions that have specific answers. And I think there's great value in all kinds of maths trails, but I chose to go for a more puzzle-style trail Yeah, and I guess for some people, like the satisfaction of getting an answer to a puzzle is part of the fun of it, I guess so.

Katie Steckles: I know what you mean though 'cause there's so much kind of maths in the world around us that you can kind of pull in and get people to think about. But yeah having, having kind of definite answers I guess is... If you stick to that as a consistent approach, that works. So what was your process for this? Having made that decision, what was your next step?

Hazel Lewis: Yeah. So I'd really strongly recommend doing as many other trails as you can. Not all of those need to be maths trails. So I've done a lot of trails, some of them on my own and some with my children, and I discovered straightaway that doing trails can be completely exhausting. So everything takes longer than you think. There's wind, rain, traffic to consider, and so this meant that I wanted to plan a route that took no longer than an hour, so that's roughly about a mile in distance while accounting for stopping to answer the clues. If you want to produce a longer trail, I'd probably suggest splitting it into a part A and B so that people have the option not to have to do the whole trail in one go, making it a bit more accessible.

Katie Steckles: I guess people will engage with this in their own way and they'll do what you want, but you want it to be something that they're likely to finish, right? You don't want them to give up halfway round because of the logistics rather than because of the maths. You know, either way you want them to get the satisfaction of finishing. Yeah. So how do you pick a route for the trail? 'Cause you're saying it's about a mile in total, but I guess you wanna take in some some good stuff.

Hazel Lewis: Yeah. So I think it's nice if your maths trail can cover major landmarks or points of interest in your town or city. So I learnt so much about the history of Leeds and its buildings when planning the trail, and it's been great to share just a few of those facts in the trails. So in a city like Leeds, I could never cover every landmark as there are far too many. So I focused on a child-friendly area of the city, which included the City Museum, the Library, and then one of Leeds's nicest green spaces, which is Park Square.

Katie Steckles: Fantastic. Yeah. I mean, when I've done trails like this before, obviously especially if it's the one where the puzzles are really simple for small kids like we're not, like as, as an adult, I'm not necessarily doing it because you know, the challenge of the puzzles. Like it's nice to do fun little puzzles, but part of it is, yeah, it just gets you to go and see some things that you might not otherwise realise were there. And potentially, you know, if it's people who are local to Leeds, there might even be stuff that they didn't know about their city that they can learn through doing something like this. So that's absolutely lovely. Fantastic. So that's the route and the plan. What about the clues? Like what were you looking for in the clues?

Hazel Lewis: So I've got the philosophy that the clue needs to be mainly about the maths rather than hunting for a really difficult to find object. So I tried to make sure that the clue sites are reasonably easy to find, and then the clue sites need to be on permanent features of the city so that your trail doesn't become out of date. So if you think that the council might move it or cover it up, then don't base a clue on it. Then it's important that the maths content is focused on the right age group and to research the curriculum so that you don't cover things that young people won't have met yet. And then finally, I like to think about variety, so I wanted 10 clues on reasonably different maths topics. So I don't just want 10 clues that are all on number. I then like to make the clues sound fun and to tie in with the Great Jewel Heist theme.

Katie Steckles: Yeah. And I guess, you know, you're saying that you're kind of looking at the level that you wanna pitch things at, you get a sense of what that age group of kids that you're pitching it at will have seen already. They're with their parents potentially, so you might be able to do something that stretches them a little bit. But you know, they're also outside. You know, there's a lot of factors going on there. So how do you think about pitching that? Like, what's the process there?

Hazel Lewis: Yeah, so realistically, you're never gonna be able to have one trail which is suitable for all age groups, which is where having different trails that follow the same route can be really helpful. And, like you say, I think doing maths outside can be a lot more difficult than in the classroom. There's so much to take in, especially when you're in a busy city with lots of distractions. Therefore, it's really important to trial the trails as much as possible so they're pitched at the right level. And, and as well as trialing them with your target age group, I'd also suggest seeking out people who you know have got a fantastic attention to detail. 

Katie Steckles: I mean, yeah, that's certainly mathematicians in my experience are good at, good at zeroing in on, on fine details and spotting things. Yeah, I think that testing is a huge part of this, I guess, just to, to sort of find all the... 'Cause you won't necessarily spot everything straight away. But yeah, that... I mean, that all sounds like you've thought about a lot of these things. And I know that one of the kind of principles behind the City of Maths is that we're trying to... I say we, this is secretly another project that I'm heavily involved in and that I'm interviewing someone about. Welcome to this podcast. But you know, one of the main goals of it, I guess, is to reach people who wouldn't necessarily engage with maths otherwise. So it's really important that things aren't gonna sort of put people off or make people feel like they can't do maths or you know... You want them to work for it a little bit. You know, it doesn't wanna be trivial, but you don't want them to feel like they're struggling with it. So do you have kind of a way of getting people to feel like that sense of achievement of doing it, but not kind of getting too stuck?

Hazel Lewis : Yeah. So fundamentally, I want everyone to enjoy the clues and to get a sense of achievement. So this is one of the reasons we've made the certificate and prize draw available to everyone who finish the trail, so regardless of whether they got all of the answers correct. Right. And then, yeah, I decided right from the beginning to provide a hint for each clue, which is available on a separate sheet and online. So this means that when someone is stuck, they could get some help. It may not mean that they can solve every clue, but it'll certainly help them on their way. Creating a hint sheet can be really time-consuming, but I think it's totally worth it in terms of making the trails more accessible to a wider group. And then this way, everyone can feel like they've done well and have a positive view of maths.

Katie Steckles: Yeah. And I, you know, that's the goal here, I guess. And even if people don't necessarily think of it as something they're doing that's extremely mathsy, like it's a fun trail, it's going round, it's seeing stuff, and it's having fun with your family and you know, solving some puzzles, I guess, which, yeah, is fun. It's a thing people do for fun anyway, so that's fantastic. So I guess this is the sort of thing where there's a lot of practicalities to it, so as well as the actual content of the questions and the route that you're choosing, what other practicalities did you have to think about?

Hazel Lewis: Yeah. So all of the trails are available online. However, we've recommended that they're printed for the best experience. So particularly for school groups, phones and devices may not be available, and so having a paper option is vital. So when you're planning your maths trails, make sure they can be printed easily. For example, avoid large blocks of color, which made the text really hard to read and print out. Also, not everyone's got a printer, so if you can make the trails available in paper form, then that's really good. So for example, they could be made available to pick up in a library, museum, or university reception. Yeah. And you know, that also gets the word out. You know, if people see it in the library, they might not be expecting to see it there, but it'll be, "Oh, oh, there's a City of Maths thing. Oh, I'll do this paper trail."

Yeah. Uh, fantastic. So how are these being received so far? Are people getting on well with them? 

Hazel Lewis: Yeah. So the trails were launched about a month ago, and so far the response has been really positive. Uh, a really great moment for me was when I saw them being recommended on one of the parents' WhatsApp groups I'm in. So in particular- (Katie: Oh, nice.) Yeah, it was good. In particular, they were being recommended as a great free holiday activity. So it's lovely to think that families in Leeds are able to get out and about, do maths, you know, have fun, and it's all completely free. And then in a few weeks the trails are gonna be advertised on a prominent billboard in Leeds, so we're really excited to see how that generates further interest. And then probably my final advice would be to think about how you could get your maths trail known as widely as possible. So have a plan for promotion, particularly with groups who don't usually engage with maths. So yeah, maths trails can also be great at encouraging people to take part in other maths activities after they've finished the trails, such as in Leeds, we hope that the trails will encourage people to visit MathCity Discovery Center, and then get involved in all the other great City of Maths events as well.

Katie Steckles: Cool. Fantastic. I mean, it sounds like you put a lot of work into this. I'm determined now to go and find one of these and try it 'cause I'm over in Leeds a little bit doing things for the City of Maths, so hopefully I'll get a chance to see one of these in action. But yeah thank you so much for chatting to us, Hazel. And if anyone wants to find out more, we'll put some links in the show notes to the maths trails and the City of Maths project and the stuff you've been doing.

Hazel: Thanks, Katie. That's great.

That's all for this episode of the Talking Maths in Public podcast. Head to talkingmathsinpublic.uk/podcast for more episodes, to suggest your ideas for future podcast segments, and to find out more about the TMiP network. Tune into the next episode for more maths on the beach, maths on the canvas, and maths on the go.

David Spiegelhalter: The Talking Maths in Public podcast is presented and edited by Katie Steckles and funded by the International Center for the Mathematical Sciences. The music is "For Her" by Liderz on Pixabay.