Katie Steckles is a math communicator based in Manchester, England. Laura Taalman is a Professor of Mathematics at James Madison University who has been on leave to work first as the Mathematician-in-Residence at the Museum of Mathematics in New York City, and now as Senior Product Manager for Education at the 3D-printer company MakerBot in Brooklyn. Both of them helped organize the MegaMenger worldwide fractal build this past fall. (I helped organize a build with the University of Utah AWM and SIAM chapters.) We chatted on Skype in January. This is an abridged and edited transcript of our conversation. It first appeared in the Association for Women in Mathematics May-June 2015 newsletter. The other interviews I’ve done in for the AWM can be found here.

Evelyn Lamb: We’ll start off with a softball: how did you get interested in math?


Katie Steckles (center) and friends work on a level 1 Menger sponge. Image: Manchester Science Festival.

Katie Steckles: It’s a bit strange for me because when I was at school, there were a lot of subjects that I was into and that I was good at, and I kind of I wasn’t sure what I wanted to do. I chose my A-levels by deciding that I wanted to do medicine. I was watching a lot of ER at the time, and I thought that would be a good thing to do. I think at that age, you don’t really know what you want to do. But I had to pick subjects, and they said that for medicine you definitely need biology, and you probably also want maths. And having done maths to that level, I realized there was so much more to it than we’d done prior to that. That’s when it starts to get really good. Then when I finished my A-levels, I’d gone off medicine. It turns out when you get into something from watching a TV show, it’s usually a phase.

I kind of wanted to pick something that wasn’t going to point me towards one particular career, something that left things a bit open. Because I’d found all of this really cool stuff doing my A-levels, I thought I’d do maths. It doesn’t seem to have a specific job that you go onto from it. There are a lot of options. A lot of people said that having a degree in maths will do you well for any kind of job. If you want to go into management or anything like that, they’ll take a degree in maths as a sign of good intelligence or whatever. So I thought, that sounds interesting. The more I did, the more I wanted to do it. By the time I finished my degree, all of my friends were doing Ph.Ds, which sounds like a really stupid reason to do a Ph.D. But all of us went up together and did Ph.Ds together, and it was great. I was like, really? Do you think I could? I wasn’t sure if I was that good at maths, and everyone was like, of course you are, you’ve just finished a degree in it, you did really well, what are you talking about? And I thought maybe they were right. Because of that, I went on to a Ph.D.

It’s a way of thinking for me. I’ve always had an approach to things that’s been quite mathematical. Maybe without realizing it, I’ve always been a mathematician.

Laura Taalman and friends celebrate their successful level 3 Menger sponge.

Laura Taalman: That’s really interesting. That’s very different from what my path was. I always knew that I wanted to do math, from second grade or something, but I didn’t know what that meant. I came from a little town, so I was always pursuing math, but I didn’t know you could major in it. I didn’t know that you could go to grad school in it until almost the end of college. I was just in this little bubble. I always knew I wanted to do it, but I didn’t really know how to do it. It sounds like you knew exactly what you were supposed to do, but you didn’t know what you wanted to do, so it’s kind of the opposite.

For me, math has always been a very escapist thing to do. I can sit in a coffee shop, and twelve hours go by where I’m not really worried about anything. I really like that.

EL: Both of you now do public math outreach as your career. (I know, Laura, you’re also on leave from James Madison.) So how did you get to the public math outreach career thing?

KS: It was almost completely by chance. While I was doing my PhD, there was an email that went around about a maths outreach project that somebody was trying to put together. It was Maths Busking, a street performance maths thing. It was a bit weird. I like explaining maths to people, and I like making an idiot of myself in the street, so I thought maybe this would work as a combination.

I went along to the first couple of training sessions, and it was really interesting because they were sort of looking at it as an approach of using techniques from street performance and the way that they engage people in that kind of environment to try and communicate maths. If you’re at a conference, and you’ve got a fun bit of maths that you want to show people, you can just talk to people about it, and they’ll say wow, that’s really cool. The idea was trying to take that outside of mathematicians, to take that out to other people as well because we’re sure they’ll find things really cool as well. And that was kind of my first taste of it.

It’s quite an extreme form of maths communication because you kind of walk up to someone in the street and say, hey, do you want to see some maths? And they say, noooo. And then they walk away. You actually have to approach it quite carefully. A lot of the stuff we did was at science festivals and places where people were expecting it a little bit. But we did actually take it onto the street near some real buskers, which was a bit terrifying. They don’t like it when you do busking and don’t ask for money. Then people expect them to do it for no money. We’ve done it in various places, and that was kind of the first thing I did. Through that I met a bunch of other people who do maths engagement.

The first point I really realized it was what I wanted to do for a job was when there was a conference in Manchester that was essentially a maths communication conference. It was called “How to talk maths in public.” They got together everyone from people who give maths talks to people who run things at science festivals to maths people who write books or make TV programs, anyone involved in communicating maths in any form. That was very cool because I got to meet some mildly famous maths people. Simon Singh was there, Ian Stewart was there, and a bunch of other people I’d seen and heard of, lots of people who just do it for a living. I thought, oh, this is a job. This is actually a thing people do for a living. At that point I was looking for something to do when I finished my Ph.D. I wasn’t sure I wanted to stay on in research. I think there was a certain amount of research that I could handle, and I was getting near the end of it. It worked out well. I did one Ph.D and that was it. That was just about the right amount for me. I thought, if this is a job, I’ll give it a go. I’ll give it six months, and I’ll try being a freelance maths communicator. I got a few bits of work through some contacts I’d made, and it worked out. I was quite lucky. I don’t know if it was luck or just the fact that I kept turning up to things, and people were starting to notice who I was. It’s gradually built up into what I do now.

LT: Can you give an example of something you did on the street? I want to know.

KS: We did loads of stuff. There’s a little trick you can do that uses binary numbers where you have little cards with different sets of numbers on each card, and you can use it to guess which number someone’s thinking of. Just by giving five bits of information, you can guess a number between 0 and 31! That was a nice one to do.

You can sort of impress people: “I’m reading your mind. Oh wait no, I’m doing maths!” They want to know how that works. I never had to ask if they wanted me to explain how it works. Some people half had an idea. It was really nice to be able to engage people to whatever level they wanted about things.

EL: Laura, how did you end up working for the Museum of Mathematics?

LT: Well, it’s complicated. I’m solving a two-body problem. 15 years ago my husband followed me from graduate school to my job at James Madison University. He has like the one tech job in our town. He didn’t want that job anymore, so we thought we’d go to New York City and see what could happen.

I’m on leave, not on sabbatical, so I needed to get a job. I’d been working at the math museum on some things. We had a recreational math research conference and other little things. They helped me get a position here so I could work with them this year, which has been really cool. It’s very different than what I’m used to.

There’s a lot more opportunity to talk about math with people with a huge range of ages. At the first workshop here, I had a kid that was 7 and a guy that was 73 or something at the same 3-d printing workshop. So that was really cool.

EL: One of the things that you did there was MegaMenger. You were one of the people behind it, and I know Katie, you did a ton of organizational stuff for it too. So tell me about that fantastic, or possibly terrible, idea.

LT: It was a fantastic and a terrible idea! Katie really made everything happen. It was the most fun thing I’ve done here at the museum. We had a ton of people coming in and making cubes and learning about Menger cubes. It was really exciting. I think it did start from a crazy idea, that somehow Matt [Parker] managed to make happen for real with Katie. Do you want to talk about it? You guys have really been the driving force of organizing everything.

KS: Yeah, one of the people that I’ve worked with quite a lot is Matt Parker, and he’s quite often coming up with ideas for things, and part of my job at the moment is to make Matt’s ideas into things that happen.

Matt ran into Laura at the Gathering for Gardner. I think Matt had vaguely seen me playing around with the business card Menger Sponge before, and he knew it was a thing that I knew how to do. He thought, oh, we could do that. From there, it just snowballed into this thing. You build something out of 20 cubes. If you have 20 of those, you can build a bigger one, if you have 20 of those, you can build a bigger one. He realized that if we just got 20 different people do to it, that would count as the next level up, even if we didn’t bring them together.

LT: He told me that you’d done something where the design of the Sierpinski carpet was actually printed on the card so that the level looked higher. When I heard that, I was like, I’m totally stealing that idea. I’ll go back to the museum, and we’ll make Menger cubes with these cards. We were talking about how you can’t make a level four, how it’s too heavy, and thought, well, there is a way.

He talked about this thing where people made the world’s largest octahedron, standing at different places of the earth. I don’t remember if it was a tetrahedron or an octahedron, but they measured out the coordinates. So this conversation kind of snowballed to what if we made 20 different sites around the world each build level threes? We’d have a level four sitting around the world the same way. Was that a project that you did, this around the world octahedron?

KS: No, that was someone else. I’d not heard about that, but it sounds very cool, to get the right coordinates. We thought about whether that would work for the Menger sponge, but we didn’t know if there was enough land mass. Someone would just have to be on a boat in the middle of the ocean.

I think it was originally Matt who had the idea of printing the Sierpinski carpet onto a bit of card. I was doing small workshops with groups of kids building a level one Menger sponge. Combining all those ideas, it sort of became this behemoth thing.

We put a call out asking who wanted to build a Menger sponge. We knew we’d make one in Manchester, and we could definitely get one in London because Matt knows enough people there. Laura was doing one in New York. We have a friend in New Zealand, and she got the University of Auckland on board. They did it at the local art gallery, and it was a really fantastic community event. Matt’s got some contacts in Canada at the Perimeter Institute for Theoretical Physics, and they were all over it! They prepped beforehand and made the whole thing in a day with a team of 50 people. He’s been out to Finland, and there were some people up for doing it in Finland as well. We just emailed people and asked who was up for doing this. It’s quite a lot of work.

EL: Yeah, it is. I was thinking, oh yeah, sure, we can do that. Then I looked at how many people we had and how much work the level three was, and we decided that level two was where we needed to be.

LT: I told the museum, I want to do this, I want to make this level three Menger cube, and they said, have you ever done this before? I said, well I’ve made a level two, and that was fine. This is just 20 times that, so I’m sure that with a lot of people it’ll be fine. They said, OK, but you have no staff and no budget. It’s a really large project. I was worried we wouldn’t be able to do it until you guys figured out how to get funding.

KS: We had an idea that we would try to get someone to sponsor it because it is a lot of stuff to pay for. In theory, you could get cards donated, but it would be so much effort. We’d much rather have the thing actually work than try on no budget and have it fail because no one managed to get it together. Matt’s technically based at Queen Mary University. He’s the Public Engagement in Mathematics Fellow. Because he’s based there, he got in touch with them and asked if they’d be willing to sponsor it. They were like, would we like our logo on a million bits of card spread all over the world? Yes please. They covered basically all the printing that people couldn’t afford to cover themselves.

It was a lot of work to pull everything together. For a long time, we didn’t even know what the 20 sites would be. I think in the end we ended up with 23 actual sites for building level threes, which is good because if some of them didn’t finish, it would be OK. I was just looking through the final numbers. In the end, we had 17 finished level threes, another 5 sites that had partial level threes, which adds up to a total of two level threes, and we’ve got 23 level two sites, so we’ve got more than a level 4 altogether. There are still a few in progress.

We’ve got all the pictures with the finished ones. It’s just brilliant to see because they all look the same! It’s terrifying that they’re all this identical thing, but that’s the idea, that they’re just all these copies of the same thing.

LT: Tomorrow I get to see one. It’s actually ours, but it moved. We can’t keep it here, so a middle school took it. So one night, we were all walking outside the Museum of Math carrying this giant Menger cube into a moving truck they got. Now it’s at this middle school, and I get to visit it tomorrow morning and see how it’s doing. I hear it’s doing fine.

KS: They sometimes sag a little bit on the joints along the top. There’s quite a lot of weight there.

LT: I like to think that so many people from all the different sites all around the world had the same problems that we did. We’re all these experts in this really restrictive task.

KS: You develop special terminology. Someone commented on that while we were building in Manchester. We were referring to things by names that we’d made up for them, things that made sense to us. They were like, you’re just inventing new terminology for everything. I said, well, that is what maths is. That’s all maths is, just inventing names for things that already exist. I mean, it depends on your philosophical point of view is, but to some extent, maths is all about notation, and it’s all about making names for things.

I’m going to see the Cambridge one on Thursday. They want me to come and give a talk on fractals. It’s got a lot of photos of Menger sponges. On Friday I’m going to the Manchester one, which is just around the corner from where I live, and start to disassemble it. It’s really sad, but they need the space back. I’ve contacted all the volunteers who helped to build it, and at least three or four said they’d like a level two sponge. We’re going to decompose it into smaller bits.

EL: I kept a level one sponge. We ended up accidentally making too many because counting is hard.

KS: I know someone built a coffee table on top of a level two.

EL: What are some of the challenges of math outreach, or the things that are more difficult than you might think they would be?

KS: There are probably a lot of things about math outreach that are exactly as difficult as you expect them to be. Some people just don’t like maths. There’s no real reason they don’t like maths, they just don’t. Maths has a bit of an image problem that you have to deal with from the outset. Different people have different ways of doing that. Mine is just to be relentlessly enthusiastic about maths until people realize I’m not going to shut up and they should probably listen.

I work with a lot of people who do general science outreach as well. There are a lot of techniques that we can share, but one of the big differences is that they’ve got these demos. They’re always talking about what demos they’re using. Are you going to explode something? There are so many different things you can do with chemistry or biology. It’s a bit more accessible for people. They can see something happening. Whereas with maths–to me, this is one of the best things about maths–a lot of it is in your own imagination.

This talk I’m giving about fractals, something I say in it is that this is a thing that doesn’t really exist. You can’t build a fractal in the real world. You can build an approximation of a fractal, but there is a smallest thing in the universe, or at least I’m told by some physicists. There is a smallest thing that there can be, so there’s no way you could ever make a true fractal. There’s no way you can iterate to infinity because you’d never finish doing that. It would take ages, you’d be really bored, and physically it’s not possible. To me, that makes fractals better because they can only exist in your mind.

It’s a challenge in some ways, and it’s also a gift in other ways because that means you get to do things quite stripped down. You don’t need to take a lot of equipment around with you. You can just go and explain things and show pictures. Equally, it’s more of a challenge to engage people in doing stuff because you have to get them to think, and sometimes people aren’t prepared to do that.

LT: Yes, it’s that first hurdle. Once they’re in and listening to you, I find people saying wow, I didn’t think math was so interesting. But to get them over that line where they’re actually listening to something, that’s hard.

The last couple years I’ve been doing all this 3-D printing, which is kind of the opposite of not having things exist. You have to actually make things exist. It’s been really interesting because some things I’ve only thought about in my brain I now have on my desk. In addition, it helps me get people over that hurdle. At James Madison, I was teaching these general education classes about 3-D printing. It’s not a class about mathematics, but they’d be modeling, writing up some code to do something, and they’d say, “Oh, I need to rotate this. I need it to have exactly this many copies and spiral up as I rotate it.” Hm, I wonder what field we could use to figure out how to do such a thing?! And the next thing you know, they have to know about some basic trigonometry or something to make that happen, and they’re interested because they want to make it.

I think some people need a reason to want to know something, which isn’t common for math people. We don’t need a reason, we just want to know about some made-up stuff, but I find getting people over that hump has been easier since I started doing the 3-D printing. They hold it in their hands: what’s this, tell me about this thing that you just put in my hand. They can see it and touch it, and if they want to make it, they need to know something.

KS: I’ve definitely heard people talk about the way maths is taught, because it’s taught in quite a functional way, here are some things you’ll be able to do. You’ll definitely need this, so here’s what you do. I think a lot of people need to have a reason to need to know something. If they can’t see when they’ll need to use it. One approach that’s been suggested has been to find things that people are interested in and show them the maths in them. And that’s what you’re talking about. If they want to 3-D model something, that’s a huge amount of maths, and they need a huge amount of maths to play around with stuff. Until you’re playing around, you don’t know why you’re learning something.

One of the ways Matt puts it is if you’re learning to play football, you’ll quite often practice dribbling a ball around some cones. That’s a fantastically useful thing to practice if you’re going to go on and play football. But if all you ever do is dribble around cones, you think it’s rubbish. Who wants to do that? Until you actually play a game of football, you don’t see the benefit of that. At school, people are often taught maths in a way that means they never have a chance to play a game of maths. Whereas when you’ve got a real-world problem that you want to know the answer to, and you can use maths to get there, that really helps. But it’s a question in terms of maths education of juggling things people need to learn and having good motivating examples, not just ones that are made up.

LT: I really believe that in addition to doing that, and I think you’re saying that too, it’s so important to have the skill of wanting to know something for no practical reason at all. At the museum, we have volunteers who present the exhibits. They’ll ask me, what is the practical application of this that I can tell visitors? And I’ll say that there is no practical application, and that’s the whole point. This is the thing we want to think about. We can stretch and say, well this type of math is used in encoding face recognition or compressing digital files or something, but that’s not why it’s there. It’s there because that’s something people want to think about. And we don’t need to have a reason. Stop asking me what the reason is! We don’t have to have a reason. Why did you write that poem? Why did you make that piece of art? Why did you write that book? What good is your book? Nobody asks that.

KS: A lot of people will ask that question. It’s good to have an answer to the question in case someone asks. For some people, the answer of “because it’s there” isn’t a good enough motivation for doing something. I always equate doing maths with solving puzzles. When you’re solving puzzles, there is a real enjoyment you get in the answer. There’s a real motivation you get to find the answer and get to the end of the puzzle. Or even to just have fun along the way. People will happily do a sudoku puzzle and get that kind of little buzz that you get from having finished something, having solved something. And that’s exactly the thing you get from doing maths.

LT: That’s right, they sit there on the train and do a sudoku puzzle, and they love it. They just don’t know that that’s what they’re doing.

KS: Sudoku’s an interesting one because it is maths, but not in the way that people think it’s maths. The fact that it’s numbers is irrelevant to the group theory, the logic and inference. People associate it with maths even though it’s not maths in the way they think it is.

EL: What is your favorite math to share with people?

LT: My family is really sick of hearing me talk about this. It’s the Euler characteristic.

I had this license plate in North Carolina that said V-E+F=2. So it was amazing. I would drive home, and occasionally someone in my family would ask, what is your license plate about? And I said, well, let me tell you all about it. They’d start to say, don’t ask her! Don’t ask her what it is!

When I moved to Virginia, they wouldn’t let me get that license plate, and I got into a real yelling argument at the motor vehicle department about the license plate. I was like, just type it! You have it right there! Type it in! I can see that you have “plus” on your keyboard, just type it in! And you can’t fight with the people at the motor vehicle department because you’ll get arrested, so I don’t have that license plate anymore.

But I love that simple equation, and I love that it works for any triangulation. It contains a lot of things in math that I think are really important for a beginner to know about. This concept that it wouldn’t just be true one way we divide a sphere up into triangles, but any way we do it. You can give a whole classroom of kids balloons and let them draw any triangles they want. They can even make squares and crappy triangles, and it’s still going to work. Then they can count it up, and except for miscounting, because counting is hard like you said, they all get this pattern. They can discover it. It gets generalized into all kinds of things in homology and Chern classes that they don’t know about. But they get to see that little piece. I like that.

Sorry, I got off on a tangent. The Euler characteristic. I think it’s awesome.

KS: I’m really struggling to think of one thing. I quite often like maths that you can build and do things with. I do a lot of things involving origami and folding. Building fractals, believe it or not, is another hobby of mine. Making shapes, making Platonic solids, all of that kind of thing. Hands-on stuff.

But there are so many things I just love to tell people about. This thing with the binary trick where you add up the numbers. I got one in my Christmas cracker. My dad said, what’s that? And I did the trick for him. He said, oh, that’s really good. How does it work? And I explained it to him. Then my brother came in, and I did the trick for him. Then he asked how it worked, and I explained it to him, and my dad listened to the explanation again. Then someone else came in. My dad said, don’t ask her how it works! She will explain it again!

I just relentlessly want to share with people the things that I find cool. We do MathsJam, which is maths in a pub, and people just bring things to play with. I like it when maths just happens. You’re just getting on with your life, and then suddenly there’s some maths. You’re like, oh, there’s some maths! It’s just fantastic.

My other half is a mathematician as well. Wherever we go, we’re looking for maths. Not consciously, but sort of subconsciously, we’ll see something. “Hey, that’s maths. Wicked!” We’ll talk about it, investigate it. If there’s anyone nearby, explain it to them.