Imagine coming to math class, expecting to do the usual arithmetic problems you’ve been practicing day in and day out, only to find a functioning square-wheeled tricycle standing on a track in the middle of the room. You look around, somewhat perplexed at the audacity of the person responsible for placing the cognitively dissonant creation in an environment normally characterized by logic, reason, and precision. And then you try it, only to be pleasantly surprised by the unexpected smoothness of the ride, and you’re oddly intrigued by the experience.
You may have a lot of questions about why someone would create a square-wheeled trike instead of the usual model we’ve come to expect to see. And Cindy Lawrence, the Executive Director and CEO of the National Museum of Mathematics (MoMath) in NYC, is more than happy to answer them; the square-wheeled trike is currently housed in the organization's main lobby. Seeing the glimmer of interest, spark of curiosity, and sheer delight in the faces of the museum’s patrons is quite literally the reason she gets up every day to do what she does.
First, Lawrence would tell you that the idea for the contraption was originally conceived by Gerson Robison, a mathematician who, in “Rockers and Rollers” (1960), wrote: “Some years ago, while picking up my small son’s toy blocks, I became intrigued with the possibility of finding a cylindrical surface upon which a plank would roll in neutral equilibrium.” Then, she’d go on to explain that he realized that in order to make the trike work, he’d have to use a surface whose cross-section is a mathematical curve (turned upside down) called a catenary. Some 30 years later, mathematician Stan Wagon of Macalester College built a full-size square-wheeled vehicle and a track for it to run on.
The square-wheeled trike is probably MoMath’s most famous exhibit and, arguably, its longest lasting one. Founded in 2012 by mathematician and hedge-fund quantitative analyst Glen Whitney, the museum was inspired by the closing of Long Island’s Goudreau Museum of Mathematics in Art and Science; it was open from 1980 until 2006, when it ran out of money and shut its doors. Whitney was just beginning to explore the idea when he met Lawrence through their children, who attended the same program for gifted math students.
The two bonded over their shared interest, and before Lawrence realized the scope of the project she casually volunteered for, she accidentally put herself on a rather unexpected career path. Shortly thereafter, Lawrence and Whitney tracked down some of Goudreau’s former volunteers and, together, began to brainstorm the new endeavor. They opened the museum four years later, on December 12th, 2012, and it quickly grew into one of NYC’s most popular attractions.
Then, 2020 happened. Although the team was thinking about offering some of its in-person programs online, they were “very busy dealing with a very busy museum.” But, in early February, when the Covid-19 became a growing threat, Lawrence pushed the team to virtualize their events with a new sense of urgency. “We had our last in-person field trip on March 12th, but we also had our first online field trip on that very same day,” she proudly recalls.
Now, according to Lawrence, people "from all 50 states and from more than 100 countries” regularly tune into their virtual events. “We’ve run thousands of programs since we’ve shut down. I think we’ve reached more than 50,000 people,” she explains. “We feel like we are playing an important role in human connectivity. Math is a universal language, and when it’s presented the right way, it’s a universally understandable language.”
ARTpublika Magazine got the chance to speak to Cindy Lawrence about her love of math, journey with the museum, and favorite projects thus far.
How did you first get interested in math?
I’ve always liked math and thought I was good at it. But, I have this very distinct memory of starting second grade and being given a sheet with subtraction problems that required borrowing. I just forgot the algorithm; I didn’t remember how to do it and probably got a zero on that page. I came home from school very upset. One of my parents reminded me that the algorithm for subtraction was borrowing and I was like: “Oh yeah! That’s how you do it.” But, I had experienced complete failure — I didn’t even know where to start — and that has stuck with me over the years.
Two things came out of that.
One is that if we teach math as a series of rules without teaching the understanding behind them, those rules are very easy to forget. Of course, some things are taught as a series of steps, but understanding why you’re doing what you’re doing, makes it a much more engaging topic. What is really important and lovely about math is that there are reasons for what we do.
The other thing is that my teacher could have looked at me and said, “She’s clearly got a problem with math, let’s put her in remedial class,” or “Let’s not put her in a class that’s as challenging,” and I shudder to think about what would have happened to me, because math was actually something I was very good at. So, I think it’s really important to recognize that children learn differently, at different times, and in different ways.
Anyway, going back to my history, other than that one traumatic experience in second grade, I always got wonderful grades. I went off to college thinking that I might be a math major. Although I did very well in my math classes — I never got anything other than an A — I got to a point in my third-year math where, suddenly, I felt like I was memorizing rules again — I didn’t understand what I was doing. No one was explaining the rationale or the derivation, and so math started to lose its meaning for me.
I spoke to one of my math professors, who said: “Well, there really isn’t a great career path in math, so maybe you should just look into graduating and getting a job. Math isn’t the right thing for you.” So, I didn’t become a math major. I went off and had a different major and a different career.
There wasn’t much related to math that was compelling in my life until I became a mom. Once I had kids, through playing with them and talking to them about math, I got the opportunity to reengage in something I’ve always loved in this fun way. Ultimately, my kids got involved with a program for gifted math students, and I started meeting the parents of other children who liked math the way my kids did. Though this network, I ended up meeting a mathematician — the father of one of my children’s friends — who wanted to open a math museum, and that marked the start of my journey with MoMath.
Interesting to think about the experiences of other young female math enthusiasts.
In my role as executive director of MoMath, I’ve spoken to a lot of women who had very similar experiences — they went off to college loving math, thinking they were going to be math majors, and somewhere along the way got turned off to it. Some didn’t see the meaning in it anymore, like me; some didn’t have a strong mentor or someone to encourage them; some had always been the brightest student in the class, mathematically, and suddenly they weren’t — at the university level that was discouraging. For a variety of reasons, there seems to be a common story among women my age who loved math and went off to be math majors, but didn’t end up that way. And then there are women who have virtually identical stories, but who stuck it out for some reason and are mathematicians today. MoMath wants to make sure that there are stories like those.
What about kids? Some really struggle to grasp certain mathematical concepts.
Math is for everybody! I do not believe that there are children who can’t do math. I do believe that in any field — whether it’s math or art or music — there are some children who have natural gifts, but that doesn’t mean that we tell other children: “Well, we’re not going to teach you, because you are never going to be able to do what that child can do, so you must not be any good at this.” We don’t do that. We tell them that if they work on it, and spend time on it, they’ll become good at whatever it is they are learning to do. And I believe the same is true with math.
What is it like to put an exhibition together?
So, let me start by saying that as much as I love math, I did not realize that math had any sort of aesthetic value. I thought of math as arithmetic — crunching numbers, solving problems — and it wasn’t until I got involved with the museum that my eyes were opened to the fact that it is an aesthetic pursuit.
Math gives you a means for expressing yourself, for being creative, and ways of looking for beauty. People who haven’t seen this aspect of math think of it as numbers on a page, it’s black and white, but there is something very elegant and beautiful about mathematics. And part of what we are trying to do is draw those lines and make those connections for people.
We actually have an art gallery in the museum, where we rotate artists. Sometimes we have artists who are very mathematical. Other times, we have actual mathematicians who make artwork. One of the very popular shows that we hosted recently was on the math of origami. A lot of people really like paper folding, and they enjoy the beautiful constructions that expert origami artists make. But, they don’t think about the fact that there’s math behind that.
The New York Times did a piece on the exhibit when it was running. We had things that you would expect to see in an origami exhibit, but we also had things that you may NOT expect to see folded out of paper, like a mathematical version of a grasshopper. Or, even more surprising, an origami skirt and an origami purse — made by a scientist and fashion designer — both of which were just phenomenally creative, beautiful, and really bridged the line between math, science, and art.
We’ve had an entire series that focused on the connection behind math and music. Bobby Sanabria, a percussionist who reimagined the score to West Side Story to incorporate a Latin influence, came with his entire band and talked about the math found in the rhythms of Latin percussion and how it was used for his project. And we actually had Jamie Bernstein — the daughter of Leonard Bernstein (1918 — 1990), the creator of West Side Story — come to talk about her father and the creation of this wonderful play.
I think that for a lot of people, those who don’t understand that math has a level of creativity and aesthetics (beauty) — MoMath is the place where they can discover that. If we don’t show the beauty of math, it becomes boring, repetitive, and without meaning. So, what we try to do, with the exhibits and our online programs, is share some of that beauty. In the first year of doing this, I met a mathematical sculptor, a mathematical dancer, a mathematical juggler, and a mathematical mime!
How difficult was it to convince people to visit a museum dedicated to a subject so many people are intimidated by?
Early on, a writer put out an article in an art magazine about the Math Museum that had a very clever headline: “A Museum of Math? It Just Doesn’t Add Up.” I respected the wordplay of the headline, but I hated what the article said. The whole piece was about how people don’t like math, and how opening a museum dedicated to it was not a good business idea. I was so indignant over the article, I found the person who wrote it and emailed her. I said: “I invite you to come and talk to us, so that we can show you our ideas and some of the demos that we have, and then see if you still think it doesn’t add up.”
So, she very nicely agreed to meet with us, and I showed her some of the things we had planned. She loved it! She loved everything that she saw. And then — I didn’t expect this — she wrote another article; at the end it said that if anyone could do it, we could, and that she planned to be among the first visitors in line when we opened our doors. I was delighted by that turnaround, because she was the perfect example of what we were trying to do. Now, the three most common words that I hear while I’m walking through the museum are: “That’s so cool!”
Out of the exhibits you’ve organized so far, which one stands out to you the most?
I can tell you my favorite exhibit, and my favorite program.
My favorite program was Pythagorize the Flatiron. There’s a theorem called the Pythagorean theorem that has to do with measuring the sides of a right triangle. To cut to the chase, the Flatiron Building turns out to be a right triangular building; if you were to measure it, you could demonstrate that the Pythagorean theorem works. We got the idea to hold the event on December 5th, 2013 — or 5, 12, 13 — which, according to the theorem, make up the sides of a right triangle, a fact you can use to demonstrate the Pythagorean theorem.
We put out an email inviting people to join us to measure the Flatiron Building using glow sticks. Over 3000 people responded! I thought we were going to have trouble getting enough people to go around the building, but it turned out instead that we were more worried about crowd control, permits, all kinds of things. It ended up being such a wild and fun event that even The Los Angeles Times wrote about it: “Some squares sum squares to celebrate Pythagoras.” So, what was great about that event, and what makes it one of my favorites, was how many diverse people came out just because they love math.
There was a couple with a newborn, who is now in grade school and comes to our programs. There was a group of senior citizens; they didn’t come with grandchildren, they came alone and were wearing fun hats that they made themselves. There was a pack of college students, who had designed their own t-shirts and were wearing those. There was a guy who had the Pythagorean theorem tattooed on his leg. There were people of all ethnicities and all backgrounds. The whole thing lasted ten minutes, but seeing the crowd was so wild. So math, I think, is very much about building community. At least with this MoMath event, we really did that.
There’s an exhibit called String Product. This piece of art, located in the center of a spiral staircase that wraps around it, has a lot of “strings,” which are actually electroluminescent wires that light up. It’s my favorite exhibit for two reasons:
We had a different exhibit planned for the area near the spiral staircase, but at the 11th hour, it turned out that we couldn’t build that exhibit, because we didn’t have enough space for what was needed to meet the building code. I suggested an idea for a new exhibit, but the problem with the new idea was that we didn’t have enough ceiling height. We could solve this problem by putting the exhibit on the staircase, where we could stretch it across two floors — from the lower level to the main level. So, I get the credit for thinking of that. But Tim Nissen, our designer, gets the lion’s share of the credit for suggesting we turn a flat, two-dimensional display on a wall into a beautiful, three-dimensional sculpture. This exhibit exemplifies the collaborative effort that it took to build the museum.
The other reason this exhibit is my favorite is because it demonstrates an interesting mathematical principle. You don’t need to know beyond 8th or 9th grade math to understand it, but I can stand there with a kid who has taken geometry and algebra and show them how it works, or I can observe a mathematics PhD playing with the exhibit, and both will experience the same moment of delight when they realize how cool it is. If you’re just learning your multiplication tables, I’m not going to be able to show you the math that I show the PhD or high school students, but you can still push the buttons; if you push a two and a three, a string that represents six will light up. So, a kid in the third or the fourth grade will just view this as a very cool multiplication exhibit and will have fun with it in a totally different way. And someone even younger will push buttons and lights will come on, and that’s about the coolest thing in the world if you’re two or three. What I love about this exhibit is that it appeals to everyone.
Is there anything you’d like to share that we did not talk about?
If you go to Alternative Perspective, you can actually explore our virtual math gallery. We have an artist who is also a very accomplishment technician, who virtually recreated our gallery exactly as it exists. But, if I could leave everybody with one message, one that is especially relevant in today’s world, it’s that MoMath is a welcoming place for everyone — no matter who you are, what your background is, where you are coming from, your prior experience with mathematics, we — in the world of math — welcome you.
Note* All images were provided by and are the property of the National Museum of Mathematics, or MoMath.