## A Peek into MoMath

The National Museum of Mathematics–MoMath–welcomes scores of budding mathematicians and statisticians in midtown Manhattan every day. Michelle Dunn and Sam Behseta talked with the president, executive director, and founder of the museum, Glen Whitney, a former hedge-fund manager with a PhD in mathematical logic. Whitney has built North America’s only math museum, with hands-on exhibits that appeal to the curious of all ages. The museum has created a physical and virtual recreational math community to nurture this generation and the next in their mathematical pursuits.

** CHANCE:** We would like to start off with the purpose of the museum. We are assuming you’re not collecting artifacts, but instead will have more hands-on activities like in the Math Midway, the traveling exhibit you built which has been touring the country.

**Whitney:** First, I want to make clear that when I use the word math, I have a big umbrella for mathematics. It’s shorthand for the mathematical sciences, in which I certainly include statistics and computer science (especially theory of computer science), operations research, and a host of other allied fields.

That said, I think it’s clear that there’s a general misperception of what the mathematical sciences are, what they do, and what it’s like to be involved with them. We want to help cure those misperceptions because there’s a lot to be enjoyed that people are missing out on. We want to share the beauty and wonder that is mathematics. And that’s where some of the physical characteristics that you mentioned come into play. We want to provide lots of experiences and opportunities for individuals who come to visit the museum to be personally involved in a physical way—to have the experience of doing math and enjoying the fruits of what mathematics has to offer.

So we’re not primarily about showing, for example, “This is the first written example of multiplying two numbers.” We’re about people discovering things for themselves through direct hands-on interaction.

** CHANCE:** Glen, why a museum? You could have written a book or done other stuff. Where did this idea of a museum come into play?

**Whitney:** There are a couple of threads to your question. It’s something of a cultural problem we have in this country. Our culture is almost imbued with a streak of—if not hating mathematics, certainly finding it irrelevant and unappetizing. It’s not just that people don’t like it in school. It’s become the field we love to hate, and that has real repercussions in that we can’t fill some of the positions that we need. For example, on the radio driving over here today I heard an announcement that the company MathWorks, which builds statistics and mathematics software, has 250 open positions. I can only imagine that’s probably because of the difficulty they have in finding people to fill those positions.

We have a national need, and it’s a cultural problem, so the way to address it is with a cultural institution. We need to have a visitor center out there where people can see a place that celebrates math, a safe and nurturing place where you can express your love for math and see other people expressing their love for math.

I grew up with a real enjoyment of hands-on interactive institutions that are really as much places to play and explore as museums, places for you to discover things on your own—like San Francisco’s Exploratorium, the Toronto Science Centre, and the New York Hall of Science. These are the types of institutions I had in mind and were an inspiration. I wanted to create a place like that, but one that would show people the wonders of math. If you look around at the hands-on science centers in North America—and there are many wonderful ones—there’s a real scarcity of mathematics.

That’s not to say there aren’t a few institutions out there that have taken math seriously over the years, but they’re few and far between. Generally, there’s not the same rich library of great math opportunities as there are for other sciences—physics, biology, and so on.

** CHANCE:** Who inspired you? We all have our mathematical or non-mathematical heroes. Is this museum a tribute to people who have inspired you and others?

**Whitney:** Well, sure. One person who was pivotal to me developing my love of mathematics was Arnold Ross, who is the creator of the Ross Mathematics Program, a residential summer program currently at Ohio State University for high school students to explore a summer of real math. Without him I almost certainly would not have entered a career in mathematics. He was one of the finest teachers I’ve ever had the pleasure of learning from—in particular, his ability to make a fact that perhaps he had taught 100-200 times before seem wondrously astonishing, like a newly-made, incredible discovery every single time. I ended up being involved in that summer program for about four years and every single time he would come to the topic conveying that same sense of wonder and newness and amazement—every single time. And that was a real gift.

Until going to the Ross summer program, math was something that came relatively easy to me—the elementary parts of mathematics. One of the great things about math is there’s a problem to challenge anyone, regardless of your particular level. You can find a place where there’s a question that probably nobody has ever worked on before. It’s at a level that you have the opportunity to attack and make real valuable progress. So the elementary parts came relatively easily for me, but they held no particular fascination for me. I think part of it is how it’s presented in our schools. It’s presented as a tool that you might use to do other things, but never something that is intrinsically valuable, beautiful, or worthwhile in its own right. That was the missing piece of the picture that I got in my first summer at the Ross program. That’s when I fell in love with math.

Obviously, I was also inspired by the example or notion of Paul Erdös, the itinerant mathematician who traveled the world solving problems and posing problems for other mathematicians. I was inspired also by Andrew Gleason, a professor at Harvard where I was an undergraduate. I had the pleasure of working with him as a course assistant. That was another very rewarding experience.

** CHANCE:** With this museum, very young kids could be exposed to real math problems that challenge them. Is that part of the goal for the museum?

**Whitney:** Certainly. A significant part of the goal for the museum is to provide a broader picture of what math is, what it comprises. We want to show that in a wide variety of ways. There will be more hooks and more places where people can say, “Wow. That’s interesting. That’s fun. I enjoyed trying to figure that out.” People can have that feeling of “Aha!” when they fit pieces together or figure out a pattern or create a new image no one has made before. That can be addictive. I think there’s something innate about the joy of discovering the unknown. That’s why there are people who want to climb a new mountain or find a new cave or go someplace nobody’s been before.

I think the joy of discovering the unknown is innate, and these days math is one of the easiest places you can do that. The amount of equipment and preparation you need to be truly mapping out unknown territory is more accessible in mathematics than in any other human endeavor.

** CHANCE:** How do you plan to reach people outside New York City, to talk about the museum and the message you just mentioned?

**Whitney:** As a newly designated national museum in mathematics, there’s a lot of ground to cover. There are a variety of strategies, and one is our traveling exhibitions. Obviously, you’re familiar with the Math Midway, and it will continue to tour well into 2014 at least. We plan to continue to always have at least one traveling exhibition. We’ll have a different focus for the next one. We also want to have a virtual museum.

Some museums these days start virtual and try to go physical. We decided to go the traditional route and start physical and then put out as many different online activities connected with the exhibits and museum as we can over the months and years following our opening. We also want to connect communities of mathematicians and learners. Some of the exhibits and museums are specifically designed to work well in engaging people at a distance.

I’ll give you one example. We have an exhibit called the Math Square, which is essentially a JumboTron flat on the floor displaying up. You can walk right onto it and it’s equipped with sensing technology, so it’ll know the location of everyone who’s standing on the floor. We have a variety of exploratory mathematical activities on that floor. We’ll have mazes that have special rules or maybe a lot of turnstiles that trigger changes as you walk through them. It shows the notion that math is about exploring the consequences of simple rules.

So the maze might look very simple, but then there’s a rule attached to it that turns it into a much more complex and challenging exploration of the consequences of that rule. Or we’ll have a fractal explorer where as you walk you can explore fractal canyons. Or we will have some graph theory examples: find the shortest path that connects up all the visitors who are on the floor, and as the visitors move around, see how that changes—lending some insight into the structure of the graphs.

Those are just some examples, but math is such a wide open field. That’s part of our point. There will be an API (application programming interface)—a system by which groups can submit their own activity to be displayed on the Math Square floor. We will invite submissions from across the country. And we’ll have a curation process, of course. If one group’s exhibit is selected, we’ll give them the opportunity through live streaming video where the class can see another group in the museum interacting with their creation and get feedback about what these other students experienced as they explored whatever puzzle, problem, or illustration the originators created. We’re looking forward to that as a way of connecting people from around the country.

The museum community in this country is extremely collaborative and welcoming. That particular idea for connection came from one of our trustees who runs an institution called Science House. Science House distributes digital microscopes so you can put microscope pictures online, and they’ll foster distance communities of these people working with the same instruments and sharing what they find with them.

We are trying to be proactive with incorporating crowdsourcing into our museum. We think it’s a strategy that’s proven itself in a number of areas. So we’re trying to be in the vanguard. I’m sure other museums have similar efforts, but it is an area of focus for us to try to make this your museum in lots of different ways—for individuals and groups to inject content. Besides the Math Square, you’ll be able to design your own version of the MoMath logo. If it’s received well by other visitors and our curation staff, you may find one day when you come to the museum that the version of our logo you generated is above our doorway.

It’s another one of many examples of how we’re providing opportunities for visitor-generated content to become a part of what others experience.

One of the ideas that’s been simmering on the back burner, and hopefully we’ll get the staff and funding at some point to pursue, is a mathematics laboratory kit. We can reintroduce physical experience into mathematics curriculum at a variety of levels around the country. We have laboratories in physics, chemistry, and biology. It would be a great benefit to people in making the lessons vivid to have math laboratories as well. Obviously, teachers need the tools to be able to do that. That’s a niche we’d love to fill.

There’s such a divide between symbolic manipulation and technique- and procedure-based learning and the world around us. It injects meaning, excitement, and value into all the manipulations. Math can be a force for bridging that divide. And that’s important in statistics as well, I think. Statistics is critical in giving us the tools we need to understand and appreciate the phenomena that we observe. If lightning strikes, is it going to strike again? We need statistics to tell us the degree to which we can rely on our observations.

** CHANCE:** I’m glad you mentioned statistics because the foundation of statistics, one would argue, is the language of probabilities. And counting and combinatorics are tightly related to probability. Are there exhibits along those lines at the museum, allowing the audience to explore various counting methods and probability calculations?

**Whitney:** Indeed. I will tell you that it was an absolute must for us at the museum to include at least one or two exhibits on probability. Probability exhibits pose a special challenge. The very nature of probability is that you don’t control the outcomes. You try to understand and classify and say things about inputs, outcomes, and aggregates. But each individual visitor has his or her own experience. So if you make some general statement—”It’s likely to come out such and such a way”—and even suppose you arrange the exhibit so that 99 percent of the time it is going to come out that way, you get one percent of your visitors having a different experience. And if that experience contradicts or undermines the general principle, then you have a recipe for ensuring that one out of every 100 people who come to the museum go home either not quite understanding the point or saying, “That exhibit was all wrong.” So we did struggle with it.

In the end, we planned for two exhibits that were directly focused on probability. And then unfortunately, because our exhibits are so much on the cutting edge and we’re pushing the envelope of hands-on interactive fabrication, and getting our fabricators to do things that in their own words, “We’ve never done anything like this before,” we ended up only having the funding for one of the two exhibits to go forward for opening day.

So we hope eventually to be able to bring the second exhibit in. But the exhibit we are going to have is the Moody’s Foundation Edge FX. You may be familiar with the Mathematica exhibition at the Boston Museum of Science. It’s also in the New York Hall of Science. It was at the Chicago Museum of Science and Industry and at the California Science Center for many years. It’s designed by Charles and Ray Eames. So there’s a large Galton board in that exhibit, a grid of pins and balls that come down and can go 50/50 at any pin. Approximate binomial distribution comes out from these accumulations of 50/50 chances. Edge FX is an exploration of the same principle. Again, it’s a Galton board. A large number of balls will come down through an array of pins. But in this case, you are equipped with a large lever which you can shift left and right that introduces a small bias—the same small bias at every pin. So now you explore if you could tilt the odds in your favor or if something was tilting the odds against you, what would happen?

And we couch this in the terms of profit and loss in a financial transaction. So if you’re buying and selling stock, imagine instead of there being a 50/50 chance that the stock you buy goes up or down you can pick things well enough to say there’s a 50.5 percent chance that things will go in your favor and only a 49.5 percent chance it’ll go against you. Well, what’s your profit and loss going to look like now? With many events—even if it’s a very tiny bias—visitors will be able to see and directly experience the way the balls end up shifting the normal distribution. They can see if there’s a very small bias, one’s expectations of earnings really change quite dramatically.

** CHANCE:** That’s wonderful, because that borders on probability theory and decision theory. The foundation of decision theory is essentially to optimize your gain through the language of probability.

**Whitney:** We are actively seeking math professionals to submit explanatory content around our exhibit. We have many folks volunteering their time to make sure the mathematical materials and descriptions running all of our exhibits are as rich as possible. So if you know any statisticians who might be interested in submitting related content, we’d be more than happy to involve them in that project.

** CHANCE:** As far as the probability exhibits go, there was one in the Math Midway with a spinner, “House Takes All.” It seems like you were trying hard to not use technology so much in an obvious way and have things be hands-on and physically engaging. That is an exhibit that would really benefit from the use of technology to accumulate the spins that have happened all day or week long.

**Whitney:** Absolutely. That’s been another strategy we’ve discussed about probability exhibits, to make sure we have running totals. We’re going to be using that strategy in another exhibit I should mention in the context of statistics in the museum. It’s called Hoop Curves. You take a regulation free throw set up—ordinary weight and size basketball. And then we have tracking and sensing equipment so it can determine the velocity of the ball when it’s released from your hands, the inclination above horizontal you threw it at, whether you had any left/right angle to it, and the height that you released it at.

We will accumulate that data over many, many visitor throws, as well as any celebrity throws—specially marked in our database—then you can explore this data set live in the museum, including highlighting your point of throw in there. There are a number of tools with which to analyze the data, various scatter plots, 3D, point plots, histograms, and so on. So each visitor can make an effort through analyzing the data to determine what seemed to be the ideal parameters for a free throw. Then you can try them out with a ball bot which will accept an angle, a speed, a height, and shoot the ball for you with exactly those parameters and you can test out your hypothesis.

So that theme of exploring large data sets is a very important trend. I was at a recent meeting at a conference called Sci Foo. One of the big buzzes of the conference was giant data—very large data sets, data mining, data exploration, and so on. We obviously wanted to include that real modern thrust in mathematical and statistical practice in the museum.

** CHANCE:** Big Data is certainly a focus within the government. Just this spring the White House Office of Science and Technology Policy rolled out an initiative on Big Data.

**Whitney:** One of the things I want to say in that regard is that the world becomes ever more complex. There are a lot of forces driving things toward greater complexity. As that becomes the case, the need for systematic disciplines, investigation, and understanding these complex systems becomes greater and greater. But that’s another definition of mathematics—the discipline and systematic exploration of the essence of a complex system.

** CHANCE:** I want to wrap up with the future. There is a bit of the history of MoMath on the website, but what’s in store for the future of the museum? Do you have plans for expansion? What are the major challenges you see ahead?

**Whitney:** The plan is for the museum to be wildly successful and popular and people will be beating down the doors. It will become obvious enough, with our many supporters, that we’ll need a far larger and more permanent place. In about 10 years’ time, we can raise about $250 million and buy a permanent home in the city. That’s the plan. But with all plans like that, one has to have a variety of other options. That is our aspirational plan.

We’re doing physical first and then will do virtual to maximize our outreach. I can’t tell you how many places we’ve gone where people said, “You should be opening here instead of New York”—Dallas, the Bay Area, Boston area, L.A. area, Allentown, Penn., etc.

We actually had one small organization say, “Could we join as a branch of you guys?” We were not yet far enough along in our development to take that on, but it was a very touching suggestion. So there is certainly the possibility of opening branches.

Most importantly, we need to reach people who are going to reach more people than we can actually accommodate coming through our doors. So reaching teachers through professional development—and entering the fray of how we should be getting our young people across the country thinking of mathematics—is definitely a long-term aspiration of the museum.

** CHANCE:** I completely agree with reaching the teachers. They’re the ones who are with the kids every day. Going back to the branches—if your exhibits were physically more spread out, then it would be easier to reach more teachers who would then reach more kids. The branch idea sounds great, especially if it could be put in as part of another museum where there are already a whole lot of people going in—the Boston Museum of Science or—

**Whitney:** Well, the Boston Museum of Science is completely redesigning its mathematics offerings altogether. We certainly have tried to make it known that we’d be happy to partner with them in that. But many museums prefer to do things themselves. And more power to them. We just want to make sure everybody knows that we’re standing by and ready to help support those kinds of activities when people do them.

** CHANCE:** And now that your museum has opened, people will be beating down your doors to ask for your help.

**Whitney:** That would be great if it does happen. There’s really a need for more innovative, engaging, and physically interactive math content out there in the world. We think we have a lot to offer in that regard.

** CHANCE:** We just want to thank you very much for your time and wish you good luck. This has been very enjoyable.

**Whitney:** I’ve enjoyed it as well, Michelle and Sam. Thank you so much for taking your time and helping us spread the word about America’s only math museum and New York’s newest and most exciting museum.