# Dialogue with Stephen Bates: In and Out of Math World

Stephen Bates, a Global Academic Fellow (GAF) of NYU Shanghai graduating from Faculty of Mathematics at Harvard University. He was the tutor on my Calculus course last semester. During the conversations with him, I gradually found that he did not belong to the category of so-called ‘math geeks’. So after a discussion with him on math, I started this conversation with him on the work of GAF.

*Y＝Yue Sun / New York University Shanghai*

*S＝Stephen Bates*

Y | Why do you decide to take a gap year?

S | I decide to take a gap year because I had never lived somewhere else in the world. I have only lived in US and only visited Canada. So I want to go somewhere else and to see what life is like in different place. I thought it would be a good time to do it to take a break in between. I just finished my undergraduate last spring, and I will be in grad school next fall. So I thought it would be a pretty good way to take a break and see a different part of the world and different people.

Y | Why did you choose China?

S | I want to see what life is like in China. A ton of people live here, it is a very important place in the world. I found this opportunity at NYU Shanghai, which seemed to me a really good fit because I kind of still have my foot in the door of university and meet a lot of people that way, and I get to live in Shanghai and have other sorts of interests.

Y | So back in Harvard, why do you choose to major in Math? There are some stereotypes Math and Physics students being geeks…

S | Are we geeks? (Laugh) Well, so I knew I like Math when I went to college, I guess it’s kind of a “nerdy” thing. But I just kept taking Math classes because every time I took them I thought they were really really cool. So I would sometimes went sit in one class and thought it was really cool and I just ended up taking that class. I didn’t know I wanted to be a Math major. But the more I kept taking Math classes, the more I liked it. So I just never really stopped. I guess it’s a little bit nerdy, but it is pretty useful in life to be a little bit of a nerd. I guess, you can know a lot of things and be able to deal with computers, numbers, or analytical things.

Y | So how do you like being a GAF here in NYU Shanghai?

S | So the things I like being a GAF are, first of all, I get to live in a really cool spot in Shanghai, so I can go explore the city and see lots of things. And at the same time there are a lot of students which, to me is cool, because I don’t speak Chinese, but I get to meet students who are from across China and other parts of the world. You get to meet people both from China and from everywhere else. You get to meet a ton of cool people. And also there are all the other GAFs here to hang out. So it’s like, if I need a people, for example to take a trip to Japan, I can go talk to the other GAFs. So definitely the other people are the best part of being a GAF.

Y | Last semester you were my Calculus GAF, so how would you see, from your perspective, the difference between the Chinese way and the other way of doing Math?

S | So I think, definitely if you look at the preparation of the average student from high school, it varies quite a bit from country to country. At NYU Shanghai we have Chinese students and American students who make the majority of the school, which may be the two most obvious places to look. I think it is definitely quite noticeable that the Chinese students have a lot more practice with certain things, a lot of practice in doing the algebra, calculation. In general they are much more mathematically prepared. The differences are a very big deal at the beginning of college, but then as you go along, the differences don’t matter so much. So by the time you are already a junior or senior, the work that you do in college is much more important than the work that you did in high school, so that kind of takes over. Maybe the Chinese way of doing Math and the American way of doing Math, I am not sure I have a really good feel of what the difference is. I think that, from what I have seen, American high schools tend to emphasize intuition a little bit more, so many more like having a rough idea of what things mean. While the Chinese schools, maybe, focus on knowing exactly how to get all the pieces together, being precise. I am not so sure about that. (Smile)

Y | So you started the Math Society, what is your incentive of starting that society?

S | I wasn’t the only one who started Math Society, actually when I came this fall there were quite a few people were excited about it. So there are a couple of professors who found out that I was interested in starting Math Society. We are all interested in starting a Math Society. I think the reason that we have Math Society in NYU Shanghai is that it gives people who have the similar interests, which you called geek interest before, like a place to come and share these interests. If your roommate studies Political Science or something else, you may not be able to have a Math conversation with your roommate. But Math Society is a place where everybody can come together and share these interests. And also maybe Math Society can start to show other people the interests. Maybe your roommate who has never been interested in Math will ask you about Math because he/she sees the Math Society has all these pretty cool people talking about cool things. So there are a lot of good things that the Math Society does and the student leadership is now taking over the Math Society. So I don’t do very much work except telling them how awesome they are, which is really cool to see the student energy.

Y | I saw your winter project’s poster, you did something about topology. Can you say something about it?

S | Sure. GAFs have this thing called Winter Fellowship Project, so over the winter when students are all gone, we are at various places but we work on some sort of academic projects for NYU Shanghai. The one I was working on was 3D printing some topological shapes. Topology is a branch of Math, it kind of focuses on abstract shapes, how to bend shapes into other shapes and consider the same. You are trying to find out what different shapes are there if you are allowed to bend anything you want. So I was able to use the 3D printing in the IMA Lab, and 3D printed out some little shapes, so that was really cool. It’s fun because you can take these abstract mathematical shapes and print out a model and you just hold them in hand and spin around. It is a great tool to explain some of the interesting things about Math to other people. It’s interesting.

Y | So can you be more specific about that? Because I am kind of interested in that.

S | Sure. I wanted to print out the shapes that would be most relative about what you learn in the first course of topology. As an undergraduate, you may take one course about topology in your junior or senior year if you are a Math major. So I printed off one of my favorite shapes that I was able to 3D print. It was the hypercube. Hypercube is like a cube in multiple dimensions, so I was able to print out a 4 dimensional cube.

Y | Wait! How can you print something in 4 dimensions?

S | (Smile) How can I print something in 4 dimensions? Well, I guess, strictly speaking, what I did was that I printed a 3 dimensional representation of a 4 dimensional object. So of course I cannot actually print something in 4 dimensions because we only have 3. But you can print something sort of like sketching. If you imagine sketching a cube on a piece of paper, what you’ve done is that you have made a 2 dimensional representation of a 3 dimensional thing. Your piece of paper is only 2 dimensions but you draw something that is 3 dimensions, which is represented from 2 dimensions. That is kind of what you do when you print out this hypercube. You have this 3 dimensional object, but it is a representation of a 4 dimensional cube. It is a good way of picturing a 4 dimensional cube because our brains are not designed for 4 dimensions directly. I was also able to print off this thing called the Mobius strip, which is something a lot of people have seen at various points. When you have a model and you can hold in hand and play, it’s kind of fun. So the cool thing about the Mobius strip is that it is a 2 dimensional object, but it only has one edge and one face. So if you imagine taking your hands or putting your fingers on the edge of the Mobius strip, if you drag all the way around, you can hit every single part of the edge and back at the same point. And if you put on the face of the Mobius strip, like the flat surface, you can drag your finger on to any point on it without lifting it up. So it is kind of a bizarre shape because most of the shapes you used to have are two sides and four edges, something like that. But the Mobius strip only has one face and one edge. So those are the two cool things that I was able to print off. I can talk forever about this, you will eventually get bored of hearing topological shapes. (Laugh)

Y | So I learn that you like hiking and all the outdoor activities?

S | Yes, so I definitely like going outdoor as much as I can. That’s one thing that it is a little bit harder to do it in Shanghai, because you are surrounded by miles of miles of city. But I really like climbing up mountains. Just getting outside and being active. So next year I will be in California, and I am really looking forward to having trips in there. Go hiking, you know, all those kind of stuff. I am not sure why it is so much fun, I don’t know if I can really describe it in words. But it is pretty cool when you get to the top of the mountain, look out, and see everything around you. And it is just a lot of fun to be active. If you spend a lot of the day sitting around doing brain work, thinking about things, typing things onto computer, when you get out, you get to move around and do physical things. It is kind of refreshing.

Y | Have you been to any mountains in China?

S | I went hiking once with some other GAFs, I think it was in Zhejiang province. That was really fun though. I am going to Huangshan pretty soon I think, hopefully. And I think it would be pretty fun to come back and go hiking on the Great Wall for a week. You know, walk on the walls, sleep in a little town, and walk. Because the wall goes thousands of kilometers.

Y | Do you have any plans after this gap year?

S | So next year I will be doing PHD in Statistics at Stanford. I guess, for me, I really like Math in quantitative things, and statistics is sort of a way to connect quantitative ideas with more real world applications. Math research is sometimes a little bit more abstract and you cannot directly feel why it is useful or what the applications are. The applications are there but they maybe not come for a little while, they are a little bit farther on the road. I feel statistics the connection is a lot more immediate, you can always feel, for the research, if you are kind of discovering new things, you can feel that it is very directly useful for doing a project with like genomics, medicine, economics, or something like that. I feel that it is something very immediate useful.