Once upon a time, there was a boy. A very accomplished boy. A senior from Acton-Boxborough Regional High School.
He loved math.
One day, he went to Washington D.C., where he and 39 other seniors showcased their incredible prowess at math and science.
There, he was deemed a finalist in the 2012 Intel Science Talent Search.
Who is this boy? Who could possibly exude this much knowledge, that of one far beyond his years? This boy is our very own Xiaoyu He.
I could go on about Xiaoyu’s accolades. I could talk about how he’s been a semifinalist at the Siemens competition, or how he’s a two-time International Math Olympiad gold medalist. I could talk about how, at the IMO, Xiaoyu was one of only six high schoolers in the entire country who were selected for the team, and how he bested 500 of the brightest young minds in the world.
But this is a different story.
This past year, Xiaoyu did research on rotor-routers at the PRIMES program at Massachusetts Institute of Technology. There, he completed a 20-page paper on his research and was encouraged to enter the Intel Science Talent Search, a nationwide competition for high school seniors.
Xiaoyu was one of 1,839 high school seniors who submitted their work into the competition. From there, 300 semifinalists were selected in mid-January. At the end, 40 were selected from across the nation to congregate in Washington D.C. for a week of gruelling presentations and nerve-racking interviews.
But it wasn’t all business. Two days of the week were devoted to the actual competition. On the other days, the students had dinner with famous scientists, went bowling, and even got to meet President Obama.
However, Xiaoyu did not place in the top 10. 17 year-old Nithin Tumma from Fort Gratiot, Michigan ended up winning with his research on breast cancer. Still, Xiaoyu went further than even he had intially expected.
No one else can articulate his thoughts or do his work justice. So here’s the man himself, adapted from an interview I had with him.
AD: Could you explain the rotor-router model to me in layman’s terms? Like what exactly is it?
XH: Basically the point is to have a deterministic way of moving around a network. A network is defined as a set of points and arrows between those points. They could be anything from a computer network to standard 3-dimensional space. A particle moves from a certain point, called the source, along these arrows until it ends up at a target. This entire process is called a walk. […] The rotor-router model is basically a rule for how to move around in the network.
At each point, you have a rotor that points along one of the arrows and whenever you enter a vertex [a point] you shift the rotor and move out along the new direction. […] The model is capable of simulating these random movements, which is very interesting because our intuition as mathematicians is that such a simple rule would not produce such complexity.
AD: Oh, how will this benefit mankind? What are its applications?
XH: It has major implications in complexity theory, graph theory, avalanche prediction, and fractals.
AD: Um, I don’t really know what any of those four things are…
XH: Darn. So here’s how a snowflake forms in real life: a speck of dust drifts into a cloud, and droplets of water accumulate randomly on the dust and freeze. They are essentially particles performing random walks and stopping where they make contact with the current snowflake complex.
Now if we replace the random walks with rotor-router walks, you can actually have a simple deterministic process that produces surprising fractals. “Fractal” is the math word for super-complex pattern. Snowflakes are a classic example.
AD: So how did you discover the topic of rotor models and why did you decide to write a paper on it?
XH: I chose it because I love discrete math because it is more intuitive and relatively young, so there is much more foundational work to be done.
Because it is a math project, my research involved a lot of paper-and-pencil derivations and experimentation. I also wrote an extensive code to generate and analyze data about the problem.
The mathematical research process involves mainly exploring and conjecturing results and then searching for deductive proofs thereof.
AD: How long did your research take?
XH: The research took about half a year. The writing took about a month off and on.
AD: Can you tell me more about your experience in D.C.? Maybe more specifically, what were some highlights of the trip? How was meeting with the president?
XH: Oh, hmm. We got minor planets named after us. We got books signed by Brian Greene, who’s a boss at quantum mechanics. We also got Steve Jobs biographies, signed by [author] Walter Isaacson, not Jobs. Obama’s hands were very soft. I don’t know what else.
AD: Wait, planets?
XH: Oh so a “minor planet”…
AD: Yeah, Obama’s not into basketball so much anymore.
XH: …is a euphemism for a small asteroid. They have around 300,000 to name. Now there’s one called Xiaoyuhe, which is around 4 km across. Woot.
AD: Nice! […] So what exactly did you do at D.C. in terms of the competition? Just presenting your research on rotor-routers?
XH: Essentially we spent most of the two days getting interviewed by random scientists about general science knowledge. Then there was a day of public presentations. Three hours to the judge and three hours to the public. You get graded on presentation skills. I don’t think I actually explained any serious aspects of my math at all though.
AD: But you still had a good time, right?
XH: Oh yeah. The [other finalists] were pretty smart and fun. It was a very friendly and noncompetitive atmosphere. I think we all realized the absurdity of grading bio people on their understanding of matrix eigenvalues.
AD: Bio people? Matrix eigenvalues?
XH: Yes. I mean, it doesn’t make sense to interview and judge someone who studied the short-term effects of cholesterol on Aquaporin 1 active transport with their knowledge of matrix eigenvalues.
AD: Oh you got judged on things unrelated to your project too?
XH: Yes, in fact that was the bulk of the events at D.C. There were four 15-minute interviews with a panel of three scientists. You sit there sweating as the first guy asks you about whether cholera has vaccines. The second asks you why pirates wear eyepatches and how to orient a satellite against solar wind. The third asks you to talk about the chemical composition of glass.
AD: Haha did those things actually happen to you?
XH: Yes. That’s just a small sample. there was no way to study since the questions were so random.
AD: What do you enjoy doing outside of math and science?
XH: Art. I’ve taken three art classes, and I’m in Junior/Senior Portfolio now. I also enjoy video games and do programming occasionally. Otherwise not much.
AD: Your plans for the future. Do you know what you want to study in college and beyond?
XH: Probably math.