On July 5, Americans around the country rejoiced when the women's World Cup team brought home the gold medal, beating out 23 teams for soccer's greatest prize.
At the same time, in Chiang Mai, Thailand, another American team was competing for victory. But instead of taking on 23 teams, this team took on participants from 103 other countries. And they won.
For the first time since 1994, six American teens won the International Mathematical Olympiad - edging out front-runner China in a grueling battle of the minds. The contest consisted of only six questions. But the catch, according to coach Po-Shen Loh, is that "you kind of have to be a genius to answer them."
Loh and two team members, 18-year-olds Ryan Alweiss and Yang Liu, join Here & Now's Meghna Chakrabarti to talk about their victory.
On the moment the team learned it won
Ryan Alweiss: "The moment that we found out that we won, most of the U.S. team was downstairs in the lobby of our hotel. So what happens is, right after they finish deciding on the results, the [International Mathematical Olympiad] people upload them all on IMO Official. So we checked the page, we refreshed it a bunch of times, finally it showed up. We clicked country results, the U.S. was on top, we all just started screaming and yelling that the U.S. won, so it felt pretty amazing."
How the United States team approached the competition
"It's hard to describe this to people who don't do math, but there's this sort of ineffable beauty with mathematics. It feels very good when you solve a problem, it feels like you've accessed this kind of truth."Ryan Alweiss
Po-Shen Loh: "So what they had to do was solve just a few questions, six questions, and they had nine hours to do so. The only catch is that, in order to solve any one of them, you have to be kind of a genius. So in some sense, there are many countries in the world who struggled to solve just a few. In the United States we're fortunate to have a fairly strong mathematical program and the Math Association of America. So I would say that, in order to solve these questions, in some sense, one doesn't need to know too much advanced math beyond what's in high school. In fact you don't even need to know calculus. But you have to think much harder about that math. And the analogy that's often used, to help listeners understand what's going on, is that, when you look at Olympic sprinters, in some sense, they're just running. My kids know how to run. But there's a lot more to running in the sense that you could deeply understand and even train your body how to drive far quicker, far faster than anyone who's an amateur or just a casual practitioner, so to speak."
On being drawn to mathematics
Alweiss: "It's hard to describe this to people who don't do math, but there's this sort of ineffable beauty with mathematics. It feels very good when you solve a problem, it feels like you've accessed this kind of truth. And it's very fun to trial the approaches, some might not work, some might. It's like a puzzle: you're working on something and you get to something."
Yang Liu: "I kind of see it like, I don't know, some sort of like digging or mining. Most of the time, when you're digging for jewels or gold, you're kind of searching around, but you're most likely not to find anything. But if you start digging in the right direction, you might find that new idea, and that's like the gem."
The coach's role in a mathematical competition
Loh: "I should say that, a lot of the training is actually done by the students themselves. So in some sense, my main objective is to attempt to inspire them as much as possible, because I feel that, in this day and age where resources are everywhere on the Internet, you could actually drive yourself to an extremely high level even if you didn't have an in-person coach."
"However, what an in-person coach hopefully can provide is some sort of inspiration to cause you to want to do this. So my goal is actually to try to communicate to as many people as possible how interesting all of these things are to do. and at the end of the day, they will go far beyond me. For example, all of the team that have been representing the United States in the past few years, are much stronger than what I am. And in some sense, it's not what I can teach them that's valuable, it's what I can maybe communicate about the point of what's going on that's useful."
On beating defending champion China
Alweiss: "China's been the perennial winner of the IMO. They lost in I think 2003, 2007 and 2012, but other than that, they've won basically every IMO in recent memory. So wining the IMO is in our minds kind of equivalent to beating China, because it's extremely unlikely that we'll beat China, and then some other country will beat China and then also beat us. So in our minds, sort of winning the IMO and beating China go hand in hand, because China always, quote-un-quote always, wins."
Try A Sample Question From The Competition
Determine all triples (a, b, c) of positive integers such that each of the numbers: ab-c, bc-a, ca-b is a power of two.
Only 5 percent of the competitors got full marks on this question, and nearly half (44 percent) got no points at all. On the U.S. squad, four of the six team members solved it correctly.
This segment aired on July 24, 2015.