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To train the best young math minds in America, Po-Shen Loh cares less about his students’ raw computing power and more about priming them for “leaps of insight.” Loh is the coach of the U.S. team that just won its second consecutive gold medal at the International Mathematical Olympiad (after 21 straight years of coming up short). His goal is like any other coach’s — to have his team perform their best when it matters most, when they face the pressure of competition. To that end, Loh and his fellow coaches train the team in diverse kinds of logical thinking and even bring in mathletes from other countries to train side by side and compare approaches.
On this week’s What’s The Point, Loh discusses his team, explains how he sees the Olympiad victory inspiring people to take up math, and presents a sample problem for listeners to solve (good luck).
Stream or download the full episode above, or subscribe using your favorite podcast app. Below, a partial transcript of the conversation.
Learning new ways to think about math
Jody Avirgan: I read that one of your innovations as coach was bringing in people from the rest of the world to train in the U.S.
Po-Shen Loh: Yes. In fact, when I was on the team in 1999 … [we were] brought to train with the Romanians, in Romania, because the national coach of the United States at that time had grown up [there]. That was very impactful for me. It was really interesting to meet our compatriots from other countries — not in a competitive atmosphere, but a collaborative one.
Avirgan: Are there differences in the way that different countries approach mathematical thinking? I imagine that a lot of people think of math as fairly standardized and universal. So what do you actually learn from another country’s mathematicians?
Loh: You learn things in the same way that you learn from meeting another country’s “X.” Meeting someone from another country automatically broadens your worldview. And especially in the next century, which [these kids] are going to be living in, they will be living in an increasingly globalized environment. So I thought it would be good and healthy for people to start thinking of the world as something much bigger than just the United States.
Avirgan: But are you saying, in a mathematical sense, you’re also learning about a different culture? Would a Romanian approach a problem differently than an American would?
Loh: Actually, they might. You gain from diversity, period. [But] different people also approach different [math] questions in different ways. Some people take a very computational approach, where they know it’s going to work and they are going to do whatever it takes to beat out the answer. Other types of people want to find the most elegant way to see why it’s true. So some people want to solve the question, just to solve it, no matter how messy the solution is. And some people are looking for that insight for why this is true. But that might be a more risky approach, because it might take longer. But you’re very satisfied with it at the end.
Increasing the diversity of U.S. mathletes
Loh: Diversity is extremely important, because you need to see different ideas in order to come up with new ideas. Monoculture is generally not very innovative. So when we choose people for these programs, we actually do it on an anonymous basis.
That said, we do recognize the need to increase the diversity [of the] pipeline [of candidates.] So the first thing we decided to approach was the gender balance because there was a particular inroad we could use. The questions that we [encounter in competition] are not the types of questions you typically see in a school’s standardized test. So it’s entirely possible that there are many people who might not qualify into the training program, under normal circumstances, because they hadn’t had that experience with the standard type of questions. But with another month of training, with more general mathematical techniques, [they] would possibly be very strong.
And so … we specifically brought in women who would be able to experience this [type of] training in a way that they might not have seen in high school. And we found that even if we brought in women who were “below” the normal cutoff, at the end of the program, their performance was in the middle of the pack. Which validates the hypothesis that if we only look at people based on their general performance on things that are close to what they are doing in high school, that may not correlate with their performance when it comes to abstract reasoning and coming up with proofs.
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