A teenage whiz's mastery of math

IN MY OWN WORDS

Mathematics always came easily to Tiankai Liu, 18. He grew up in Silicon Valley, the child of software engineers, surrounded by math and science. In middle school, he competed at math olympiads against hundreds of students.

While at Phillips Exeter Academy in New Hampshire, Liu earned two first-place finishes in the USA Mathematical Olympiads, two gold medals in the International Mathematics Olympiad, and two gold medals in the International Olympiad in Informatics, a contest in computer programming. This fall he will enter Harvard University as a mathematics major. Here, in his own words, is how he accomplished so many mathematical feats, all while working on the school's newspaper and watching French movies, ignoring the subtitles.

When I was in junior high, I attended the math circles in my community, where there would be a professor who would speak about some topic of interest that was accessible to high school students for two hours every week. Those helped to prepare me for the math olympiads. . . . The problems involve proving some sort of statement. They aren't just short-answer or multiple-choice. . . . I'm usually cool and confident going into the test. How I am when I come out depends on what happens. But for me personally, I think the amount of rest and food I get are very important to me. It's actually quite surprising. If I'm not well rested, then I can't really feel it, but it just happens over and over again that I score less well if I haven't had enough sleep. For me, it's usually eight hours. Before the competition, for various reasons, for jet lag and how excited I am, it's pretty impossible to get too much more.

I've decided to go to Harvard, and the plans currently are to major in mathematics there, but not necessarily to pursue that as a career. I think there are other possibilities out there that I want to consider. . . . I have a lot of other dreams of varying degrees of feasibility . . .

Some people think that math is a set of arbitrary rules that one has to memorize. For example, multiplication tables or the quadratic formula. But I think people should be taught and realize that in reality, everything in math is there for a reason. Everything is built on logic, and some people are intimidated by the amount of abstraction in it. Abstraction is always done for the purpose of illuminating the basic reasons behind concrete phenomena. And if people realize it's possible to develop an intuitive understanding of abstractions, I think that will aid greatly in one's appreciation for math.

I haven't gotten to the point where I see my friend walking down the street and think of a number. But I imagine that I tend to analyze things more than most people. Sometimes when I'm doing math, I get very sleepy and just moments before I fall asleep, I have these crazy math dreams. I don't know -- all these abstract notions in math come to life for me, and they take on these absurd connections with things that are happening in my life . . .

Competition I see as more of a means than an end in itself. There are very many brilliant kids who are extremely good at math but just don't have that competitive tendency. . . . For any student, I say they can go to their local library to find books on math and just problem books, or some kind of math for fun. And I think even though it's for fun, you can learn a lot about math that way. It teaches you that math is really about thinking and not just calculating."

As told to Anand Vaishnav of the Globe staff.

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