HOFFMAN ESTATES (AP) — If you look past numbers and computations and distill math to its essence, it's all about creativity, 17-year-old James Tao says.
"When I think of math, when I think of coming up with a proof where there wasn't a proof before, I really put this in the same category as starting with a blank canvas and producing a painting, starting with a blank score and producing a music piece," said James, a senior at the Illinois Mathematics and Science Academy.
"Math is just as the arts, because there is always more than one way to do things. In the end, which perspective you choose to take on a problem, that always ends up being more of an aesthetic decision than a logical necessity."
James knows what he's talking about. This year, the Hoffman Estates resident made the uber-exclusive, six-member U.S. math team and competed in July in the International Math Olympiad held in Colombia.
He and three teammates were among 40 competitors who earned gold medals in a field of 527 contestants from 97 countries.
"There is nothing mathematically I did (at IMO) that I hadn't done elsewhere. What was different was the psychological intensity of it," James said.
"Being put on the spot in a foreign country, knowing that in some vague sense you're responsible — even if just a little bit — for how people perceive the U.S., I've never felt that much pressure. Sitting down and pushing through was a sort of formative experience in and of itself."
James is the most advanced geometry student that IMSA math teacher Michael Keyton has taught in 48 years, 12 of them at the prestigious Aurora school.
"Our basic student is superb, but he's the first student that I have ever gone to this level with," Keyton said.
By junior year, James had taken all the math classes IMSA offers — course offerings the equivalent to a small college's — so he delved into independent study focusing on graduate-level commutative ring theory.
The keys to James' success are curiosity and motivation, Keyton said.
When he was just a middle-schooler, James got a book with 1,500 advanced problems in geometry then worked his way through them on his own.
"It's this drive to achieve and to know," Keyton said.
Each year about 200,000 students in the United States take the American Mathematics Competition, the first in a series of tests that whittles down competitors for the six-member national math team, said U.S. math team leader Po-Shen Loh. He was deputy leader when James competed.
James has the potential to eventually become a U.S. math team coach, Lo said.
"I think he's a very exciting person. What I like about James is that he not only has extremely good math ability; he also has very good people skills, not usual among people of his caliber," he said. "He has the potential to be a leader — not just strong mathematician."
James attended Plum Grove Junior High School in Rolling Meadows and then Fremd High School for a year before transferring to IMSA as a sophomore.
Unlike many of his high-level peers, James got into math relatively late when a friend's dad started a Math Counts team in the sixth grade.
For the first time, James found himself stumped.
"I realized, 'Hmmm, I actually can't solve these problems and I also don't understand the solution,'" he said.
So he asked for help from his father, who got him books from the Art of Problem-solving website.
"Those books made a conscious effort to present math as a creative process," James said.
Brian Tao, a senior engineer at Caterpillar, said he was able to help his son only for a couple years thereafter.
"My knowledge couldn't help him at all after about ninth grade," he said. "He doesn't like much to repeat a lot of old things. He likes more to create or discover or invent some new things."
Math is not about memorizing proofs but about figuring out key concepts and ideas, James says.
"Right now there are probably about 1,000 problems you can ask me about and within five minutes, I could tell you the proof. But I don't have 1,000 fully written proofs stored in my head," he said.
"A computer can remember a proof. To distill a proof into a few key ideas, and how you get from one idea to another, is something that at this point only humans can do."
James is working on algebraic geometry with Izzet Coskun, a professor at University of Illinois at Chicago.
"He works very hard. He is also very curious. He is constantly asking very good questions. This is rare in a young person. He is also a very good problem solver," Coskun said. "I am sure he will be very successful in his field of choice. I expect him to develop into a leading scientist at the end of his undergraduate and graduate studies."
James said he hopes to attend MIT or Harvard. Beyond that, the future is still unclear — he might become a math professor and do research, or could get into computers and data manipulation, or even be happy as an actuary, he said.
His unequivocal focus on math has come, in a way, at the expense of expanding his learning, James said. Some of his peers from math camp, for example, also compete in high-level computer science, an area James has just begun to delve into.
"Had I had a more balanced and complete perspective in the past I probably could have pursued other interests," he admits.
Success in math competitions, just like in standardized tests, relies in part on what he calls "noise," or that element of random chance. James performs best when there's a lot of geometry, and more time to think, rather than rapid-fire format.
He has rituals to calm himself, like pulling on his earlobes with his arms crossed, and sings songs like Green Day's "Good Riddance (Time of Your Life)" with the line, "Make the best of this test and don't ask why."
"I don't enjoy the competitive part of competition," he said. "The higher stakes, the more nervous I feel and the more difficult experience it is. Some of the best tests (I've done) are the ones no one hears about."
Not that he doesn't want to win, of course.
"With respect to everything, I like to be very intense. If we have a debate in English class, I try very hard to win. I'm not opposed to doing things that I don't necessarily enjoy but are just intense experiences."
The best part of competitions is meeting kindred spirits, James says.
"I'm fairly introspective — it's easy to get labeled as a nerd, someone who thinks too intensely. I meet people who like to think about things creatively."
James is a perfectionist, said his mother, Xiaorong Cygan of Hoffman Estates, a project manager for Motorola Solutions.
"He always wants to be perfect for a lot of things. That worries me a little bit because everybody makes mistakes, nobody is perfect," she said. "But I feel a little bit better now because I see him getting better about that."
James' interests range beyond math. He has volunteered at the Xilin Chinese schools in Naperville and Hoffman Estates, and he's performed on piano at the Granquist Memorial Music Competition in Geneva.
"Learning piano pieces I never felt the same creatively I felt with math," he said. "When people think of music, they think of this very creative, passionate thing. When people think of math, they think of this dead subject, more the domain of Spock than the domain of da Vinci."
"But for me, it was reversed."