# 1 in 3000: Derek Liu

## Into the mind of mathematician Derek Liu, an International Math Olympiad Gold Medalist

Pencil in hand, Derek Liu (12) wanders through a foggy forest, searching for his solution. A set of alluring trail heads is all that is visible.

“You never know which one to take,” Liu, an International Math Olympiad Gold Medalist, said. “You can’t see far in front of you, so the only way to tell is by going down one and seeing where it leads.

From a young age, Liu has had a curiosity about numbers and patterns. Standing in the toy aisle at Costco as a child, he remembers being more drawn to the price tags than the toys themselves. And, at the checkout counter, he recalls his furious attempts to beat the cash register at calculating the total price on the receipt (he was successful a few times).

Now, as one of the top high school mathematicians in the U.S, the problems he works on are far more complicated than simple addition, but his strategy when solving one remains the same.

“It is taking well-known concepts and creating something new out of them,” Liu said. “Even if you have all the knowledge, it is not at all clear how to proceed. ”

However, getting to the solution involves more than just aimless wandering.

“It is about having the intuition of what you think has a good chance of working, and that intuition comes from having seen a similar type of problem before,” he said. “Math, at its core, is about looking for patterns.”

For example, take a seemingly complex chessboard problem: given a bunch of dominoes that each cover two adjacent squares on a chessboard, is it possible to completely cover a chessboard that has two opposite corner squares cut off using exactly 31 dominoes?

“Of course, the messy way is to try every possibility. That is going to take forever,” Liu said. “But, there is also a very elegant solution, using the coloring [of the chessboard].”

A standard chessboard has 64 squares with 32 of each color. Taking away two opposite corner squares leaves the board with 32 squares of one color and 30 of the other.

“However, a domino is forced to cover one black and one white, which means that 31 dominoes have to cover 31 blacks and 31 whites,” Liu said.

Therefore, it is impossible to cover a chess board that is missing two corner squares with 31 dominoes, he eagerly deduced. It is this outside-of-the-box thinking that has made Liu so successful over the years – it is how he navigates through the forest.

This past summer, he traveled to Oslo, Norway, representing the U.S. in the International Math Olympiad, where the U.S. team placed third out of over a hundred countries. Individually, he placed 12th among nearly 600 total participants, earning him a gold medal. But, despite being a talented mathematician for most of his life, his recent success has still come as a surprise.

“A year ago, I could never see myself where I am now,” Liu said.

His upwards journey has been filled with regular self-doubt.

“When I was in ninth grade, I was like, ‘oh yeah, I’m very good at math,’” he said. “And then I went to this camp called the Mathematical Olympiad Program.”

It was at this program, which accepted only the top 60-or-so math students in the nation, where Liu realized that his “view of math was quite limited.”

But more importantly, it was where he learned to accept his imperfections.

“It is not about being the best,” Liu said. “It is about learning from the best and improving.”

He credits much of his current success to his teachers, mentors and friends, even those who aren’t in the math community.

“I owe my thanks to not just math teachers, but all the teachers I’ve had,” Liu said. “All of them have been supportive of my journey.”

Eventually, Liu dreams of becoming a professor to both teach and explore the heights of higher math

“Hopefully, I leave my mark on mathematical history,” he said.

His goals are high, but so is his ambition. For the past seven months, Liu has begun working on a research question about the “tilings of polyhedra in three or more dimensions” with a mentor at MIT.

Yes, it is as complicated as it sounds, he said.

There is no doubt that Liu’s future will be one of numbers and variables, problems and solutions. He will reach dead ends and have to trace back his footsteps through the fog to start all over again.

Yet, it is this unknown that drives his mathematical interest forward. In Liu’s forest, the fog never lifts.

And that is how he likes it.

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