“A regular octahedron has a surface area that is 44 percent…”

A buzzer sounds. Freshman Nathan Liu looks up from the screen in front of him and says:

“One seven two eight.”

Up 3-2 against his opponent, this question was the only thing between him and the title of 2025 RTX MATHCOUNTS National Champion.

“Correct!”

The full question was “a regular octahedron has a surface area that is 44 percent greater than the surface area of a smaller regular octahedron.

This smaller octahedron has a volume of 1,000 cubic inches. What is the volume, in cubic inches, of the larger octahedron?”

And in less than four seconds, Liu had seen past the octahedron, realized that a 44 percent increase meant a side length increase of 1.2 (by taking the square root of 1.44), calculated that the volume would be 1.2 to the third power (which is 1.728) and by multiplying the original volume, he got his answer of 1728.

During the 2024-25 school year, tens of thousands of sixth to eighth graders competed in the MATHCOUNTS competition, which culminated in the national championship from May 10-13, 2025, where the top 224 middle school mathematicians competed against each other for the title.

All participants have to progress first through school, regional and state-level competitions before being able to compete, with only the top four from every state making the cut.

Before even making it to the head-to-head matchups with the 12 best mathematicians in the nation, Liu had to first make it through the written rounds, each aiming to focus on different aspects of problem solving. The sprint round consisted of 30 problems in 40 minutes without a calculator, focusing on speed and accuracy. Then came the target round, where participants solved four pairs of problems with six minutes for each pair, testing their problem-solving and mathematical reasoning. Finally came the team round, where Liu worked with the other three best mathematicians from Texas to solve 10 problems in 20 minutes.

Coming out of the written rounds, Liu placed first overall, winning the title of the MATHCOUNTS written national champion and securing his place in the head-to-head rounds. Being first overall after the written rounds, Liu had cemented himself as one of the best middle school mathematicians in the nation. As a result, the head-to-head rounds became more of a game, with Liu just having fun with the questions.

The head-to-head rounds, also known as the Countdown rounds, consisted of two participants competing in a buzzer race to four points. These rounds focus completely on speed, with each question having a 45 second time limit. While Liu had won the written portion, Liu was not projected to do well in his Countdown rounds.

“My second opponent in Countdown was a real challenge. I was expected to lose against him, like four to one, and he did almost beat me,” Liu said.

In his third and final round, Liu found himself down once again, with a score of two to zero.

But in the end, Liu pulled through and claimed his second national champion title, this time the champion of the Countdown Round. Surrounded by applause, Liu felt at an all-time high from winning both titles.

“It was a lot. Happiness is not a good enough word for how I felt,” Liu said.

Behind the wins, however, was a lot of work that had to go into ensuring he was at the top of his game. To excel in MATHCOUNTS, it’s crucial to read quickly and identify key information, as each problem is entirely new.

Preparing for competitions such as MATHCOUNTS comes down to a lot of self-studying, going over the available textbooks, practice tests and practice problems.

“It’s more of practicing problems and doing as many as you can,” Liu said. “It’s like how you practice piano, you just keep doing it.”

In addition to self-studying, Liu worked a lot with the math teams on campus. Originally starting with the Middle School Math Team and its sponsor, Valerie Davis, Liu quickly moved up to practicing with the Upper School Math Team and their sponsor, Dr. Zuming Feng. Feng was a particularly important figure for Liu.

“He’s one of the best teachers in the world,” Liu said.

With MATHCOUNTS and over $20,000 in prize money now behind him, Liu is aiming for bigger and harder competitions in the upcoming years.

Liu hopes to progress through the United States of America Mathematical Olympiad (USAMO) to reach the Mathematical Olympiad Program (MOP) summer program in the near future, and long-term hopes to compete in the International Mathematical Olympiad.