Jim W. Cheung '95 is also a Math 25 student, and, like Ancel, is extensively involved in mathematical research. Although he has not yet published his own theorem, his research ideas were revolutionary enough to satisfy the "top-10" judges of this year's Westinghouse Science Competition.

Cheung says his research is applicable to number theory and the use of continued fractions.

"I used continued fractions over the ring of Eisenstein integers to approximate complex numbers. In my proofs, I was able to show that the continued fractions over this system do not necessarily converge," explains Cheung.

Like Ancel, Cheung's intense interest in mathematics was greatly spurred by summer math programs.

"I attended the Ohio State University Summer Math Program for three years during high school, in addition to doing some reading on my own," he says.

Cheung says that he got started on this particular topic in high school, while he was still at Bronx Science in New York.

"I started on this problem in the summer of '89 at the beginning of my junior year. I began the project by just experimenting and toying with the idea, and it just kind of grew from that," says Cheung.

When asked whether he plans to submit his findings to a scientific journal soon, Cheung seemed cautious.

"I probably won't submit my proposals right away. I still plan to do some more work with it before I feel that it is truly complete," he says.