TITLE: Research done by high-school students
QUESTION [59 upvotes]: I'm giving a talk soon to a group of high-school students about open problems in mathematics that high-school students could understand.  To inspire them, I would like to give them examples of high-school students who have made original contributions in mathematics.  One example I have is the 11th-grader from Hawai'i named Kang Ying Liu who in 2010 "discover[ed] nine new geometric formulas for describing triangle inequalities."
Do you have any other examples of high-school students who have made original contributions in mathematics?

REPLY [5 votes]: Sylvain Cappell's paper, "The Theory of Semi-cyclical Groups with Special Reference to Non-Aristotelian Logic," won him the 1963 Westinghouse Talent Search when he was 16 years old, as recollected in this Boy's Life article. This was the first of Sylvain's many important mathematical discoveries. Tangentially interesting is that the runner-up in this contest, Sylvain's rival, was a certain William Leonard Pickard.