WASHINGTON, D.C. (March 10, 2009)—Eric Larson, 17, of Eugene, Ore., took home the top prize at this year's Intel Science Talent Search here—a $100,000 scholarship—for "classifying mathematical objects called fusion categories." His work, according to Intel, "describes these in certain dimensions for the first time."

Here, we will attempt to explain what that means. (We expect readers sharper than we are to do a better job, so please comment away.) Fusion categories are a discipline of group theory. Basically, a group is a collection of actions that is self contained. Rubik's Cube is a good example of group theory: You can do twist a, then twist b, and the result will always be contained in the set of allowed moves.

Larson took second place in December in the Siemens Competition in Math, Science and Technology, and he's published on the subject in arxiv. Here's what Siemens had to say about his project last year:

These extremely complex structures are a far-reaching generalization of groups, which are the algebraic structure traditionally used in mathematics to model symmetries. The main result of this project identifies and completely classifies a new class of fusion categories which, for the first time, contains non group-theoretic examples.

Larson was joined in the winner's circle by William Sun, 17, of Chesterfield, Mo., who took second place and will get $75,000, for a biochemistry project "that studied the effects of a recently discovered molecule that could potentially help efforts to treat bacterial infections or prevent neurodegenerative disorders such as Alzheimer’s disease," according to Intel. Third place and $50,000 went to Philip Streich, 18, of Platteville, Wis., whose project focused on carbon nanotubes. (We highlighted his work here.)

Former secretary of state Gen. Colin Powell told the finalists he had read all of their bios, "and that's some scary stuff." He praised public education, noting that despite graduating from City College in New York with just above a 2.0 grade point average, there were now college buildings named after him. Andy Grove, the third person to join Intel, earned a City College degree in chemistry, while Powell earned his in geology. Geology, Powell said, somehow turned into digging foxholes, while chemistry turned into making silicon chips.

Nobelist and current secretary of energy Steven Chu urged the students to use science to solve humanity's pressing issues, citing global warming. "All the great discoveries have not been discovered," Chu said. "It's a wonderful profession to be in." He pulled an example from physics: "All we know about dark matter is that it behaves like matter but we don't know what it is. Dark energy is even worse."

The gala dinner capped a hectic fun-filled week for the 40 finalists, who stayed in the St. Regis Hotel, toured the nation's capital and even met President Obama in the White House. Not to mention they had asteroids named after them.

These kids are wonderful examples of "what the United States has to replicate many thousands of times over with our young people if we want to be successful," Intel CEO Craig Barrett said of the finalists at the gala dinner honoring them tonight.

"This is why we can be hopeful for our collective future," said Elizabeth Marincola, president of the Society for Science and the Public, which organize the awards.

See our in-depth report for all of our Intel STS coverage.

Photo of Steven Chu by Laura Vanderkam/copyright Scientific American