His finalist year: 1965

His finalist project
: Figuring out potential crystal structures

What led to the project
: As a kid growing up in the 1950s and '60s in Louisville, Ky., J. Richard Gott loved studying geometry. In those early post-Sputnik days, there was "great energy and great excitement" about math and science in the schools, and his teachers encouraged his interests.

So for an independent research project, he decided to look at metallic crystal structures. In a metal like sodium, each atom occupies a certain space in the crystal. These atoms arrange themselves in ways that can be represented with certain patterns of polyhedrons—geometric shapes with flat faces and straight edges. Gott tried to figure out arrangements of polyhedrons that would completely fill a space. For example, the simplest one would be a set of cubes stacked like blocks, though there are others that are far less intuitive.

He came up with enough interesting results that his work won him a finalist spot in the 1965 Westinghouse Science Talent Search.

The effect on his career
: Gott went to Harvard University to study physics and then to Princeton University to earn his PhD in astrophysics, graduating in 1972. After short stints at the California Institute of Technology and University of Cambridge, he returned to Princeton to join the astrophysics department in 1976. His Westinghouse experience had quite a large influence over one of his early major studies, "The Spongelike Topology of Large-Scale Structure in the Universe," which looked at galaxy clusters in space.

At the time, there was some controversy over their density and arrangement. Were the clusters like meatballs, with small high-density areas separated by vast low-density ones? Or were they more like Swiss cheese, with voids in the midst of denser regions? Gott surveyed these schools of thought, decided that "neither one of them could be right," and proposed more of a spongelike structure that incorporated some of the same lessons he had learned from arranging polyhedrons to completely fill a space. (Today's higher-power telescopes have shown he was close to the mark.)

What he's doing now: These days, Gott occasionally makes headlines with an even hotter astrophysics topic: time travel. (He discusses it on a 2008 episode of SciAm.com's Science Talk.) The author of the 2001 book Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time, Gott maintains that there is nothing in physics that prevents it. Although you can't build a spaceship that goes faster than light, using curved spacetime you might be able to beat a light beam by taking a shortcut, either around a pair of moving cosmic strings or by jumping through a wormhole; these potential solutions could allow a time traveler to circle back to visit an event in his own past. So why then aren't there visitors from the future showing up in time machines on the White House lawn?: It would not be possible for time travelers to visit a time before such a machine existed—and they haven't been invented yet.

Although this sounds like science fiction, "Gott is a serious and respectable scientist whose work on time travel is absolutely mainstream and in line with the general theory of relativity," says John Gribbin, the popular physics writer, and author of In Search of Schrödinger's Cat: Quantum Physics and Reality.

In addition to his astrophysics work, Gott served as a judge for the Westinghouse Science Talent Search for much of the 1980s and 1990s—an experience that has given him many opportunities to reflect on science education in America. "People sometimes wonder whether the quality of the best science students is going up or own," he says. "The answer is that it's the same high level."

What he finds particularly fascinating is the "clusters" of semifinalists and finalists that appear in different locations from time to time. First, a school that has never had a finalist or semifinalist before will produce one. Then, the next year, there will be two or three semifinalists from the same school. This sudden flurry of activity is usually evidence of a top-notch teacher gearing up a research program. Unfortunately, it also suggests that there is "quite a lot of undiscovered scientific talent" out there, he says. In the absence of such programs and teachers, many high-potential kids never land on the radar screen.

But over time, he hopes, the big scholarship prizes and attention will spur more such programs. After all, in the wake of Olympian gold medalist Michael Phelps, there are "a lot more people jumping in the pool," he says—and science needs the same thing.