Michael Stephen Briggs, 17, the Adelphi high school student who this week was awarded the $10,000 top scholarship in the Westinghouse Science competition, is so knowledgeable about his arcane field of mathematics that even his teachers don't know for sure how he does it.

"I still don't understand the project," which involved a new approach to mathematical game theory, said Sally Buckler, chairman of the science department at High Point High School in Prince George's County, where Briggs is a senior.

"He is academically superior," she said. "I was told by (a university mathematics professor) that his project is the equivalent of an honors project in college."

Briggs, of 8504 Laverne Dr., Adelphi; David Theodore Vader, 18, of 19732 Meredith Dr., Derwood, Md., and Joseph Paul Dougherty, 17, of 1637 Morrill Court, McLean, were among three of the 40 finalists named last January in the 37th annual Science Talent Search contest.

Briggs was awarded the top honor at a black-tie dinner attended by 500 people in the grand ballroom of the Mayflower Hotel. Vader and Dougherty each will receive $250 scholarships.

Yesterday morning Briggs and the other nine top national winners appeared on the Today Show, an event that capped off what finalist Dougherty called a "fabulous" week, including a visit to the White House and a visit from President Carter.

"It was very nice of him, considering how busy he was," Dougherty said."We didn't know it at the time, but he was working out the Taft-Hartley matter with the coal miners. When he came in to talk to us he looked tired. He talked wistfully about his own career as a scientist."

Briggs said his winning project involved figuring out a way of estimating the number of potential situations within infinite games, a conceptual tool that previously had not existed.

While reading an article on computer chess, Briggs realized that mathematicians didn't have a way to estimate the number of potential solutions in "games" of infinite possibilities. "So I devised a method whereby one can construct" those estimates, he said.

He did this by working out a way of finding two finite games within any infinite situation, making the estimated results far more predictable than before.

Vader, a senior at Col. Zadok Magruder High School in Rockville, worked on a project "investigating the efficiency of certain materials in absorbing sunlight for solar heating systems," according to rosemary Behrens, his chemistry teacher.

Joe Dougherty, 17, a senior at McLean High School, said he was involved in a project at the National Bureau of Standards analyzing the breakdown reactions of chemical compounds in laser-chemistry situations.

Originally more than 13,000 students entered the competition. Only the New York City area han more finalists from a metropolitan area than did the Washington area, represented by Briggs, Vader and Dougherty, according to contest officials.