When he was 5, Samit Dasgupta could solve math problems that could stump a fifth-grader. By eighth grade, he could whip any junior high school student in Maryland in math competitions.

On Monday night, it became official: The 16-year-old from Silver Spring is one of the nation's top high school science students. The Montgomery Blair High School senior took fourth place in the prestigious Westinghouse Science Talent Search. Five former scholarship winners in "the Westinghouse" have gone on to win the Nobel Prize.

At the award dinner Monday night at the Mayflower Hotel in the District, surrounded by 39 other finalists, the shy and lanky Dasgupta was nonplussed when he learned that he was among the 10 top finishers and that he had won a $15,000 scholarship.

"I don't know what really to say, sir," he said in an interview. "I mean, I'm excited and . . . very happy," said Dasgupta, who spent five months writing a project on number theory titled "On the Schinzel Hypothesis for Polynomials."

Dasgupta has applied to Harvard, MIT and other top universities in hopes of pursuing a career in math research, physics or computer science.

Irene Ann Chen, a 17-year-old from San Diego, won the first-place $40,000 scholarship for her study of two genes in the spread of cancer. Griffin M. Weber, 17, of Newport News, placed eighth and won a $10,000 scholarship.

For the first time in its 54-year history, Westinghouse presented a posthumous award. Soo Yeun Kim, of Brookville, N.Y., died in a car accident in November. Her classmates completed her research project, and Westinghouse judges selected it as a finalist without knowing she had been killed. Her high school was awarded $5,000.

Dasgupta is the sixth Blair High School student to win one of the top 10 spots in the competition. No other Montgomery high school students have made it to the finals. This year, Dasgupta was the only student from the Washington area or Maryland to make it to the finals. His project dealt with Schinzel's hypothesis, which says that an infinity of whole numbers can be substituted into certain algebraic expressions to produce prime numbers (numbers that can be evenly divided only by 1 and themselves). Dasgupta's work involved an effort to extend the hypothesis to show that the number of algebraic expressions of a certain type that satisfy a similar set of mathematical conditions to those involved in Schinzel's hypothesis also is infinite.

Dasgupta credited his parents, physicists Ranjit and Arati Dasgupta, and several math teachers for his impressive skills. His staff adviser for his project was Blair teacher Eric Walstein. University of Maryland math professor Larry Washington is another mentor. He also credited his math teacher at Takoma Park Middle School, Darylyn Counihan.

But his parents say he is the one responsible for his achievement. "He is the one who pushes himself," said his mother, Arati. "He is the one who will spend hours trying to figure something out. We gave him the right atmosphere, perhaps, but he is the one that developed the joy you need to do the type of things he has done." CAPTION: Westinghouse winner Samit Dasgupta, 16, smiles as he relays the good news to friends and family.