At age 3, he was adding numbers in his head. He finished calculus in the eighth grade and then recorded a perfect score in an international math olympiad at 16.

But yesterday, 18-year-old Jacob Lurie, of Bethesda, scored his biggest triumph yet, claiming top prize in one of the nation's most prestigious science competitions -- the 55th annual Westinghouse Science Talent Search -- and becoming the first Washington area student to capture the honor in 18 years.

The Harvard-bound senior at Montgomery Blair High School receives a $40,000 scholarship and national recognition for what his teachers and the competition's judges say is an uncommonly promising talent as a mathematical theorist.

"There's this instant recognition when you are talking with him that, Aha! Here is a fellow mathematician who is well on his way,' " said Carol Wood, a mathematics professor at Wesleyan University and a judge in the Westinghouse competition. "He sees the things in mathematics that really matter. . . . I've seen such a student only once before."

Lurie, for his part, politely dismisses the idea that he's a boy genius. "I don't know what one feels like. I feel like me," he said matter-of-factly.

Lurie was genuinely at a loss for words about his award. "It was unexpected," he said.

Prompted by another finalist, who said Lurie needed to come up with a quip to get on the David Letterman show, Lurie responded, "I feel surreal, sure," a reference to his award-winning project.

Lurie won the Westinghouse competition by making sense of the seemingly incomprehensible so-called surreal numbers that include the infinitely large and infinitesimally small numbers that are supposed to be too difficult to measure. A surreal number, for example, might describe the square root of infinity.

Lurie's work focused on those surreal numbers that can be calculated by a computer, and he described what properties those numbers might have.

"This is way beyond the ability of the generic whiz kid," said Bill Gasarch, a University of Maryland computer science professor who has been a mentor to Lurie since Lurie was in the 10th grade. "There are aspects of his paper that I, as his mentor, do not understand all that well."

Gasarch said Lurie is one those rare students who are both "deep thinkers and able to do the tricks."

Lurie's mother said her son always has been determined enough to succeed at what he put his mind to -- like when, at 7, he stopped eating meat because he didn't want to hurt animals. Or when he took up piano or learned to play the flute. He's currently trying to write a fugue.

Nora Bailey Lurie said her son didn't inherit his mathematical ability from his immediate family. "I'm a corporate tax lawyer," Bailey Lurie said with a laugh. "My husband, who also is an attorney, is a bit better with numbers, but Jacob passed him by in the seventh grade."

Patti Harburger, Lurie's preschool teacher, recalls a 3-year-old Jacob who was able to figure 3+4+8+7 off the top of his head. "He'd lay on the floor and look up at the ceiling and then give us the answer," said Harburger, directress of the Children's House of Washington, a Montessori school. "He was always asking questions."

Jacob Lurie was one of five Washington area students among the top 40 finalists in the Westinghouse competition. The others included Paulina Susan Kuo, 17, of Great Falls, who attends Thomas Jefferson High School for Science and Technology in Fairfax County; Brian Michael Green, 17, who attends Yorktown High School in Arlington; Katherin Marie Slimak, 17, who attends West Springfield High School; and Mani S. Mahjouri, 17, who attends Atholton High School in Columbia.

Lurie said he's "not sure" what his grade-point average is at Blair, but he said he long ago advanced past the math classes at Montgomery County's only math and science magnet school, having completed calculus in the eighth grade.

"I'm mostly on my own now," he said, seeking help from mentors and others he finds with the aid of his parents.

At 16, Lurie was the youngest member of a six-person team of students who represented the United States in the 35th International Mathematical Olympiad in Hong Kong in 1994. Each member of the team scored a perfect 42 points on the two-day, nine-hour competition, unprecedented at the time and tops among teams from 69 countries.

As much as the olympiad brought him much acclaim, Lurie said he will treasure more the experience of the Westinghouse competition. "This is more about the work that you do." he said.

Lurie said he plans to study mathematical logic at Harvard, with hopes of becoming a logician.

However, he said he's not good at everything: "I tried to take up the violin, but I haven't been very successful."

"He told me," his mother added, "that learning to play the violin well is something you really have to start doing when you are 3." CAPTION: Montgomery Blair senior Jacob Lurie, left, is congratulated after receiving Westinghouse award at the Mayflower Hotel. CAPTION: Jacob Lurie's preschool teacher recalls how Lurie could add figures in his head at age 3.