When most of the other children their age had yet to "see Spot run," Samit Dasgupta and his brother were solving math word problems and impromptu brain teasers devised by their physicist parents.

"We come from an area of the world where academics is very important," explained their father, Ranjit, who, like his wife, Arati, is a native of Calcutta. "We tried to prepare them by engaging them intellectually, but we tried to make it natural and fun, rather than pushing them around."

Their benevolent social engineering efforts appear to have paid off. Samit Dasgupta, a 16-year-old senior at Montgomery Blair High School in Silver Spring, recently was named a finalist in the prestigious Westinghouse Science Talent Search.

Dasgupta, a math whiz, is among 41 students nationwide who made the last cut from the pool of 300 semifinalists. A total of 1,667 entries were submitted to the scholarship competition.

Dasgupta's entry was a research paper in which he formulated a new hypothesis in number theory, a discipline that explores relationships between numbers. It is an academic realm that is unfathomable to many people. Dasgupta "has a sense of these relationships that even the ordinary gifted kid doesn't have," his math teacher, Eric Walstein, said. "He has an innate intellectual curiosity and the ability to latch onto an idea and see in the abstract."

Dasgupta's work, a 20-page compendium of formulas and nomenclature guaranteed to intimidate anyone with a math phobia, is an extrapolation of Schinzel's Hypothesis, which poses that classic mathematical question: How often do polynomials take on prime values? (A polynomial is a combination of numerical terms that includes constants and variables. A prime number is evenly divisible only by itself and one, such as two, three, five, seven, and so on.)

Schinzel's Hypothesis says a polynomial will take on a prime value an infinite number of times, which is basically what Dasgupta conjectured in his hypothesis. He tested it with a mathematical formula he devised that was then corroborated by a super computer. The computer needed a half-day to complete its calculations.

"When I saw the results, I said, Wow . . . this is good; they're really close,' " Dasgupta remembered. He is a low-key, lanky youngster who lives in the Wheaton area.

Dasgupta's paper, which took five months to complete, is the outgrowth of a research project he began last summer while participating in a gifted students program at the Massachusetts Institute of Technology. The Research Science Institute selects 70 students from the United States and abroad to work with mentors. Eight of the current Westinghouse finalists were RSI participants, according to Mark Saul, RSI director.

They all have one thing in common that sets them apart from other brainy students -- an uncanny ability to use their intuition to solve problems and to go beyond that when necessary.

"They can turn things completely upside down and ask questions that other people don't ask," Saul said. "When you see it happening, it can take your breath away."

Larry Washington, a math professor at the University of Maryland who worked with Dasgupta on his project, said his young colleague somehow "sees right to the heart of a problem immediately."

"He's able to invent new things on the spot, to react to new situations," Washington said. "He's always thinking. And he has good technical powers to carry things out. If he was a quarterback, you might say he was going places."

By his own admission, Dasgupta wasn't always operating at that level, even though he has consistently been an exemplary student. "I wasn't the best in math at all in elementary school," he said.

That changed at Takoma Park Middle School, where Dasgupta blossomed under the tutelage of math teacher and math team coach Darlyn Counihan. "She was very enthusiastic, and she made it lots of fun for us, very positive," Dasgupta said.

"I basically told him there was no limit to what he could do," Counihan said. "You need talent, and he has it, but it's not enough. The key is setting high standards and high goals, and he's learned to do that. He's very persevering."

Counihan described Dasgupta as mature, humble and honest. "He has a whole lot of integrity," she said. "He's a sensitive, caring person. I just feel lucky to teach kids like him. I'm a pretty good {math} problem solver, but I'll never be on the same level as people like him."

Counihan said Dasgupta may well have been influenced by her long-standing love of math. "I find there's a lot of beauty in math that you don't see in other places," she said.

Dasgupta was asked to explain his attraction to the subject. "It's very elegant," he said with an embarrassed chuckle, "the way things come together; it's all connected. It's almost as if there's something out there that's waiting to be discovered. And it's all very structured."

Dasgupta, however, said he is not by nature a structured person. "If you saw my room," he added, "you wouldn't think so."

The mantel over the fireplace at the Dasgupta home is stocked with trophies and awards Samit Dasgupta has collected in the last several years from math and computer science competitions at the local, state and national level. But he's no slouch in the humanities either, as indicated by his membership each year on the high school honor roll. (The Dasguptas' other son, age 24, is in the master's program in electrical engineering at the University of Texas at Austin).

Samit Dasgupta has applied to Harvard, MIT and other top universities, where he hopes to prepare for a career in math research, physics or computer science. He has several other interests outside academics, including tennis, basketball and chess.

"We don't only talk about math and science and things like that," his father said. "We discuss other things too, such as how stupidly the Redskins played."

Said the son: "Don't even talk about the Redskins."

Saul, of RSI, said gifted students such as Dasgupta help shatter a stereotype. "These are not nerds," he said. "They're not shut up in their rooms with nothing else to do. This is a living, breathing kid."

Dasgupta is the only Westinghouse finalist from the Washington area. New York led all states with 15 finalists, including five from New York City. All finalists receive a $1,000 award, but the top 10 finishers will get scholarships ranging from $10,000 to $40,000. Winners will be announced in mid-March.

The competition promises to be stiff if the titles of the finalists' papers are any indication. One paper submitted from Texas is titled: "Characterization of a Choline Oxidase-Chemiluminescent Detection System and Its Potential Use in Phospholipase D- and Immunodetection Assays." CAPTION: Samit Dasgupta, 16, a senior at Montgomery Blair High School, stands in front of projected numbers he uses for his new hypothesis in number theory.