At the age of 17, Jordan Ellenberg of Potomac has a three-page, single-spaced resume. From it, one can learn that when he was in eighth grade, he took honors calculus classes at the University of Maryland; when he was a junior at Winston Churchill High School, he earned a perfect of score of 1600 on the SAT; and this year as a senior, he placed second in the national Westinghouse Science Talent Search. Now, his resume has a new entry. This spring, he won the foremost of high school math competitions, beating 400,000 U.S. and Canadian students who entered the USA Mathematical Olympiad. According to the judges of the contest, sponsored by the Mathematical Association of America, the Montgomery County youth wrote the best answers to five very difficult problems in a 3 1/2-hour essay exam that is the final part of the three-stage competition. Now, he and two dozen other students, including Demetrio Munoz of Fairfax County's Thomas Jefferson High School for Science and Technology, will train for four weeks at the U.S. Military Academy at West Point, N.Y. Six will be chosen as the delegation to an international Olympiad next month in West Germany -- a delegation on which Ellenberg has served for two years. To Ellenberg's family and his teachers, his first-place finish was not entirely a surprise. This is, after all, a young man who taught himself to read at the age of 2 by watching "Sesame Street." His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says 'Bethesda is to the right.' " In second grade, he helped his teenaged babysitter with her math homework. By fourth grade, he was participating in high school competitions as a member of the Montgomery County math team. And by eighth grade, he had started college-level work. "He can know things and understand things that 99.9 percent of the public cannot do. And he does it at 17 years old," said Eric Walein, a math teacher at Montgomery Blair High School who said he has come to feel "like an uncle" to Ellenberg through a decade of work with him and his parents, who are both statisticians with PhDs. "He's definitely the top high school problem-solver in the country," said Lawrence Washington, a mathematics professor at the University of Maryland at College Park who has taught Ellenberg for several years. "If he were a high school football player, you could say he is a pro prospect, a future Hall of Famer." Ellenberg isn't exactly unassuming about this year's Olympiad or his string of previous awards. "I don't think you can ever be surprised to get a problem right," he said. "Once you see a solution to a problem, it seems so obvious and clear." But he is wary of publicity, of being misunderstood. "I guess if there was one thing I'd want people to know," he said, "it is that I do these things because I care about them, not for some self-aggrandizing reason." Math, he is careful to point out, is not his only outlet. He plays the piano, is captain of his school's "It's Academic" team, has a flair for languages, and has won state and county prizes for fiction. "He's smarter in everything, and math is just one of the ways it shows up," Washington said. But math is what he intends to study when he enrolls at Harvard in the fall. It is his special gift, his teachers say, and his passion. Ellenberg is gangly, and he paces when he thinks aloud. He speaks softly in rapid bursts, his thoughts dissecting one another. He'd rather talk of ideas than of himself. Ellenberg on mathematics: "I always think of it -- this is kind of crazy -- as a zoo. There are a million different mathematical objects. They are like animals. Some are like each other and some are unalike, and they are all objects . . . . There are things in different guises. The amazing thing is, it all connects. Anything you prove with trig{onometry} is just as true if you do it with algebra . . . . I think it is kind of amazing actually, if you think of it from an emotional point of view." On learning math: "My feeling is that a lot of people expect not to be good at math. If you see calculus and trig, to a seventh-grader, they see it as something very difficult and very arcane, when maybe the trick is to relax a little bit . . . . Many things you can understand on two levels. If you look at a novel, a novel can be very hard to interpret, but you can still read it and see what happened. With math, there is no real surface level. It is already written in a sort of obscure language. You don't have the comforting template. You only have the deep structure, and that can be very off-putting." On the practicality of math: "Why is it important to have read any Shakespeare for your everyday life? To tell the truth, I can get through the day without ever using a Shakespeare quote, but I think Shakespeare is useful, and I think math is useful." On his future: "If you're going to be doing math, which is not a certainty but a probability, you can be in the university system, or you can be working for a big corporation, IBM or Bell Lab. I think it is ludicrous to say before you go to college what you want to be. I would never presume to make a career plan at this point." There is an uncharacteristic pause, and a slight smile. "I'll find something to do."