UNLIKE MOST of the famous names of the Washington area, Charlie Fefferman is home-grown. He grew up in Silver Spring, where his family still lives, and went to junior high school in Takoma Park. He did his undergraduate work at the College Park campus of the University of Maryland, where he returned last Friday to receive an honorary doctorate of science.

If you haven't heard of Charlie Fefferman, you will. At 30, he has already demonstrated that he has one of the most remarkable minds the Washington area has ever produced.

His professional peers believe that Charles Louis Fefferman, to give him his full style, will prove to be one of the great mathematicians of the 20th century. Last year he won the Fields Medal, which is to mathematicians what the Nobel Prize is to scientists. Before that he won several other glittering awards, most notably the Waterman, which gave him a stipend of $150,000. The University of Chicago made him the youngest full professor, at 22, in any major university. Princeton wooed him away from Chicago at 23 and made him the youngest full professor in its history, Princeton is where he is today.

Charlie Fefferman isn't teaching; he's just thinking, thanks to the Waterman award support. What he thinks about and has thought about is a cluster of granite-hard, time-tested mathematical problems, ones nobody has solved so far. His Waterman award came for his "researches in Fourier analysis, partial differential equations, and several complex variables." Fefferman's thinking has already "contributed signally to the advancement of modern mathematical analysis," the citation says.

The main credit for all this goes to that splendid genetic accident which gave Charlie his extraordinary mind. After that, credit goes to Arthur and Lilo Fefferman of Silver Spring, his parents. Charkie's father is a tax economist with a distinguished career of his own; his mother, to use a modest term, a housewife. They've raised their wonder-child not only with love but with understanding.

There's still credit left, and much of that can go to members of the mathematics department at the University of Maryland. For them, the whole business began when Jim Hummel, an authority on complex variables, was sitting in his tiny office one morning in July 1961. He got a phone call from the Feffermans. They had this avid 6th grader who was consuming math textbooks like candy. Would Prof. Hummel talk with him? Prof. Hummel would.

So Mrs. Fefferman drove Charlie from Silver Spring to College Park in their trusty Dodge. "i wasn't scared," Charlie recalls, "but I was really excited." Once a week for the rest of the summer, the two met for mathematical talk.

Charlie was bright, indeed, so Hummel invited him back for the next summer. At a certain point during that second summer, Hummel realized that Charlie was a genuine mathematician, that he was already "thinking like a mathematician." The point came when Charlie asked a searching question about the Peano axioms for integers.

His first year at Eastern Junior High in Takoma Park, Charlie moonlighted at Maryland. The next year he enrolled at Maryland fulltime. He was 14. It wasn't easy. The chairman of the math department, Leon Cohen, kindly and wise, shepherded a special permission for him right through the university's Board of Regents.

During his first couple of weeks, Charlie attended John Horvath's beginning calculus class. Then Horvath jumped him upstairs into John Brace's honors section in calculus. Charlie sat in the front row so he wouldn't miss anything. Throughout the semester, when his turn came to go the blackboard, he had to stand on a chair to reach the top of the board.

His new professors discovered what Hummel already realized: that you never needed to tell Charlie anything more than once. Accompanying this phenomenal memory was phenomenal insight. Pretty soon the coolest students in the back row, where all cool students sit, were inquiring plaintively of John Brace: "Are we supposed to understand the questions the little kid asks?"

Yet they were polite to the little kid. "All those other students must have thought it weird that I was in the university, but they never gave me a hard time," Charlie says.

When he reached his second year on campus and was taking mathematical logic, he published his first article. Appearing in a German journal, its title was "Cardinally Maximal Classes of Non-Equivalent Order Types." He was graduated from Maryland in the spring of 1966 with high honors in physics as well as mathematics. His high school in Silver Spring-or what would have been his high school, Montgomery Blair-presented him with an honorary diploma.

There was something else that helped Charlie besides being at Maryland. In the late afternoons, home from the university, he made a habit of getting together with his old buddies. In College Park he rated as an intellectual marvel, but in Silver Spring he was a nice kid with a sense of humor. "My friends meant a lot," Charlie remembers.

"I think I was privileged to go there," he says of Maryland. "And I'll always be grateful to the mathematics department for doing a delicate job very well."

How so?" "The delicate part came because the members of the department could have pushed me too fast or, on the other hand, held me back. They didn't do either one. I believe they found exactly the right pace for my development."

After graduation he went to Princeton, where he earned a doctorate. He kept his College Park contacts, though, and his friends in the math department remained ready to listen and advise. They still do.

Clearly, with the help of his family and faculty friends, he has escaped the pitfalls, both personal and professional, that often await youngsters of enormous talent. Life for too many child prodigies ends in dislocation or despair or in realizing only a glimmer of their potential. Given a different set of circumstances, it's quite possible that Charlie would have spent his days simply as the finest auto mechanic in Silver Spring, since he's also a whiz with engines.

Instead, he's established at Princeton in a situation as close to the ideal as one can find in this imperfect world. Several years ago he married a violinist, Julie Anne Albert, and six months ago they had a baby girl named Nina. They live in a three-bedroom ranchstyle house; one small bedroom serves as Charlie's study. They don't keep the Fields Medal there, though. Because it's solid gold, they store it in a bank vault. To stay in shape Charlie does Canadian air force exercises. Next fall, when the Waterman fellowship is finished, he'll go back to teaching a pair of math classes at Princeton. If all goes well, however, he'll spend most of his time thinking.

When you ask Charlie how a premier mathematician thinks, his answer is hesitant, but Charlie can furnish at least a metaphor for the process of mathematical thinking. He says it's like making music. It has similar qualities and similar esthetic satisfactions. That he thinks the metaphor is sound is attested by the fact that he's beenteaching himself to play the piano.

If we still have encyclopedias a century from now, there'll probably be a "Fefferman" entry in them, and mathematicians will still stand at their blackboards building on his ideas. "Of course I like being well known as a mathematician, and it's rewarding to see my work esteemed so early." is he afraid he's going to slow up after a while? "No, not afraid, but nervous-just as I imagine anyone else is who'sdeep into anything creative." CAPTION: Pictures 1 and 2, Charlie Fefferman in 1961 at the University of Maryland, above, and at his home in Princeton, left.