"The truly real takes place almost unnoticed, and is, to begin with, lonely and dispersed . . . Those among our young people, who 30 years hence, will do the things that matter, are, in all probability, now quietly biding their time; and yet, unseen by others, they are already establishing their existences by means of an unrestricted spiritual discipline."

-- Karl Jaspers, philosopher

At age 3 she began to read. At age 6, her father gave her piano lessons. At age 7, she had a math tutor. At age 8, another tutor taught her Latin. At age 9, she took up the violin. At age 11, she studied calculus. At age 12, she took French at a local university. And this fall, at age 15, Valerie Beth Vigoda, the only child of a pianist and his wife from McLean, became the youngest member of the freshman class at Princeton University.

Door after door has been opened before her, as if the nature of her genius might reveal itself behind the next one. She has many interests, from music to genetic engineering, but so far Valerie Beth Vigoda has no obsessions, no passions. The doors are still opening, the nature of the genius yet a mystery.

"I haven't done anything big yet," she says. "I have this gift, and I don't want to waste it. I want to contribute it."

Valerie Vigoda is an adolescent on the threshhold of maturity, a 15-year-old college freshman whose plea is the cry of adolescence: She wants to fit in and be accepted by her peers. "I don't want to threaten anyone," she says.

Those who know her are dazzled by the promise of her genius IQ, her precocity at calculus, which is overwhelmed by her literary gifts and her prowess with the violin. And everybody -- those who know her intimately and those merely acquainted through her formidable array of academic qualifications -- awaits the ultimate returns with the eagerness of those who send explorers to an unknown land.

In her mother's words, it all comes down to potential, which is not enough. "I tell her potential and 25 cents will buy you a cup of coffee," says Geri Vigoda, a housewife and former secretary who is revered by her husband as the one in the family with the common sense. "IQ -- who cares? The question is: What have you done lately?"

Her daughter's potential, to the extent it can be measured, is awesome: Her score on the Stanford-Binet IQ test at age 7 was 212. (100 is average, over 132 is considered gifted, over 180 extremely gifted.) Frances Goldman, the school psychologist who tested her, has never found another child with so high an IQ.

Even so, Goldman thought Valerie could have scored higher, "but she got pretty bored answering the questions at the end."

Another psychologist, Julian Stanley, who is director of the 11-year-old Study for Mathematically Precocious Youth at Johns Hopkins University, tested Valerie shortly after Goldman did and described her as "exceedingly brilliant intellectually . . . almost unbelievably bright."

Bob Vigoda, Valerie's father, was overwhelmed. He recalls his amazement at one of Goldman's predictions, now fulfilled: "She told us we'd better get used to the idea of Valerie going to college at some incredible age like 15."

For Valerie Vigoda, so far so good. Behind the ivy-covered walls of one of the nation's most prestigious universities, she is solving problems in honors multivariable calculus, reading the works of Thomas Mann and Franz Kafka and traveling by train to Baltimore every other week for violin lessons. Another teacher has already said that within five years she could find a place with a major symphony; her list of musical accomplishments includes a stint as concert mistress of a chamber orchestra at Baltimore's prestigious Peabody Conservatory. The walls of her bedroom at home are hung with academic and music awards.

Psychologists decline to use the word, but laymen have little trouble calling Valerie a genius. In addition to demonstrating the dazzling talents implied in the word, she shows one thing more: Genius need not be abnormal or perfect.

The lesson surprises even her father, who graduated from college with a degree in philosophy. "Sometimes I think that if Valerie were potentially as smart as everyone says, she'd get all A's and be the most outstanding student anyone's ever seen, and she's not that." His daughter's lowest final grade was a B. She graduated with a 3.55 average -- that besides a frenetic schedule that included weekly violin lessons, up to four hours a day of practice, traveling to competitions and her participation in a local quartet.

Almost everyone who meets this teen-ager with the long brown hair, wide-set blue eyes and ready laughter agrees she is bright, articulate and poised beyond her years. "I just think of her as a very sweet girl who happens to be a genius," says her aunt Joan Collier, an English teacher from Salinas, Calif. Her niece does not show off, as some bright children do, with conversation about the language of computers, the profundities of Nietzsche or the poetry of Shakespeare. Valerie can discuss these subjects, but she would just as soon talk about: her favorite mystery writer, Agatha Christie; the latest movie she has seen, E.T. -- "I thought it was great"; what she considers to be the foolishness of a friend who aspires to be a housewife -- "Imagine aspiring to that!"; the delights of Szechuan food; the friends she made at music camp last summer including a cellist she liked particularly -- "He was so reflective."

She ponders such unanswerable questions as, "What is death?" and "Is there a God?" but this college student who says she has not yet been in love also wonders: "What will the young men at Princeton be like?" Her ignorance in some areas -- geography, for example, which she missed entirely in her flight through school -- is a family joke. At dinner one night before she left for Princeton, she happened to ask sincerely, in a conversation about a friend who had gone to Europe, "Isn't Brazil near Yugoslavia?"

One week after classes started at Princeton, she dropped physics. "I was terrified," she says. "It was too hard. The textbook was unreadable." She switched to chemistry.

She is impressed, perhaps a little awed, by some of her colleagues. "There are so many experts. They say, 'I'm a sculptor; I'm a photographer.' People here know all about international relations, politics, religion . . . There's so many things I've never thought about."

She loves such classical composers as Brahms and Dvor,ak and enjoys going to the Kennedy Center, but she also wishes her parents would let her go to a rock concert. She likes Billy Joel, Elton John and Barry Manilow. Dostoevski is one of her favorite writers, but her summer reading included Seventeen magazine, and she freely admits she had trouble understanding in The Brothers Karamozov the chapter about the Grand Inquisitor. Though gifted in math -- she scored 780 on that portion of the Scholastic Aptitude Test last year out of a possible 800 -- she rejects the suggestion of a career in pure mathematics. "I imagine some wimpy guy with big glasses sitting in some shabby room with a big sheaf of papers and a calculator."

Shirley Grossman, a family friend who has watched Valerie grow up, says, "Valerie wants to go to the prom, she wants to play softball. She's not the stereotype. She's prettier than Einstein . . . I don't know how she's stayed so down to earth because she's been treated as a gifted person from very early in life -- almost as a national resource."

Valerie is aware that adults who look for the genius in her sometimes are perplexed, perhaps disappointed. "I'm supposed to be interested in computers and current events," she said. "I'm not . . . I don't have a specific interest yet . . . I'm not obsessed with anything. Maybe I will be later."

What does interest her then? "Life."

When she was 11, she went on the MacNeil-Lehrer television show as the local angle in a story about an Illinois couple suing the public schools because they felt their son, who had a 170 IQ, wasn't getting the proper education. Lehrer seemed to be expecting a brainy misfit. A scared and all-but-tongue- tied Valerie told him, "I just feel like I'm pretty normal."

If that has become one of the themes of her life -- to be normal, not to be set apart -- then she has succeeded for the most part. Her education was kept within the public schools, though it was carefully and aggressively directed by her parents, who immersed themselves in the literature of the gifted child and conferred often with teachers.

She has a large circle of friends, an intense and often fun-loving group that includes a violinist who wants to be a world famous soloist, a violist who hopes to join a European orchestra, a cello- playing composer, a poet from California, a girl who wants to be a biochemist, another who wants to be an accountant and, of course, the girl who wants to be a housewife. They signed her yearbook with the usual, "You're a sweet girl" inscriptions and made affectionate jokes about her age: "Remember, when all of us reach that dreaded big 30, you'll still be a youthful 26." She went to the senior prom with the violinist, 17-year-old Marc Ramirez, who says, "She would rather people not think of her as weird. People ask her if she's a brain. She just says, 'I don't know.'"

Over a long, raucous dinner at a Chinese restaurant four days before her departure for Princeton, Valerie and Marc and eight of Valerie's other friends discussed everything from the definition of a lerp ("worse than a wimp, a totally worthless person") to the meaning of life, a question that was addressed cynically by the composer, 15-year-old Tony Daniels, who said, "Life's a bitch, then you die." They listed Valerie's merits, as they saw them: She is "funny," "spontaneous," "adventurous," "carefree," "not a shallow person." "She laughs a lot." "She is herself."

Eric deWaardt, 18, the cellist, who will be studying at the Juilliard School in New York this year, sympathized with Valerie's burden of brilliance.

"You're supposed to want to know: 'How does a cigarette machine work? How do they get the tobacco in there? Why, why, why?' You're supposed to be walking around all day long asking 'Why?'"

The others said they don't give Valerie's intelligence much thought. What is important, they said, is to be the best that you can at what you do. "You can't waste yourself," Tony said. "You wouldn't chop off a hand."

"You wouldn't become a lumberjack," said Liza Barons, who is a freshman at Wesleyan.

"What's wrong with being a lumberjack?" Eric demanded. "If you like being a lumberjack, be a lumberjack . . .I know so many of my friends, their parents come home and say, 'I hate my job . . .'"

Valerie, who seems to have inherited her mother's practical streak, interrupted impatiently, "You're not going to be happy every minute."

When she entered Langley High School at age 11, it helped that Valerie looked 14, and at first the other freshmen assumed she was their age. But she confided her age to a new friend, who promptly told half the school. Valerie was crushed and angry. "I wanted people to know me, before they knew about me," she said. Ask her about that astronomical IQ, and she says, "It goes down as you get older." She maintains that her mind is not extraordinary -- "It just works faster" -- and says, "I didn't seem like the smartest kid in school. My grades weren't incredible. I wasn't always prepared."

Twelfth-grade biochemistry was just as tough for her as it was for many other students. "Sometimes I'd think: 'Oh, I'm supposed to be so smart, why don't I understand this?'"

Julian Stanley at Johns Hopkins, who has had a keen interest in Valerie over the years, explains the workings of her mind: "She has a wide range of general information. She picks up information easily and remembers it well . . . She's much faster and surer about it, the same way Mozadt was much faster and surer about composing music when he was 5 . . . Her greatest abilities are verbal and musical. She's just excellent at math." If she does not sound brilliant, he says, it is because "she's comfortable with her brilliance. She doesn't need to show it off. When she needs it, she uses it . . . She's not a pedant."

As for why and how and from where it all came, he cannot illuminate the mystery more than this: "There was some very fortunate coming together of the genes in that child."

On her mother's side, her grandfather was an Irish-born airplane mechanic who refused all his life to ride in a plane; on her father's side, her grandfather is a cantor from Czechoslavakia who first dreamed of becoming a doctor but was thrown out of medical school in Transylvania during World War I because he was a Jew. The 89-year-old cantor, Samuel Vigoda, who lives now with his wife in the Bronx, could not be prouder of his granddaughter. "It's from the generations," he said. "It's handed down. It's in our family . . . I was a brilliant child. She got it from me."

He had three sons, who grew up to be Valerie's father the pianist, who plays everything from classical to the blues at parties and clubs; a Harvard-educated lawyer whose clients include Stevie Wonder; and a cardiologist. The cantor dreams of his granddaughter becoming something grand, like a famous violinist. "I hope at least she'll be very successful and grow up to be somebody that people will adore and appreciate, and she'll reflect glory on all of us."

But the cantor cautions that Valerie is young, still untested, certainly not a genius. "Genius is a big word. She's too young yet to say that she's a genius . . . She might grow up to be a genius. Princeton -- that's the place for geniuses. Albert Einstein was there. The place is filled with the ghosts of geniuses." He pronounces his granddaughter "an almost genius."

There is a sense that everyone, including Valerie herself, is waiting to see what she will become. Her parents say they simply want her to be happy. Her father, who says his parents looked upon him as a musical prodigy when he was a child, says, "We just hope that she will thrive and bloom there (at Princeton), in many ways bloom more than she has up to now. Whatever potential she has, we'll find out."

Valerie's mother, who went back to work as a secretary to help pay for tuition at Princeton, says her dreams for her daughter over the years have become more realistic. "I'm no different from any other mother in the world. When I saw her playing the violin, I had visions of her being a humongous star, immortalized . . . My dream now is that she be successful in whatever she chooses . . . That she be doing important work, that she be safe and happy."

The world expects much of children like Valerie, and it is perhaps tempting for those who watch with fascination from the sidelines to wonder how such gifts can be applied. Could they cure cancer? Conquer inflation? Compose brilliant concertos? Create great and illuminating literature?

William Durden, who has worked with hundreds of gifted children as director of the Johns Hopkins Educational Programs for Intellectually Gifted Youth, says that is not the point of all the tutors, the special courses, the grade skipping. The point for children like Valerie, he says, is "to prepare them to meet chance . . . prepare that child, that human being, to fulfill their personality."

One of the results of Valerie's rapid education is that she is going off to college at an age when her peers are just starting the 10th grade. The Vigodas are understandably worried. Their daughter is a college freshman forbidden because of her age -- and restrictions set by her parents -- to drink, drive, see an R-rated movie or stay out all night. "She's ready for academic work now," her father said. "She's able. There's never been any doubt of it." But he was close to tears when he looked at his daughter one afternoon a few weeks before she left and said, "We hope you don't get hurt."

Valerie will probably have more rules and guidelines set by her parents than will the average college freshman. Her parents say there will be frequent visits, almost daily telephone calls in the beginning. "The bottom line in this house," Mrs. Vigoda says, "is Mommy knows best." Valerie, with characteristic self- confidence, expressed no fears -- not of academic or social pressures -- only an eagerness to begin. In the weeks before she left, she gave a daily countdown: "Ten days, nine days, eight days -- I can't wait."

Several weeks before classes, the Vigodas traveled to Princeton where Valerie opened her first bank account and saw her dormitory room in an old building with ivy climbing the stone walls. She and her parents also took a round-trip bus ride from Princeton to New York City so that Valerie, a child of the suburbs, could learn the route. (She had originally planned to take violin lessons with a Juilliard teacher, instead of in Baltimore). Once in New York, they caught the subway from the Port Authority building on 42nd Street ("There are hookers out there," Mrs. Vigoda warned her daughter) to the Juilliard School at Lincoln Center. Valerie winced at the screeching brakes and the stench of the underground. Her father approached two police officers in the subway and, with a glance at his daughter, asked: "Are you guys here all the time?"

By his own admissions a somewhat dreamy man, he finds his daughter's facility for remembering things helpful in unexpected ways. On his way to a pay phone to call his parents, he turned to Valerie, "What's my folks' phone number?" At Princeton, Valerie looked, in her blue jeans and red "Have a Coke and a Smile" T-shirt, like hundreds of girls on hundreds of college campuses. She would soon be one outstanding freshman among 1,130, in a class that includes 481 class valedictorians (out of 1,398 valedictorians who applied), the principal cellist for the Cincinnati Youth Symphony, the principal harpist for the Memphis Youth Symphony, the 1981 National Champion in Extemperaneous Speaking in the National Catholic Forensic League, the second highest SAT scorer in the state of New York, the third-place winner in the prestigious National Westinghouse Scholarship competition.

Princeton wanted Valerie badly. Admissions Office Regional Director Robert Van Vranken says it had been "a personal goal" to convince Valerie and her parents to choose Princeton over the other colleges that had accepted her: Yale, Swarthmore, Smith, Georgetown, Johns Hopkins and Peabody Conservatory in Baltimore. "There were 11,780 applicants--and then there was Valerie," he said. "I remember it was late at night when I read her application. My wife had gone to bed. I was finishing up the V's, and I came to hers. I went running up the stairs to my wife and told her, 'You've got to read this!'"

There followed, for the Vigodas, a trip by train to Princeton, a tour of the stately campus and lunch in the faculty dining club with Van Vranken. Valerie recollected, "There were all these great professors. Mr. Van Vranken was pointing them out. He was saying: 'That's a great anthropologist. He has written great books.'" Van Vranken says that among the ranks of the distinguished he had pointed out that day was a Nobel Prize winner, physics professor Val Fitch. Valerie, who saw many professors and buildings that day, does not remember him and admits that, like many people, she confuses the Nobel and the Pulitzer prizes. To her, there seemed to be an abundance in the dining room of "bald old men."

If all goes according to plan, Valerie will receive her undergraduate degree at age 19. But the girl described by her grandfather, the cantor, as "always the youngest and the brightest" will not be setting any records. Princeton's youngest freshman in recent history was a 13-year-old math whiz. He is now 15, the same age as Valerie, and a junior. Always, it seems, at Princeton as in life, there is someone younger, brighter, in more of a hurry.