BOZEMAN -- The girl with dark hair falling down to her waist smiled for her graduation photo, looking a lot like any other student about to graduate from Montana State University. She and her mom laughed as they tried to figure out which end of the black cap goes in front. Mom secured the mortarboard with bobby pins to keep it from flying away in the breeze. Then they posed together, touching foreheads. Mom smiled and looked right in her serious girl's eyes and said how very, very proud she was of her daughter. She may look like any other student about to graduate, but Promethea Olympia Kyrene Pythaitha is only 14.
In about a week, when she walks up to receive her diploma in mathematics, wearing the gold tassel that means highest honors, she will be the youngest student ever to graduate from MSU.
Her grade point average is 3.83, she said, adding self-critically, ''It isn't perfect."
She actually was 13 when she completed her degree on Dec. 17, 2004, according to MSU's registrar's office.
Math professor Warren Esty verified that Promethea will be MSU's youngest graduate -- an honor previously held by his own daughter, Norah, who was 17 when she graduated seven years ago.
Graduation is bittersweet for Promethea.
She wants to keep studying and earn four or five more bachelor's degrees. But paying for it is an obstacle. A local family, whom she would not name, generously volunteered to pay her tuition up until graduation. Until she figures out how to get back into class, she feels frustrated and sometimes depressed.
''I'm grateful for being given by Montana State University and the people who paid for my education the opportunity to learn," Promethea said. ''But I can't feel well-accomplished, because I have so much to learn, so much to do with my life."
She'd like to study physics, chemistry, biochemistry, electrical engineering, computer science, and then plunge into nano-technology and fuzzy logic.
Every other child in America can go to school for free until they're 18, said her mother, Georgia Smith, 51.
''I feel almost discriminated against," Promethea said.
Promethea speaks with a touch of an accent, a mild version of her mother's native Greek accent.
A year ago, Promethea went to court to formally change her name from Jasmine Li Lysistrata to something that better reflected her aspirations and personality. She chose heroic, feminist names from Greek mythology. She picked Pythaitha, which means oracle, she said, because ''I kind of think I've got something important to do, like fulfilling an oracle."
She ticks off the world problems she wants to solve -- global warming, acid rain, ozone depletion, nuclear pollution, cancer, diabetes, AIDS.
''I want to use all this knowledge," she said, ''to do research, to serve humanity."
Smith worked cleaning houses and offices, often the midnight shift, so she could accompany her daughter to all her classes, to keep her safe and support her emotionally.
''She sacrificed everything for me," Promethea said.
It was hard for Promethea, being elementary-school age in an adult world. Some students were supportive, and those she'll never forget. But others ignored her, put her down or refused to work in labs with her.
''I felt like a hologram, like a fantasy" to other students, Promethea said. ''Sometimes students treated me like a bucket of animal waste. I've gotten used to it. I understand human nature better.
''Humans do make mistakes, but I still love humanity."
Like any good college education, Promethea's changed her and opened her eyes to new ideas. Sometimes it left her disillusioned.
''Einstein used to be my idol, my hero," she said. When she learned he contributed to the creation of the atomic bomb and to the deaths of hundreds of thousands at Hiroshima and Nagasaki, she tore down her Einstein posters. Plus, she said, he turned out to be ''a lousy father, a lousy husband."
''I'm not going to be a scientist who's not morally upright," she said.
Promethea audited her first MSU class, calculus from professor Richard Gillette, when she was 7.
She had been taking advanced math classes over the Internet since she was 5 from Stanford University's Education Program for Gifted Youth. When the CBS network broadcast a report about ''whiz kids," she was one of the children featured.
After that, the late MSU President Mike Malone then let her enroll as a regular student, earning credit toward graduation.
''He opened the university to me, he opened the gates of heaven," Promethea said.
It was a bright moment for a family that has experienced a lot of tragedy. Smith said when she was a girl, her single mother couldn't support her and had to place her in an orphanage.
''When I was 9 years old, my only dream in the orphanage was to have a child who would save the world," Smith said.
Her older daughter, Vanessa, was left paralyzed by a car crash, and her son, Apollo, grew up developmentally disabled. He also seemed exceptionally bright as a baby. His mother blames the change on his bad reaction to immunizations.
For several months when Jasmine, as she was called then, was 4, the family was homeless, living in a car in San Francisco. That's when her mom started teaching her advanced math.
Promethea said she'd never have made it to graduation without the help of MSU Registrar Chuck Nelson and math department chair Ken Bowers. They have been like father figures, she said.
Since finishing her studies, Promethea has been trying to fix up the house she and her mom moved to near Livingston. They described it as a fixer-upper with many problems. The shower and toilet aren't working.
Promethea has been learning to use power tools, trying to do electrical repairs, and teaching herself carpentry and concrete work from how-to books.
Promethea said she doesn't feel that she lost out on the things that make up a normal childhood. She doesn't really relate to kids her own age, who tend to giggle at her, and she has ''absolutely" no interest in boys or makeup.
She seems happiest when talking about the great professors she had at MSU -- whether in math, chemistry, quantum mechanics or American Indian studies.
Asked what she'd wish for the future, Promethea's first reply was ''Dismantle nuclear weapons." That's what she'd wish for the world. For herself, her wish is to ''get back to school."