Sho Yano is a case in point. He's been in college since 9. Four years ago, Correspondent Ed Bradley met up with the student, who was lugging his books through the hallowed halls of Loyola University in Chicago.
Yano got in after acing the SAT tests, scoring 1500 out of 1600. His parents chose the fast-track approach, and encouraged Yano and his teachers to pile on the learning.
"Some people really think I'm, like, a really pushy mom," says Yano's mother. "But if your child is going so fast and doing so well, enjoying his life, you cannot just let him stop."
"I'm gifted. I got my gift from God, and I think I better not waste it," says Yano, who made it through Loyola in three years, graduating at 12.
Now 14, Yano is in his second year of medical school at the University of Chicago.
Child prodigy Greg Smith wants to go into medicine, politics, and outer space. When Correspondent Ed Bradley caught up with him a while back, he was only 9, and about to graduate from Orange Park High School in Jacksonville, Fla.
"All throughout my life, I was always so glad when school started again," says Smith. "Just gave me that feeling that I'm back into what I love to do."
Most kids in the summer are happy to be away from the classroom, playing. But Smith says, "I was the only one on this block that was bored."
Smith is the only child of Robert, a microbiologist, and Janet, who once worked as a director of a performing arts center.
"By 14 months, he could recite, memorize books. And by the time he was 18 months, he could add and subtract," recalls Janet, who had Smith tested. "[His IQ] is in the top one quarter to one-half percent of IQs in the world."
What's it feel like to know that in some ways, intellectually, Smith will eventually run circles around his parents? "I figured that there would come a time when Gregory's intellectual ability would surpass mine," says Janet. "I just didn't dream it would be when he was 6."
Smith's favorite game is one he invented. With small colored pieces representing invading armies, he takes himself, or anyone else willing to listen, through a history of the world.
For the first six years of Smith's life, his family lived in Lancaster, Pa., and Smith went to school with children his own age. But by first grade, there was a problem. Smith was so far ahead of the material being taught, he was getting bored.
"So what they ended up doing was giving him a lot of busywork to do," says Janet. "And we weren't looking for more work for him to do, we were just looking for work at his own pace."
So the Smiths decided to look for a school system that would advance their son according to his ability. When they found one in Jacksonville, they moved there. That year, Smith started in second grade, but then quickly moved into the fourth grade. During the last quarter of the year, he was moved in sixth grade – and he was learning Algebra.
After that, Smith skipped the seventh and eighth grades altogether, and completed grades 9-11 in just a matter of months. He's a member of Orange Park's student government, and as class historian, he's frequently asked to speak to the school.
His parents have made an effort to make sure he spends some time playing with children his age, but Smith says he can only take so much play: "It's not the best thing and the most fun thing to me."
So what's the best thing for him? "I'd probably say reading and learning," says Smith. "That's what I like to do most."
But his parents are worried that their son has missed, or will miss, his childhood. "We worry every day," says Janet. "Are we doing the best for him? I think it concerns us greatly."
"But what choice do we have? What do we say,'" adds Robert.
"I have three major occupations that I want to go and try to work in. One is I want to be a research doctor. I want to try to find out new cures for diseases," says Smith.
"And another one of the things that I want to do is be a politician and try to bring peace to the world. And the third occupation that I want to do is be an aeronautical engineer and build space stations in space."
He's estimated that he'll be in school for about another 24 years. By that time, he'll be 34.
"Hmmm. You can't be president until you're 35," says Bradley.
"I know. That's the idea that I'm trying to do," says Smith.
When Bradley met with Smith six years ago, he was posing for his high school graduation picture. He went on to Randolph-Macon College, getting a degree in mathematics at 13. Now he's 15, and going for his Ph.D. in math at the University of Virginia.
There are many mysteries of the human mind. What combination of DNA, upbringing and luck makes a child a prodigy, a genius? And how do we explain the talents sometimes displayed by young people with severe mental disabilities?
Correspondent Lesley Stahl reports on Rex Lewis-Clack, a musical prodigy. He's blind, unable to dress himself, or remember his way around the house in Los Angeles. But he has a talent, and an uncanny ear for music.
His mother says it started with a keyboard he got for his second birthday. "It was like he was being transported into another world," says Cathleen Lewis.
Rex is a musical savant, and profound disabilities and musical talent co-exist in his brain. He can play games of "Can You Top This?" with a piano teacher.
This 9-year-old boy is now performing in public, rescued from the darkness of disability by music.
"He loves the applause," says Cathleen. "It really hooks him into the rest of the world."
Correspondent Morley Safer also talked to a group of musicians who are prodigies, too, in their own unique way. They have a condition called Williams Syndrome, a rare birth defect in which just 20 of the 35,000 genes in the brain are missing. It's enough to cause severe disability.
But the people that he met with Williams Syndrome seven years ago are all thriving; because of a singular talent they developed as children.
Gloria Lenhoff remembers more than 1,000 songs, yet she can't add 5 plus 4. Michael Williams can play almost anything, yet he can't go out the door without getting lost. And Megan Finn studies music in college, but can't tell left from right.
Safer met these remarkable people at a music camp in Massachusetts. They are people with profound disabilities, but with an equally profound passion for music. They often have unusual, almost elfin features. Their IQ's average in the 60s, but they have the social skills of talk-show hosts -- what's been called cocktail party personalities.
To a stranger, however, any sense of their handicap quickly disappears, and one is overwhelmed by their friendliness, their openness.
How important is music? "Music is a huge part of my life," says Finn. "To me, music is like soup. Music comes down to your throat and feels so warm. So music is like soup. It tastes good."
Lenhoff can sing in 25 languages, including Macedonian, Korean, Bulgarian, and Yiddish.
Among the things that seem to be common among people with Williams Syndrome is extremely sensitive hearing. For instance, they can hear whispering.
But they are among the happiest people you've ever met, and they are always smiling.
Williams always knew he was different, but he only learned last year that his condition had a name. At the music camp, he met other people just like him for the first time. "Somehow, I felt that I fit in," he says.
He is most comfortable at the piano, and composed the piece he was playing. But as a child, his parents never dreamed he was capable of handling the complexities of the instrument.
"My other kids had piano lessons. He didn't. We didn't think he could do it," says Frank Williams, Michael's father. "After they went out to play, he went down—plink, plank, plink, plank—for hours on end, for days on end. And all of a sudden, one day he played a song. 'What Now, My Love?' was his first song."
Frank Williams admits he was devastated when his son was born, and he clearly wasn't normal. But that changed a long time ago. "We were blessed," says Frank.
"The opportunity to study an individual with Williams Syndrome is exciting. It provides a window on brain development," says Dr. Barbara Pober, who runs a Williams Syndrome clinic at the Yale University School of Medicine.
It's a pathway to understanding how perception works by understanding the effect of those 20 missing genes.
"Surely their language skills must be a great aid to scientists because you really can learn something from them about their condition, no," asks Safer.
"Right. I mean, we can learn an awful lot about what it means to have a handicap from folks with Williams Syndrome," says Pober.
They can also learn what it means to be shunned and isolated. Last year, Finn tried living in a college dorm. While she did make a few friends, her mother, Liz Costello, says Finn had a rough time.
"'Why don't people call me? Why don't my friends, who are nice to me in classes, ask me to do something on the weekend,'" recalls Costello. "She doesn't fit in. She knows she doesn't fit in. That's very hard."
Michael Williams and the others are still performing. And Sept. 7, 2004, was proclaimed "Mike Williams Day" in his hometown of South Glens Falls, N.Y.
Jay Greenberg, 13, has written five symphonies already. He wrote "The Storm" in just a few hours. And to hear him describe it, the process is more like taking dictation: "The unconscious mind is giving orders at the speed of light, you know?"
He wrote it at 8, astonishing his parents. At 10, he entered Juilliard, New York's premiere music conservatory. "We are talking about a prodigy of the level of the greatest prodigies in history when it comes to composition," says teacher Sam Zyman.
So, if you see a young fellow humming and conducting himself on New York's Upper West Side, quiet. It's a composer at work.
Julliard is also home to five musicians, all in one family, who showed remarkable talent from the time they were toddlers. Correspondent Scott Pelley reports on the Brown family, and they all play the piano.
Desirae and Deondra Brown are getting ready for what in many ways is the biggest date they'll ever have. They're going to a concert of the Philadelphia Orchestra, one of the world's greatest.
It's the Brown sisters' first date with a major orchestra, and they hope that talent agents in the audience will hear a perfect performance. A bad night would jeopardize everything that they, and the Brown family of Alpine, Utah, have ever worked for.
Desirae, the oldest, is now 22. Back then, she says "we were practicing seven hours a day, probably, together."
The Brown family includes three girls, and two boys with a singular gift: music. Their mother Lisa has a music degree in voice, and started lessons just to give her kids an education in music. Soon, they moved five grand pianos into the house so they could all practice at once. It raised such a racket that their dad, Keith, had to go outside, just to use the phone.
"It wasn't 88 keys. It was 88 times two, times three, times four, and eventually times five," says Brown.
Ryan is the youngest at 16, followed by Melody, Gregory, Deondra and Desirae. They rehearse for six hours a day. When they were small, their mother used to wake them up at 4:30 each morning, just to fit in all the practice.
Their days was jammed, and something had to go. So the Browns decided to have their kids schooled at home.
But what about college? If you're a piano student, there is one school that you are desperate to attend. It's the Juilliard School in New York City, but the chance of getting one child into the school is slim.
Veda Kaplinsky, chairwoman of the piano department, says the school admits about 10 percent of all applicants. So the Browns couldn't believe it when Desirae and Deondra auditioned and both were accepted. The very next year, Ryan, Melody and Gregory were accepted.
Kaplinsky says Juilliard has never had five pianists from one family at the school before. After all five were accepted, the Browns rented a house just outside New York City, and moved with their five pianos, so the family could stay together.
What do five kids in Juilliard come to? "If you count room and board, it's roughly $30,000 a year, per kid," says Keith, who couldn't afford that on a salesman salary. So the family applied for every scholarship and student loan they could.
Kaplinsky teaches all five students. "Gregory [the oldest] is the virtuoso. He's the one with the big hands, the one that storms, the one that, the athlete. Melody, she's a sweetheart. She's just the sweetest girl on earth and that comes out in her playing. And Ryan is a storyteller. Ryan has great imagination."
Desirae and Deondra will be the first of the Browns to attempt to make a career of the family obsession. They're going to try as a sister act, an unusual concert duo.
"When those girls play together, it sounds like one instrument," says Kaplinsky. "They somehow read each other's minds."
Is it genetics? "The biggest factor that got them this far is the parents," says Kaplinsky.
"It was our mother's goal at the beginning, but then it became our goal when we, when, it was that turning point of, you know, 'Do I really want to do this or not,'" says Melody Brown. "And from that point on, it was ours."
The Browns seem like typical American teenagers from the 1950s. Some of that comes from their devout Mormon upbringing: little TV, no video games, and no caffeine. They are happy, optimistic, and not at all self-absorbed as some artists can be.
Who's the best piano player? "We all respect each other's playing," says Melody Brown.
Kaplinsky says all the Brown pianists have the potential of being a great concert pianist, but "I don't know if they all will be able to realize it."
Desirae and Deondra Brown had a chance to impress the right people and begin a career. They played Francis Poulenc's "Concerto for Two Pianos," and it was a flawless performance.
"I know they're not the type to step on other people's toes," says Kaplinsky. "They're the type that will work hard, and the rest is up to fate. And hopefully, the world will be kind to them."
Since that story was first broadcast three years ago, the Browns have signed a record deal. All five Browns play on their first CD, which comes out this week.