There's a story in math circles that a famous Hungarian mathematician, Paul Erdos, used to speak of the Riemann hypothesis, a famous unsolved problem, saying that all infants were probably born knowing how to prove it, but then forgot the proof by the time they learned to talk.
While babies working out mathematical proofs may be a bit of a stretch, the news that a 16-year-old may have solved a 350-year-old problem (whether true or not), poses the question of just how youth approach math differently than adults.
Edward Frenkel, a Professor of Mathematics at University of California, Berkeley, and currently Eilenberg Visiting Professor at Columbia University, is now 44. But by the age of 21, he had already been invited to be a visiting professor at Harvard.
"When you're young, you're fast and quick and able to solve things quickly ... but you may not be able to see how the different pieces of mathematics fit together," he said. "That comes with experience."
In the last few years, he's been working with the The Langlands Program (a system of advanced mathematical ideas developed by Robert Langlands in the late 1960s with the goal of tying together different areas of mathematics). When he was younger, he said, he couldn't possibly have seen the big picture in that way.
"Mathematics is not like running the 100-meter dash," Frenkel said. "It's more like a marathon."
Still, he says "there's something to be said for not being spoiled by the traditional educational system when you're young." What is essential, he believes, is the right mentorship. "Math is so abstract, you need guidance. You need someone to open the door."
Mathematics professors who work with teens say that they often see glimpses of brilliance in kids as young as 13, and that "often these long-standing problems are solved by a mathematician who takes a completely different approach," says Jonathan Rogness, assistant professor and director of the Mathematics Center for Educational Programs at the University of Minnesota.
Still, working on famous, unsolved problems is rare until later in a career.
"Usually these problems are unsuitable for study by very young researchers, since they are too hard, too well studied, and require too much background to do anything of value," said MIT mathematics professor Pavel Etingof, who also works with a high school research program at MIT.
Etingof, who was 24 when he received his Ph.D., says that success in math comes from a combination of brainpower and experience.
"Brainpower starts to decrease after a certain age, while experience accumulates over years," he said. "Experience is not as important in mathematics as in some other fields, but it is important. So the power of a mathematician often peaks in his/her 30s. Which means that young people do have an advantage. But not people who are 16. Certainly someone who is 32 has a lot of advantage over someone who is 16."
Rogness agrees that mathematicians are not in their prime until their early 20s.
"Mathematics is so highly specialized, you need to spend years and years studying general topics and then one specific area before you're at the cutting age," he said. "That said, there are certainly mathematical wunderkinds who sop up everything you give them, essentially finishing up the standard undergraduate curriculum and moving on to graduate level courses while still in high school. They could certainly make significant mathematical discoveries at an early age. But that age is more likely to be in their early twenties than their early teens."
And the key to longevity in math?
"I. M. Gelfand, the great Russian mathematician, said at his 90th birthday conference: 'I am just a student all my life,'" Etingof said.