Is there a way to bypass wonder and just get to the answer?
How much difference is there between creating and appreciatingâ¢
Is knowing that a solution to a problem exists the same as actually solving it?
These questions anyone can ponder, but answering them -- and proving the answer is correct -- is one of the world's biggest mathematical challenges.
It's called the P versus NP problem.
Carnegie Mellon University computer scientist Steven Rudich and Russian mathematician Alexander A. Razborov will receive a prestigious award in June for proving that a solution to the problem can't be proved -- at least not with math as we know it.
"I'm desperately, always hoping for somebody to say something different," Rudich said. "I'm not a professional pessimist, though some people think I am."
The Association for Computing Machinery's 2007 Gödel Prize will be awarded to Rudich and Razborov in San Diego at the association's annual meeting the week of June 11.
"It is a very important prize -- it is one of the two or three most important prizes in the theory of computing field," said Leonard Schulman, a computer science professor at the California Institute of Technology.
Fifteen years ago, Rudich and Razborov presented a paper called "Natural Proofs" at the Symposium on Theory of Computing. It brought decades of mathematics to a screeching halt.
"They, at once, killed off a whole futile little industry," said Schulman, director of Caltech's Center for the Mathematics of Information.
That 'industry' -- or group of mathematicians and computer scientists -- was trying to answer whether P equals NP. In other words, are easy-to-solve problems (P) the same as problems that have easy-to-check solutions (NP)⢠Rudich and Razborov didn't answer the question, but they did show that scientists couldn't do it with current mathematical tools.
Rudich uses music to put the mind-bending question in perspective.
"We all have a faculty for appreciating music and saying, 'I like that song,' " Rudich said. "But if you're so good at knowing what you like, why don't you compose a song⢠It is very intuitive that that should be a much harder thing. But why?"
Anyone who proves a solution to P versus NP will be rich. The Clay Mathematics Institute, a foundation in Cambridge, Mass., will pay $1 million for the answer to that or six other so-called Millennium Problems.
Rudich promotes that sense of wonder on a smaller scale as director of Andrew's Leap, a local summer program he helped found in 1991 that encourages children to explore math and science. He takes a simpler approach to reach adults: He entertains them through magic.
"For me the just to-die-for-thing about magic is giving adults the experience of being a child," said Rudich, an accomplished magician who starts each of his undergraduate classes with a trick. "There's just so few things in adult life where you get to just think, 'Wow,' and question the things you know."
