Is there a way to bypass wonder and just get to the answer? How much difference is there between creating and appreciating• 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.”

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