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Try this next time you're at a party: If there are 30 people in the room, the odds are 2 to 1 that two of them will have the same birthday.

It's an amusing parlor trick, but there's some serious math behind it.

Mathematicians call it "The Birthday Problem."

Another puzzler called "The Monty Hall Problem" is named after the moment in the old game show, "Let's Make A Deal," when Monty asks the contestant whether she wants to switch doors.

"You should always switch doors," says Jonathan Mattingly, professor of mathematics at Duke University. "Your chances are twice as good as they would be if you stick with your original door."

Mattingly, along with 50 other mathematicians from around the world, has been in residence at the Mathematical Sciences Research Institute in Berkeley for the past six months, thinking and talking about dynamical systems -- the study of how things evolve over time, such as water flowing or climate changing.

In August, two other groups of math hotshots will be in residence at MSRI for six months to study "Geometric Group Theory" and "Teichmuller Theory and Kleinian Groups."

Future sessions include such esoteric subjects as "Combinatorial Representation Theory," "Analysis of Singular Spaces" and "Ergodic Theory and Additive Combinatorics."

This isn't the math you learned in grammar school. But MSRI is trying to help the next generation learn it by sponsoring after-school "math circles" for local school kids.

One of them is Danny Stoll, 11, of Oakland, and he doesn't think of math as drudgery.

"It's fun!" he says. "I really like not understanding something for a long while, and then suddenly it pops into my head, and I get it."

By "it," Danny doesn't mean the correct answer. He couldn't care less.

What interests him is why it's the correct answer.

"One plus one makes two is not a proof," he says, "because it doesn't tell you why."

That's music to the ears of MSRI's director, David Eisenbud, professor of mathematics at UC Berkeley.

"What makes mathematics powerful is not a specific answer; it's a theory that applies to many different things at the same time," he says. "You get more bang for your buck."

Eisenbud is retiring Aug. 1 after 10 years at the helm. His successor will be Duke professor Robert Bryant.

Like many mathematicians, Eisenbud finds parallels between math and music, and MSRI sponsors a concert series each year. Eisenbud himself plays flute and sings art-songs, especially Schubert, Schumann, Brahms and Debussy.

He is also an accomplished amateur juggler who -- naturally -- has written an academic paper on the mathematics of juggling.

MSRI also hosted "The Fermat Fest" at The Exploratorium in San Francisco, where 1,000 people gathered to hear how Princeton professor Andrew Wiles solved the 350-year-old mystery of Fermat's Last Theorum; a discussion of the mathematics behind the imaging in "Toy Story;" and talks by playwright Tom Stoppard and comedians Steve Martin and Robin Williams, who discussed the use of mathematics in their work.

Situated on a hilltop high above Cal's Memorial Stadium, with a breathtaking view of San Francisco Bay, MSRI is a place where mathematicians come to do nothing but think. Or, as an old joke puts it, "Mathematicians are machines that convert coffee into theorems."

"I remember the day this place opened in 1981," says associate director Kathy O'Hara. "Somebody interviewed a mathematician, and the reporter remarked on the beautiful view. The mathematician replied, 'I come in the office and close the shades so I can do my work.' This attitude is very typical."

Such single-mindedness is necessary because math is a very frustrating life.

"You spend a lot of time in a fog of confusion, waiting for those 'eureka!' moments, but they don't come very often," says Mattingly. "Here, you can interact with people and exchange ideas. At the very least, it gives you something to do while you're stuck."

So why does he do it? "It's addictive, like a drug. You can feel your mind being stretched. For a long time you don't understand something, and then suddenly you do."

Everywhere you look at MSRI, the place abounds in elaborate mathematical jokes -- if you know enough to understand them.

The artworks on the walls appear to be nothing more than abstract art, but they're actually visual representation of mathematical formulas.

Even the address -- 17 Gauss Way -- is an inside joke.

Karl Friederich Gauss -- known as "the prince of mathematicians" -- was a 19th century mathematician and astronomer who invented the bell curve and was the first to realize that space could be curved. A unit of magnetism, the gauss, is named after him, and his name is even used as a verb, as in degaussing your television set.

"When he was 19, he solved a 2,000-year-old mystery that had been left over from antiquity," says Eisenbud. "The question was what regular polygons can be constructed with a compass and straight edge alone? Gauss proved a 17-sided polygon can be constructed and completely solved the problem."

References to the number 17 can also be found throughout the building.

The light fixture over the conference table is a 17-sided polygon -- called a heptadecagon -- and so is the table beneath it.

Curiously, when Eisenbud first approached his counterpart at the Silver Space Science Center, just up the road, with the suggestion that they name the street after Gauss, the man readily agreed but asked with a puzzled look, "Oh, did Gauss have something to do with mathematics?"

"Gauss was equally famous in the field of astronomy," explains Eisenbud. "He was even director of the Royal Observatory."

MSRI is an independent, nonprofit corporation that derives most of its financial support from the National Science Foundation.

It is one of the major postdoctoral training sites in the mathematical world, with about 25 postdoctoral fellows in residence each year.

Only one in 10 applicants is selected for these 10-month positions, and more than 90 percent of those selected accept the invitation.

"It's one of the most important things we do," says O'Hara. "We like to mix them up with the best minds in the field at a young age, and create a worldwide network they can tap into for the rest of their careers."

"We don't do any contract work for the government," says Eisenbud. "But the NSA supports us because they need more American mathematicians, and they consider us the best possible training ground."

MSRI is also supported by more than 85 colleges and universities, including M.I.T., Cal Tech, Harvard, Princeton, Stanford, Columbia and all the mathematics departments in the UC system. UC Berkeley also provides MSRI's building rent-free, and contributes senior faculty time, the director's salary, a joint visiting professorship, and access to campus libraries and facilities.

Support also comes from corporations that use advanced math in their business -- including risk analysis, genomics, signal processing, cryptography and dynamical systems -- or whose CEOs happen to be math buffs, such as Will Hearst, former publisher of the San Francisco Examiner, who was a math major in college.

Much of the mathematics at MSRI's is pure research, but practical applications are not unknown.

"You never know what the result will be," says Mattingly. "The pure coding theory of the generation before became the error correction codes in today's CDs. You have to take the long view. I mean, how many writers is it worth to support to find one Shakespeare?"