Robert Bryant knows what people think of him and his kind. They are seen as "disembodied, bloodless and solitary creatures," who do strange and obscure things behind closed doors.

"In fact, mathematicians are very social," Bryant said. "You really need to know how somebody feels about things - not just the formula."

He is director of the Mathematical Sciences Research Institute, a place where mathematicians from all over the globe can think, work and interact in an airy, light-filled building in the hills above the UC Berkeley campus.

During a five-day 25th anniversary celebration that begins Saturday, they'll be even more social than usual - converging on the international institute for panels on everything from random packing to gauge theory to Dirichlet duality. Two other sessions will be aimed at the public, along with a conversation with pianist and math fanatic Christopher Taylor.

More than 1,700 mathematical scientists visit MSRI in an annual migration that allows them to do research and attend workshops and conferences. And every year, the institute further extends its reach to ordinary people.

Bryant, 54, a UC Berkeley math professor whose five-year term as MSRI director began in August, is well aware of how esoteric math can seem to the average person. When he tells someone he's a mathematician, the questions are usually predictable.

"They'll say, 'Oh, I hate math. I liked geometry but after that I get lost,' " Bryant said. "Then they'll ask, 'What do you do?' They think of it as glorified arithmetic or bookkeeping."

They also wonder how it's possible to do research in math, Bryant said, because they assume everything has been figured out already. And they believe all mathematicians dwell in academia.

"I hated arithmetic as a kid," said Bryant, who grew up in rural North Carolina and graduated from high school with the same 30 classmates he'd had in first grade.

Just before the eighth grade, he discovered his uncle's college math books in algebra and calculus. That was all it took.

"I was hooked on math," said Bryant, whose field is differential geometry.

He sympathizes with the bemused and befuddled, and can quickly point to examples of relatively recent mathematics that show up in the real world - in derivative trading and hedge funds, models of the Earth's climate, the so-called unbreakable codes used for secure electronic transactions, compression and storage of digital images, and the algorithms that allow Internet search engines such as Google to go through millions of Web pages in seconds.

Robert Osserman, special projects director at MSRI, said the independent nonprofit institute started operating in 1982 solely as a haven for research, but began courting the public in 1993 when its "Fermat Fest" at the Exploratorium drew more than 1,000 visitors.

"That was a turning point," said Osserman, an 81-year-old mathematician who has held conversations about math with playwright Tom Stoppard, comedians Robin Williams and Steve Martin, and actor Alan Alda - who appeared at a sold-out Berkeley Repertory Theatre last week - as part of MSRI's series of public events.

The institute administers weekly Berkeley Math Circle lectures for middle and high school students, co-sponsors the Bay Area Mathematical Olympiad, brings together teachers and math researchers, and has developed a streaming video system to make its lectures available.

"We realized there really is a longing for this," Osserman said. "There is a sea change in public perception - and it surprises me. I've been interested in this thing all my life, but most people found it inaccessible. Mathematicians even have trouble communicating with each other. That's one of the main reasons for MSRI's existence."

Monica Vazirani, an associate math professor from UC Davis who is spending a semester at MSRI, said, "They do everything possible to make it a space you can do math in. There are chalkboards here and a little group of chairs there. You can break into conversation anywhere. People have their doors open. They'll wander out and join in. And chalk is always within reach.

"You can create and learn. It's very communal."

Vazirani got her first glimpse of the institute in 1992, when she was a Harvard undergraduate attending a summer program at Mills College in Oakland that included a tour of MSRI.

"They told us that this was something we could aspire to," she recalled. "Maybe it was a little ivory tower-ish, but there was this very pure idea of bringing together the best minds in this distilled environment, away from all the other details of the world."

She said it seemed like the holy grail. And it still does. Vazirani returned while she was getting her Ph.D. at UC Berkeley and also did postdoctoral work there. When she needs isolation and solitude for her research, MSRI provides that. When she wants sociability, she finds that as well - because the abstractions of math often can't be grasped without intuition, and contact with other mathematicians can help unravel the thinking that went into their concepts.

"People have picture in their heads that are not always conveyed in the written word," Vazirani said.

Although she is a woman in a field dominated by men, she was at ease right away at MSRI. "The tampon machine is free," she said. "When I saw that, I felt I was welcome there."

On a recent afternoon, the front patio's long rectangular blackboard - a magnet for chitchat and debate - was uncharacteristically almost empty. "Sweet space," someone had written. "Happy New Year!" Three raptors dipped and soared overhead.

If it's a clear day, visitors to MSRI can see four bridges. A white sculpture titled "The Eightfold Way" occupies a garden and represents the Klein Quartic, an abstract surface of 336 symmetries. Colored tiles on a wall are full of math tidbits and puzzles, and a swirling line painting on glass illustrates the 17-gon invented by mathematician Karl Gauss - the institute's address, by no coincidence, is 17 Gauss Way.

Bryant is the institute's fifth director. He taught at Rice University in Texas and Duke University in North Carolina before relocating to UC Berkeley last summer. He had to make the move: Directors of MSRI must be on the Cal faculty.

"The three founders were Berkeley professors," Bryant said. "They always had in mind a close synergy."

Calvin Moore was one of those founders, along with the late Shiing-Shen Chern and I.M. Singer.

Moore said the National Science Foundation issued a call in the late 1970s for proposals to create a math institute.

"We won," said Moore, 71, who added that the institute was in downtown Berkeley until its hilltop home was built.

"I continue to be amazed that it works," he said.

In some ways, the institute has changed very little, he said, especially with its rotating senior faculty and changing themes for each year's programs.

"It advances the discipline and trains the next generation," Moore said. "It's what we hoped for and it's been successful perhaps beyond our dreams."

ANNIVERSARY PROGRAM

The Mathematical Sciences Research Institute will have its 25th anniversary program at 4 p.m. Saturday with pianist "Christopher Taylor in Conversation with David Benson and Robert Osserman," with a reception afterward.

A panel at 4 p.m. Monday will feature leading experts in math education, and one at 4 p.m. Tuesday will focus on "MSRI: Past, Present and Future."

All events are free and open to the public and will be at the institute, 17 Gauss Way, Berkeley.

For more information, go to www.msri.org.

PHOTO CAPTIONS (Paul Chinn, photographer, The Chronicle): (Top, left) A wall of mosaic tiles featuring math computations is at the entrance to the Mathematical Sciences Research Institute near UC Berkeley; (top, right) Monica Vazirani (right) reviews a mathematics project presented by North Carolina State University graduate student Julie Beier at the Institute; (bottom, left) MSRI offered a conference focused on women in mathematics in its Simons Auditorium in Berkeley on Thursday; (bottom, right) Robert Bryant, MSRI Director, is shown next to the sculpture, The Eightfold Way by Helaman Ferguson.