His mind is on the eighth dimension

Several years ago, David Vogan was having lunch in Paris with a fellow American mathematician. At a nearby table, some American tourists were having trouble communicating with the waiter, so his friend, who spoke French, stepped in to assist.

The two groups began chatting, and the conversation got to the "What do you do?" phase.

"My friend said, 'I'm an English teacher,' " Vogan remembered. "Telling someone you're a mathematician is a conversation-killer. I usually tell people that I play with computers."

It's understandable that Vogan, a 52-year-old math professor at MIT with shoulder-length hair and a salt-and-pepper beard, is reluctant to get into what he does. His recent work is "frightening to think of geometrically," he said, and so complex that it has left a trail of crashed computers -- very powerful computers, mind you -- all over the world.

Vogan and an international team from the American Institute of Mathematics announced last Monday that after four years of work, they had mapped something called E{-8}, one of the largest and most complicated structures in mathematics. If printed on paper, the calculation would cover 49 square miles, according to Vogan, which is more than twice the size of Manhattan. While the data for the Human Genome Project would fill less than one gigabyte of space on a computer, E{-8}, would fill 60.

OK. But what is it? When asked the question recently in a conference room on the MIT campus, Vogan let out a smile that implied, "You're not going to follow this, but since you asked . . ." Then, rather than reach for a supercomputer, he picked up a piece of chalk and drew a cube on a blackboard.

"Now, a cube has three dimensions and eight corners," he said. "To draw a picture of E{-8}, it would have eight dimensions and 240 corners."

We're sort of following you, but how does an eight- dimensional object factor into a three-dimensional world?

"A lot of people ask that question," Vogan said, before reaching for another concept that a layman might understand. "Try and think of it like the movement of the planets around the sun. Each planet has a position that's three-dimensional and a velocity that has three dimensions, so you would need 54 dimensions to map the position of the planets. For E{-8}, you would need 248 numbers to describe where you are instead of just two numbers to find where you are in a city."

Vogan has been a math superstar since his undergraduate days at the University of Chicago, according to Paul Sally, 74, a Roslindale native who was his mentor there. "His progress was just phenomenal. He's one of the top two students I've had in my 42 years teaching undergraduates. He quickly became one of the truly bright young mathematicians in the world. He's not young and bright anymore; he's just one of the best."

But math superstars are not above a bit of geek criticism. A reader on Slashdot, a website that bills itself as "news for nerds," compared Vogan to the Vogons, who are responsible for destroying the earth in Douglas Adams's "The Hitchhiker's Guide to the Galaxy." The book describes Vogon poetry as the third worst in the universe.

"The title of my talk" announcing the findings was "The Character Table for E{-8}, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness,' " Vogan says. "Someone called it the second-worst poetry in the universe.

"So I was elevated one level above that, which is nice."

Hometown: Grew up in Bellefonte, Pa.; lives in Arlington.
Education: After receiving his bachelor's degree in mathematics at the University of Chicago in 1974, he earned a PhD at MIT in 1976.
Family: Wife, Lois Corman, is a church administrator; son, Jonathan Vogan, 27, works with Doctors Without Borders; daughter, Allison Corman-Vogan, 18, is a senior at Arlington High School and will attend Brandeis in the fall.
Hobbies: Hiking in the White Mountains; reading mystery and science-fiction novels. What draws him to difficult math: "It's like crossword puzzles or mountain climbing. It's something that's possible to do, but just barely."
Where to find him on Sunday mornings: Ringing the bell atop the Old South Church at exactly 10:45 a.m.