Spring 2002 -- Vol. 19, No. 1

FACES OF PENN STATE

Paul Baum
Evan Pugh Professor of Mathematics

Mathematician Paul Baum says an awful lot of people don't appreciate the fact that mathematics is a developing subject. Many people, he says, somehow think that mathematics is finished.

It's fitting that Paul Baum sometimes uses baseball metaphors to describe mathematicians, considering he grew up in New York City, home of Major League Baseball's fabled Yankees. But, at an age when most boys were enthralled with baseball, Baum was falling head over heels for mathematics.

"When I was in 10th grade at the Bronx High School of Science I had a teacher for plane geometry who was just absolutely marvelous," Baum recalled. "I liked the subject so much that from that moment on I said to myself, 'This is for me. This is what I want to do.' And I never really changed my mind."

Nor does mathematics ever stray far from his mind.

"I think about it consciously and subconsciously all the time. I'm never not thinking about it," Baum said. "I'll wake up in the morning sometimes and say to my wife, "I had a wonderful mathematical night.' "

Baum's lifelong pursuit of mathematical solutions has led him to concentrate on a new discipline—non-commutative geometry—a complex, advanced fusion of algebra and geometry.

It's a topic not easily explained to the uninitiated. But, Baum contended, mathematicians must endeavor to explain their oft-misunderstood profession.

"I think it is incumbent on mathematicians to try to give the world some idea of what it is we do. There are parts of the subject that you can explain."

Part of the explanation centers on popular misconceptions about mathematics.

"Many people seem to somehow think that mathematics is finished, that there's nothing more to say. Intelligent, well-educated people have said to me, '2+2=4, what more is there to say?,' " Baum said. "There's a huge amount that we do not understand, that is unsolved. It is extremely unlikely that we will reach a point where we can say mathematics is completed."

When he's not transfixed on some equation, Baum works out to keep both his body and mind fit. If not walking or jogging, he could be found on one of the exercise machines he owns. Baum said there's a basic unity between mind and body, and exercise sometimes provides a catalyst for inspiration.

It's the type of inspiration his 10th-grade teacher provided. Some years later, the same teacher read an account of a Baum lecture in the Notices of the American Mathematical Society. The teacher later wrote him to inquire if Baum was one of his former pupils. Baum wrote back and said, "It was in your class that I first glimpsed the power and the beauty of mathematics."

And, true to his New York roots, that appreciation enabled Baum to embark on a big-league mathematical career.

"There are a small group of superstars who set the directions, who inspire us all and point us forward toward the new mathematics that is always coming to be," Baum said.

"It has been my good fortune to have written papers and worked with superstars."

-- Andy Elder

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