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Faces of Penn State, 2005: W. Dale Brownawell

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Distinguished Professor of Mathematics
W. Dale Brownawell

Dale Brownawell enjoys teaching and says, “Just going into a class that's interested is a lot of fun.” The challenge, he says, is to provide utility while opening the door to beauty. He observes, “Tedious hours memorizing addition tables and such things in school do not provide a good basis for experiencing the fun and beauty of mathematics. Folks at many levels come to mathematics for its usefulness. But if they stay, they stay for its beauty.”

Years at Penn State: 35, as of 2005

Academic Background: doctoral degree in mathematics, Cornell University (1970); bachelor’s degree in German and mathematics, University of Kansas (1964)

Summer 2005 -- Watching W. Dale Brownawell talk about mathematics is like watching an artist sketch out his next painting. Speaking calmly, he reveals the truth of it as his hand glides effortlessly between equations, drawings of X and Y axes, and diagrams of curves and planes.

Many artists would agree that Brownawell’s description of developing a proof is the same for any creative process. “You can feel it happening but you really don’t know what it is at first,” says the unassuming Distinguished Professor of Mathematics. “You can see this is going somewhere, but it’s like looking through a glass, darkly. So basically you’ve got some intuition when you’re doing it that something is going on, and you kind of feel and grope your way, then you reach a point where you’re pretty sure this is it, and you nail it down.”

Brownawell leans back in his chair with the comfortable expression of accomplishment. “Then you’ve got to be able to explain it to somebody else. You strip away all the scaffolding that helped you get there, and you display in the end the finished painting.”

The world-renowned mathematician, son of a farmer and Santa Fe Railway car inspector, studied both German and mathematics as an undergraduate. After a year in Germany, where he met his future wife, Eva, he returned to graduate work at Cornell University . Mathematics would become his future, or more accurately, German would not. “Eventually, I decided I didn’t want to teach freshmen dative case for the rest of my life,” he says, smiling. “Math, on the other hand, is fun,” he continues gleefully.

Part of Brownawell’s work focuses on transcendental numbers, investigating the hypothesis that there are no surprising relationships between constants that come from analysis. But he may be best known for his discovery regarding the Hilbert Nullstellensatz, which is one of the four fundamental theorems that connect algebra to geometry. His work rendered the theorem more surely applicable to robotics, image reconstruction, and more.

Though mathematicians are a comparatively solitary bunch according to Browna-well, he admits that finding like-minded colleagues was one of the more pleasant experiences of his career. “I can’t explain the feeling when I went to my first international conference and other people were working on similar things and I didn’t have to define all of these things,” he says, nodding to a white board full of arrows, letters and numbers. “Instead of getting eyes glazed and muttering disingenuously, ‘How interesting,’ they would say, ‘Hey, that’s a great idea.’ I didn’t have to persuade them that there was something possibly interesting. And for me that was just amazingly energizing!”

At the end of the day, this veteran scholar and world traveler spends his off time inline skating, studying languages, and enjoying time with his wife. “If I get home early enough to have tea with Eva, that’s a treat,” he says.

Suzan Erem

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