The pursuit of beauty

MU professor says finding patterns nobody else can see is the thrill of being a mathematician
Monday, January 30, 2006 | 12:00 a.m. CST; updated 5:32 p.m. CDT, Monday, July 21, 2008

A photograph of Nigel Kalton, taken when he was 8, seems to foretell his destiny. In it, his neatly combed hair frames protuberant ears, and round-rimmed glasses dwarf his face. His smile reveals two buckteeth. He wears a black blazer, striped tie and a stiff-collared white shirt. They are components of Nigel’s school uniform, but they make him look like he raided the closet of The Absent-Minded Professor.

At a typical American middle school, little Nigel would have been a nerd. But at London’s prestigious Dulwich College, he was a mathematical prodigy.

The school knew it; Nigel received a government scholarship to study there. His family knew it; they joked he could be a quiz show marvel with his talent for mental arithmetic. And it’s clear, from his high-held chin and mischievous eyes, the boy in the photograph knew it, too.

Now 59, Kalton has grown up to be a renowned mathematician. In 1979, he left the University of Wales Swansea and joined the math department at MU, where he continues to be a star attraction. He has published three book-length research articles for the American Mathematical Society, 215 scholarly papers and one book. One more book will appear in 2006. The Kalton-Peck space, a mathematical entity he introduced in a joint paper with N.T. Peck, bears his name, and in 2004, he won the Polish Academy of Sciences’ coveted Banach Medal for his work in the mathematical field of Banach Spaces.

A Banach Space is an infinite-dimensional construct, which provides a framework for the study of many important mathematical problems.

Kalton’s inability to wake up in the morning led to his specializing in Banach Spaces. As a student at Cambridge University, where he completed both his undergraduate and graduate degrees, Kalton had to choose one area of study as his concentration: algebra, topology or analysis. Lectures in algebra and topology were held at 9 a.m., so he chose the analysis lectures, which allowed him to ease in at 11 a.m.

His favorite analysis professor introduced him to Banach Spaces, and the elegance and beauty of the theory captivated him. He is now considered one of the world’s experts on the subject. A conference on Banach Spaces will be held in April — in honor of Kalton’s 60th birthday.

Kalton’s mellow persona coexists with a keen and focused mind. In his graduate-level class on Banach Spaces, Kalton races through proofs on the board, but he always pauses to thoroughly address his students’ questions. Occasional moments of comic relief punctuate the mathematical discussion, such as when Kalton drops the chalkboard eraser and cannot find it.

Simon Cowell, a student in the class and Kalton’s graduate assistant, says ease graces the professor’s interactions with others. Cowell fondly remembers Kalton treating the students in his graduate seminar to a round of drinks at the Heidelberg and joking that the outing was their final exam.

Over the course of his 26 years in the United States, Kalton has exchanged his blazer and tie for sweatshirts, jeans and Reeboks. His hair, now gray, is longer and less tidy. He has twice been mistaken for Jerry Springer, but nothing could be further from Jerry Springer’s bloodlust than Kalton’s rapture over the abstract.

In his sparsely decorated office, Kalton leans back in his chair and smiles as he describes sojourns in a strange land most people will never see.

“I mean, for me, it’s the pursuit of beauty,” he says. “You’re looking for patterns in some sense. When you see that pattern, and it’s like nobody else can see it, that moment you know, you have this thrill of something beautiful. Like a discoverer might have, but it’s a rather bizarre form of discovery. It’s all internal.”

Kalton is a pure mathematician. He does math for math’s sake. He does not worry about the applications of his research.

Jenny Kalton, Nigel’s wife of 36 years, knows firsthand that his disregard for practicality extends beyond his mathematical interests. Jenny says Nigel is often in “math mode.” When he chews his fingers and stops communicating, Jenny knows his mind has left this world to explore another. If she’s in the car, Jenny won’t let him drive because she suspects he’s “mathematizing.” She has sound evidence to back her suspicions: Once Nigel arrived in Memphis without remembering his five-hour drive there.

When Jenny started dating Nigel, his preoccupation with math worried her. She was working as a secretary in the economics department at Cambridge when she met him at a party. He spilled a drink on her. But as they continued their courtship, Jenny discovered Nigel’s fun side. Once, they even crashed one of the university’s fancy May Balls.

Every May in Cambridge, after the exams are over, people dress in their finest to attend these formal dances. Because they feature pop stars and freely flowing champagne, tickets are expensive. Nigel couldn’t afford to go. One year, he and a friend, emboldened by alcohol, found an attendee wandering around campus and asked him to bring them some champagne. Because it was after midnight, the man presented them two free tickets that, earlier in the evening, he would have scalped. Nigel attended the ball as Mrs. Olive Smith and drank as much champagne as he wanted.

The next evening Jenny, who had heard about the previous night’s mischief, also wanted to go to a ball. Jenny and Nigel tried to climb over a wall in their evening wear, but a night watchman caught them. They improvised a convincing yarn about needing fresh air and not wanting to go in the long way. Jenny’s parents, who were attending the ball, had smuggled the couple pins that designated attendees as legitimate ticket holders. Because Jenny and Nigel were wearing them, the night watchman let them in.

During these adventures, it is possible Nigel Kalton was calculating a problem in some part of his mind. Math is Kalton’s madness. It is also his drug. Peter Casazza, one of Kalton’s colleagues at MU and one of his closest friends, understands this. Casazza has rearranged his whole life to study math. He goes to bed at 2 p.m. and wakes up at 10 p.m. so he can research all night, undisturbed by the rest of humanity.

“Really good mathematicians are driven,” Casazza says. “We’re not even necessarily doing it because we like it that much. We are driven by something, and half of the time, we don’t even know what that thing is. All we know is, we are unhappy any day that we don’t get to do mathematics. We are unhappy unless we’re moving forward on a theorem.”

Kalton jokes that he never looks like he’s working, but his affability camouflages his drive to be the best. His grandchildren have learned that he won’t let them win at hide-and-seek, and Casazza has learned that Kalton plays to win their racquetball matches.

Math is no different, except Kalton’s competitor — himself — grows increasingly difficult to beat.

“Because of his apparent lack of arrogance, people think he doesn’t know how good he is. He knows full well how good he is,” Casazza says. “But he’s not comparing himself to other people — only to himself. The most important thing is not, ‘Am I better than others?’ but ‘Am I as good as I want to be?’”

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