| Dan Kalman’s mathematical world BY MIKE UNGER If, when engaging in pleasantries with math professor Dan Kalman, it strikes you that maybe he’s not fully invested in the conversation, that his mind may be elsewhere, consider yourself in good company. “The way I look at the world is indelibly influenced by the fact that I’ve spent all my life in math,” Kalman says. “You can do it anywhere at any time. I think about it when I wake up in the morning and when I go to sleep at night. During dinner my wife will tell me about her day and I’m not listening because I need my fix. It gets me in trouble. Math has completely taken over my life at this point.” But don’t misconstrue: Kalman is no John Nash, so absorbed by his discipline that he has problems communicating with the non-math world. Quite the contrary, in fact. Kalman is an affable man who just happens to harbor an unyielding passion for the subject that has captivated him since the seventh grade. While equations and mathematical problems often take up permanent residence in his brain, Kalman has dedicated much of his academic career to explaining mathematical concepts in ways digestible to the masses. “Most mathematicians have a specialty area where they’re very focused,” he says. “What I do is on the borderline of research and exposition. In exposition, the idea would be to try to take known mathematics and simply explain it in a clear way, and an attractive way, so that an audience of people who don’t know about this subject would be interested to read about it.” To demonstrate, Kalman hops out of the desk chair in his Gray Hall office, grabs a piece of chalk and begins to scribble away. He does this three or four times during the course of the hour, writing numbers, formulas, fractions, shapes—the language of math—on the old-fashioned green chalkboard hanging on the wall. This time he’s demonstrating how legendary Greek mathematician Archimedes explained the formula for calculating the volume of a three-dimensional sphere. Kalman had the idea—he’s not sure where it came from—to expand on Archimedes’s work and explore questions surrounding the volume of four- and five-dimensional spheres. “A question like this could lead to something interesting or it could lead absolutely nowhere,” he says. “[But] I’m at my happiest when I’m working on a problem and making headway.” Born in California, Kalman attended Harvey Mudd College with the idea of becoming a high school math teacher. It wasn’t until the end of his undergraduate experience, just before he went on to the University of Wisconsin where he earned his PhD, that he considered teaching at a higher level. After four years of doing just that at Wisconsin-Green Bay, Kalman decided to enter the private sector. It was the mid-1980s. “There was an awful lot of stuff going on about how many teachers at the high school level and above were leaving teaching and going into industry,” he recalls. In 1985 Kalman and his wife, Linda, moved to Los Angeles where he took a position as a computer programmer at Aerospace Corp., analyzing the performance of proposed space-based programs. While he enjoyed the work, he yearned to return to the classroom. “I never really got out of academia. I was doing research and writing papers the whole time I was in industry . . . The problems were stimulating; I enjoyed the people I was working with, but at the end of the day, I really didn’t much care whether a surveillance system got put up [into orbit] or not. I would read in a newsletter about the way someone was teaching calculus, or ideas for reform, and I cared very much about those things.” Kalman arrived at AU in 1993 and quickly began the tenuous task of developing a new math course for freshmen who didn’t test out of the subject in high school. His course, centered around mathematical modeling, replaced Finite Math, which he thought held little intrinsic value. “Everybody tells everybody else how important mathematics is and how applicable it is, but in formal education, students are very unlikely to see any sort of [legitimate] application,” he says. “When I worked at the Aerospace Corporation, there was never a day when someone walked in my door, put a textbook down on my desk and said ‘solve problem 28.’ What happens is someone walks through my door and there’s something they’re thinking about. You get into a negotiation back and forth, you try to explain things that are possible, the other person tries to decide well is that analysis going to help me? “Part of what I try to do in this course is to give the students some sort of insight about what the true nature of mathematical application is, what’s called mathematical modeling. The idea that you have some situation in the real world which you approximate in some mathematical fashion.” Finite Math: Elementary Modeling is still taught today, and Kalman turned the materials he used to craft the course into a book, Elementary Mathematical Models: Order Aplenty and A Glimpse of Chaos. Kalman doesn’t harbor any fantasies that his course will turn previous math-phobes into budding Pythagorases. “I don’t have any illusions that if a certain type of student is given a choice between going to this lecture about how mathematics operates in everyday life, or, you can do anything else you want . . . that they’d choose the math class,” he says. “But they don’t get to make that choice . . . so my goal is they’ll walk out of the math class and say, ‘That was something worthwhile.’” For Kalman, math is embedded in the very essence of his being. “In the same way that some people are consumed by crossword puzzles or Sudoku now, a good math problem is one that’s doable but not easily doable. The harder the problem the greater the reward when you triumph over it. The only assistance I have is the power of my brain, and when I trample that problem under my feet I get a euphoric sense of accomplishment. The experience of that is habit forming.” |
