Unlike many of his colleagues, mathematician Edward B. Burger doesn't teach concepts like number theory, geometry, or topology through equations and a blackboard.
Instead, the Williams College professor favors a more creative approach. To teach about topology, the geometry of surfaces, for example, he asks students to figure out how they would remove their pants and put them back on with their ankles tied together. Burger, wearing huge Red Sox boxer shorts under his trousers, demonstrated that challenge last summer at the Boston Public Library.
Burger, 41, has taught at Williams for 15 years, and is the co-author of a new book, "Coincidences, Chaos, and All That Math Jazz," with Michael Starbird of the University of Texas, Austin. The book, published by W.W. Norton & Co., gets double billing in the Library of Congress catalog: filed under both math and humor.
In a recent interview, Burger spoke with Globe correspondent Lisa Palmer about his work.
Q: You've written numerous professional articles on mathematics and five textbooks on the subject. Why did you decide to write a math book for the math phobic?
A: First of all, the idea of mathematics phobia annoys me. There's no history phobia, no English phobia, no sociology phobia. . . . Somehow mathematics phobia rolls right off the tongue with no problem. On behalf of all of those math-hating people, I personally apologize to them for their experience [laughing]. . . . Some books say they are for the general public, but you open them up and you see all these equations. Our book has no equations. It's for math fans and math-phobes. You don't need to read our book with a furrowed brow. While equations are wonderful and allow scientists to communicate really deep ideas, they are really a language. In schools we are teaching people a language that they will never use again. This is not a useful language. If you're not a scientist, chances are you're not going to speak the language of mathematics.
Q: Why do higher math concepts remain out of reach for many people?
A: For most, the concepts can be brought into reach. Currently, if you look at all the people who think mathematics is dull, it's because of their experience. When we teach mathematics, we are not sensitive to the audience. Teachers are performers in front of an audience. Some teachers don't realize they have to reach their audience.
Q: You have pretty imaginative ways of thinking about math. What prompted these teaching methods?
A: As with any intellectual journey, there's an evolution. For the first third of my career, I was very passionate about articulating my ideas in a crystal clear sense. I worked really hard at the challenge, from calculus on up, to bring clarity to it. The next third, I moved to a different level, not necessarily a higher level but a different plane. I not only wanted to have my students understand mathematics, I wanted them to have an appreciation for mathematics on some other level, to appreciate the creativity in mathematics thinking.
Q: You've said that creativity in mathematics helps us see our world in a clearer view. How does that happen?
A: Through surprises. Thinking creatively requires a certain basic mindset. If you train your mind to think creatively, you can transport your mindset and find novel and interesting solutions to everything going on around you. If you say, ''I'm just going to find patterns in the world around me," the act of searching for a pattern will enable us to look for structure as it emerges. Then all of a sudden the world view sharpens a bit. Not through solving for X, but through the mindset of mathematics.
Q: When teaching number theory or geometry, you make origami shapes or tell a story or offer practical applications like the remove your pants with your ankles tied together maneuver. Tell me about that last one.
A: Is it possible to take a cord of rope 6 feet long and tie it snugly around your right ankle and your left ankle, take off your pants, turn them inside out, and put your pants back on without ever cutting the rope? This is the challenge I put out to people. [laughing]. . . . The moment you start to try it, you come up with new insights about whether this is possible. You have a surprising discovery when you begin to think about it. . . . The moment [students are] surprised, they're asking ''Why?" Then, I know I've met them on their terms.