Last spring, as I strolled back to my office after enjoying a Barney's sandwich, I encountered the familiar sight of a campus tour guide introducing Columbia to a group of nervous high school students. "That is the mathematics building," she said, "Nothing terribly interesting happens there except, of course, the bartending classes in the evening."
My immediate instinct was to leap into action and deliver an impromptu lecture on the beauty of mathematics and extol the virtues of the intellectual delights that awaited them in the math department. I have spent most of my adult life studying and inventing mathematics at various universities, and to me, the subject is a living, breathing being that inhabits the world's deepest mysteries and most profound secrets. But to many, it is a collection of dusty and arcane textbooks studied by equally dusty and arcane university professors whose job is primarily to weed out engineering majors.
There are some good reasons for people to have a bad attitude about math. For instance, learning math really is hard, at its core, math is humanity's attempt to clarify the imprecise and counterintuitive aspects of our descriptions of the world, so the subject wouldn't need to exist if it came naturally to us. But I think that math's severe PR problems are caused primarily by several persistent myths:
Myth: Math is dead.
Reality: The foundations of just about every area of mathematics were overhauled at some point in the 20th century, and a variety of new areas (such as topology, noncommutative geometry, and arithmetic algebraic geometry) sprang into existence. In the past 20 years alone, mathematicians have solved some of our oldest and most difficult problems.
Myth: Math is useless.
Reality: Math pays you back for your investment. Most people can largely avoid math for most of their lives if they choose, but those who take the time to learn the subject properly see patterns and find solutions that others miss. The PageRank algorithm, RSA encryption, and fractal image compression are but a few technological achievements that began as purely abstract mathematics.
Myth: Math isn't for creative people.
Reality: Understanding and appreciating mathematics is much more a matter of asking the right questions and noticing unexpected connections between seemingly different ideas than doing rote calculations. Mathematicians do not consider a problem completely solved until the most elegant solution has been found; in the words of the great G.H. Hardy, "There is no permanent place in the world for ugly mathematics."
So as the current semester begins and your college career progresses, try to interact with mathematics in a new and better way. Use the creative part of your brain to question assumptions and seek new connections instead of just memorizing calculations. Think of new problems to which your current techniques might be relevant, instead of focusing on the narrow range of problems that you were taught to solve. Ask your math professors what they are working on and how it fits into the developing history of mathematics, and try to relate their answers to your own interests. Thinking like a mathematician is hard and the payoff is not always obvious at the outset, but you will be astonished by how it helps you grow as a student and as a person.
I didn't stand up for mathematics in front of that campus tour last spring, but it did make me think about why I do mathematics and how it can help make people's lives better. In the end you will have to find your own reasons, but I'll be in my office if you need help.
The author is an assistant professor of mathematics.