What's the Question?

There is a video I show in the senior capstone that always provokes a lot of snorts and eye rolling. It's a documentary about Andrew Wiles, the Princeton mathematician who devoted seven years of his life in near isolation to solving Fermat's Last Theorem, which may be at once the world's most difficult and most useless math problem. As one of Wiles' colleagues points out in the documentary, "Not all of mathematics is useless, but Fermat really is useless. If it's true it doesn't imply anything important."

The students find Wiles perplexing. At one point in the film he says that solving Fermat was the single greatest accomplishment of his working life. Nothing he ever does again can compare to it. He actually begins to weep and asks the cameras to stop filming. The students just stare up at the screen with incredulity. Why, they wonder, would anyone invest so much time, effort and emotional energy into discovering the answer to a simple true/false theorem that doesn't have any practical application?

In an attempt to explain Wiles, I always ask the athletes in the room if they would still want to break a world record even if no one saw it or ever knew about it?

"Sure," they say.

"Well, it's kind of the same thing."

They usually wrinkle their nose at this analogy because it's not the same thing to them at all. In fact, something fundamental to the difference in the way students and professors think about knowledge is present in these exchanges. For professors, knowledge is an intrinsic good, an end unto itself, a summum bonum, but for students "knowledge for knowledge's sake" is an entirely foreign concept.

I sometimes ask my class if there is such a thing as completely useless knowledge and they always sputter back, "Well, something may seem useless, but you never know. It could lead to something useful one day." Sometimes, too, they will say, "What if you found yourself on Jeopardy and that piece of knowledge was the final jeopardy answer? It would be pretty useful then." These responses are themselves interesting because they indicate how deeply-oriented students are to the idea that knowledge and utility must ultimately be connected.

Unfortunately, those of us who teach in the traditional liberal arts core disciplines seldom explain the value of studying art, history, or literature; nor do science or math professors always make clear to non-majors the value to a human being in thinking scientifically or mathematically. In one sense, we don't have to justify ourselves because the students are served up to us (often against their wills) by core requirements. More importantly, though, we often operate under an assumption that the value of our disciplines is so obvious that it goes without saying. Sometimes students will ask us "Why do I need to take history?" or "Why in the world do I need to take biology if I'm a human services major?" Now it's our turn to gape back with incredulity.

I have tried to keep this student/professor difference in mind as we designed the architecture for the new core. One of the important principles we put into the proposal is that all core courses make it a primary goal to help students understand why a discipline matters. I've called this a general rather than a specific approach, but that may have been a mistake. When my colleagues hear the word "general," they tend to think we are asking them to dilute the content of their courses, but what we are really asking them to do is to keep the big questions front and center.

Why are things the way they are? Why do people see things differently? What is the nature of this world we inhabit? What can we know? Why are we here? What is to be done? Putting these questions first is not dilution. It's our raison d'ĂȘtre. Indeed, our disciplines exist because people have wanted and will continue to want answers to these vital questions.

More importantly, students can see the value of a discipline when they grasp that it's in service to answering fundamental human questions. Of course students should gain knowledge of content, but not at the expense of understanding why a disciplinary perspective matters. A 16-week course in any core subject is unlikely to lead to mastery, but it can help students broadly to understand how practitioners in a given discipline construct knowledge and the real human value of doing so. I'm no expert, but I do know this: human beings learn best when they see that answers matter, when they grasp their implications, or when, like Andrew Wiles, they find that they have just got to know.

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