The first 13 years of math are basically computation-oriented, Jones explains. "You're handed a technique, and you apply it to a bunch of examples." Growing up mathematically means understanding "why things happen, why the proofs and techniques you've learned actually work."
Jones found an intellectual home in algebraic geometry, where his work in graduate school involves understanding how a curve is expressed in polynomials, mathematical expressions like a + bx + cx2. To analyze these curves, he uses what he calls "advanced machinery — not something you can hold in your hand and throw at a piece of paper," he explains, but sophisticated techniques.
Jones is bringing some new techniques — Kodaira's vanishing theorem and Macaulay's initial ideals — to a traditional problem, his dissertation adviser, Mark Green, says. His work is "connected to a very important conjecture in algebraic geometry and represents an interesting point of view," Green says.
When he started graduate school, Jones saw research and teaching as equally desirable parts of an eventual job at a major research university. Now, he says, "I really like the teaching significantly more than the research." For his work as a teaching assistant, Jones has already received the Distinguished Teaching Award from the Department of Mathematics.
While academic mathematicians often have a strong passion for their field, "that's not the only passion we respect," Green says. "Matt is equally passionate about different things and unusual in his early commitment to teaching."
Jones has landed an appointment as a lecturer at California State University, Fullerton, for Fall 2001. He understands that his new work is more likely to involve remedial math and intermediate algebra than the "grown-up" kind of math he's been doing at UCLA, but "that doesn't bother me," he says.
Teaching motivates him. "If you're conscientious about it, after every lesson, you can see what worked and what didn't. There's a constant improvement process on your part to get a few more people to understand the next time you go around."
Jones will bring to his work a philosophy about math phobia. "If people fear math, it becomes a big obstacle," he says. "They see math as a disorganized jumble of things that they need to learn to do." His experience has shown that "people who do better are those who look for ways to find patterns and make sense and superimpose order on things."