Talking with peers helps unravel math mysteries

By Craig Pearson

Created:
11/17/11 8:30pm

Last updated:
11/17/11 8:30pm

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“This isn’t a knot,” says Dr. Matt Hedden, assistant professor of mathematics at Michigan State and a recent winner of the Sloan Research Fellowship.

He holds up a piece of string that’s been unraveled from a yo-yo, which he appears to keep handy for the purpose of demonstrating his research on knot theory.

In mathematical terms, one can call a regular, circular loop of string the “un-knot.” When you untie the ends and start twisting them around, that’s when things get complicated.

Hedden describes a set of tools mathematicians use to analyze complex knots and how his research advanced the field: “On the face, knot Floer homology looks very challenging to compute. What I was able to do was compute it effectively.”

What differentiates mathematics research from many of the other disciplines is that there’s not much to work with physically. Hedden doesn’t spend his time tying and untying tangled pieces of string.

“A lot of work gets done at coffee shops,” he says.

Because the research is so idea-based, it can be mentally exhausting. But that’s what Hedden was attracted to in the first place, what he calls “the mysteries of seeing the same object appear in very different contexts.”

Although some researchers crawl deep into their own heads and live a hermetic, academic life, Hedden describes himself as more of a talker. He works on several problems at once, and interacts with as many people as he can. This social, collaborative approach is what helps him look at ideas from different angles.

“It’s the process of coming back to a problem,” he says. Instead of being consumed by theory, he moves to other ideas and, upon returning to one that’s been left on the shelf, he often sees the problem in a new light. It’s the subconscious, he says, working in the background.

Working in the background is a good description of the life of a mathematics researcher, but honors like Hedden’s Sloan Fellowship give a welcome and humbling burst of recognition.

“It meant a lot to me that people in my field and in other disciplines think highly of me,” Hedden says of the award. “Mathematicians are some of the best people I’ve ever met.”

The support of the community, which has already helped him with his work, is something of a reward in itself, completing the circle.

Or, one might say, the un-knot.

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