Mathematician Melanie Matchett Wood seeks creative ways of solving open math problems
“Many people don’t realize that there are math questions that we don’t know how to answer,” says mathematician Melanie Matchett Wood of Harvard University and the Radcliffe Institute for Advanced Study at Harvard. She recently won a MacArthur Fellowship for her work seeking solutions to some of those open problems. The award honors “extraordinarily talented and creative individuals” with an $800,000 “no strings attached” prize.
Wood spoke to Scientific American about her recent win, her favorite mathematical tools and tackling “high risk, high reward” problems.I’m drawn in by questions about foundational structures, such as the whole numbers, that we don’t really have any tools to answer. [These] structures of numbers underpin everything in mathematics. Those are hard questions, but that is certainly exciting to me.
It seems so simple. Yet such rich mathematics can come out of just the number 2. For example, 2 is kind of responsible for the concept of whether things are even or odd. There is a tremendous richness that can come from just considering things in complicated situations, about whether numbers are even or odd. I like it because even though it’s small, it’s very powerful.
Starting with my training in graduate school, I have always come from this arithmetic statistics perspective, in terms of wanting to understand the statistical patterns of numbers, [including] primes and how they behave in larger number systems. Harvard mathematician Michael Hopkins described your work on three-dimensional manifolds as “a dazzling combination of geometry and algebra.” What is a three-dimensional manifold?
We show that if you take a random space in a certain way, there is some positive probability that you’ll get a certain kind of space. This is a beautiful way that mathematicians know something exists without finding it. If you prove that you can do something randomly, and there’s some positive chance, no matter how small, that you can get it from some random construction, then it must exist.
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