The Singular Mind of Terry Tao

Source: NYTimes, Jul 2015

… the mathematician Terence Tao mused about the possibility that water could spontaneously explode. A widely used set of equations describes the behavior of fluids like water, but there seems to be nothing in those equations, he told me, that prevents a wayward eddy from suddenly turning in on itself, tightening into an angry gyre, until the density of the energy at its core becomes infinite: a catastrophic ‘‘singularity.’’

Tao has recently been working on an approach to a solution — one part fanciful, one part outright absurd, like some lost passage from ‘‘Alice’s Adventures in Wonderland.’’

As he talked, Tao carved shapes in the air with his hands, like a magician.

Tao told me that his view of mathematics has utterly changed since childhood. ‘‘When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed,’’ he said in a lilting Australian accent. ‘‘I sort of imagined a committee would hand me problems to solve or something.’’ But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians.

Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. ‘‘It’s as if your only experience with music were practicing scales or learning music theory,’’ he said, looking into light pouring from his window. ‘‘I didn’t learn the deeper meaning of the subject until much later.’’

to be a mathematician is to experiment. Mathematical research is a fundamentally creative act. Lore has it that when David Hilbert, arguably the most influential mathematician of fin de siècle Europe, heard that a colleague had left to pursue fiction, he quipped: ‘‘He did not have enough imagination for mathematics.’’

Math traffics in abstractions — the idea, for example, that two apples and two oranges have something in common — but much of Tao’s work has a tangible aspect. He is drawn to waves of fluid or light, or things that can be counted, or geometries that you might hold in your mind. When a question does not initially appear in such a way, he strives to transform it. Early in his career, he struggled with a problem that involved waves rotating on top of one another. He wanted to come up with a moving coordinate system that would make things easier to see, something like a virtual Steadi­cam. So he lay down on the floor and rolled back and forth, trying to see it in his mind’s eye. ‘‘My aunt caught me doing this,’’ Tao told me, laughing, ‘‘and I couldn’t explain what I was doing.’’

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