Andrew Wiles on the State of Being Stuck

A Persistent Answer

Ben Orlin is a math teacher who publishes the clever essay blog, Math with Bad Drawings. Last year, Orlin had the opportunity, during a press conference at the Heidelberg Laureate Forum, to ask a question of Andrew Wiles, the Princeton Professor (now at Oxford) who in 1994 finally solved Fermat’s Last Theorem.

As Orlin reports on his blog, he asked the following:

“You’ve been able to speak to an unusually wide audience for a research mathematician. What are some of the themes you’ve tried to emphasize when talking to a broader public?”

Wiles’s answer, according to Orlin, can be summarized in six words: “Accepting the state of being stuck.”

As Wiles elaborated, research mathematics unfolds as follows:

“You absorb everything about the problem. You think about it a great deal—all the techniques that are used for these things. [But] usually, it needs something else. So, you get stuck.”

At this point, he explains, “you have to stop…let your mind relax a bit…[while] your subconscious is making connections.”

Then you “start again.” Day after day. Week after week. Until, one day:

“You find this thing…Suddenly you see the beauty of this landscape…[before,] when it’s still some kind of conjecture, it seems really far away…[but now] it’s like your eyes are open.”

Wiles admitted that the enemy he fights against most is “the kind of message put out by, for example, the film Good Will Hunting.”

And, in particular, the idea that for some people math comes easy (Matt Damon glancing at the chalkboard, and then dashing out the solution to the impossible problem), and for all others it’s hopeless.

The reality, as Wiles knows, is that math is just plain hard. Regardless of who you are. But it’s also amazingly rewarding if you’re used to the feeling of persisting even when you have no idea about how best to move forward.

A Good Response

I liked this answer (and Orlin’s commentary on it) for two reasons.

The first is personal. As a theoretical computer science I spend a lot of my professional life stuck on math problems. It’s hard to explain to outsiders what this is like, and Wiles’s  response does a good job of capturing the competing forces of frustration and joy that come from tackling such things on a regular basis.

The second has to do with my recent post about how we lack a good vocabulary for describing the varied cognitive efforts that comprise deep work. Wiles’s answer is a good step toward filling in some of those blanks.

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For more on Andrew Wiles’s attack on Fermat’s Last Theorem, see Simon Singh’s popular book, Fermat’s Enigma. For a more raw and technical treatment of what it’s like to do Fields Medal-caliber math, see the more recent Birth of a Theorem. The image above is taken from Wile’s proof, as it appeared in the Annals of Mathematics.

(Hat tip: Amin)


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