This past Thursday at Back To School Night, I’m sitting in my 5th grader’s classroom chair scribbling a note on his dry-erase desk for him to see in morning. His mother is filling out a parent survey that helps the teacher get up to speed on your kid. It looks like she’s finished when she slides it over to me to answer a question she left blank — “What would you like your child to focus on this year?”
An article I read this summer immediately popped into my mind — The State of Being Stuck by math educator Ben Orlin.
The article begins:
Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.
Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.
Ben, like me staring at that survey question, didn’t want to waste the opportunity. He wondered…
…before settling on this question:
Here’s what Ben got back:
The essence of Wiles’ answer can be boiled down to just six words: “Accepting the state of being stuck.”
For Wiles, this is more than just a vague moral, an offhand suggestion. It’s the essence of his work. It’s an experience at once excruciating, joyful, and utterly unavoidable. And it’s something desperately misunderstood by the public.
“Accepting the state of being stuck”: that’s the keystone in the archway of mathematics. Without it, we’re left with nothing but a pile of fallen bricks.
Wiles began his answer, like any good mathematician, with a premise everyone can accept: “Many people have been put off mathematics,” he said. “They’ve had some adverse experience.”
It’s hard to argue with that.
“But what you find with children,” he continued, “is that they really enjoy it.”
In my experience, it’s true. Kids love games, puzzles, learning to count, playing with shapes, discovering patterns—in short, they love math.
So how does Wiles account for our alienation from mathematics, our loss of innocence?
“What you have to handle when you start doing mathematics as an older child or as an adult is accepting the state of being stuck,” Wiles said. “People don’t get used to that. They find it very stressful.”
He used another word, too: “afraid.” “Even people who are very good at mathematics sometimes find this hard to get used to. They feel they’re failing.”
But being stuck, Wiles said, isn’t failure. “It’s part of the process. It’s not something to be frightened of.”
Catch me and my teacher colleagues any afternoon, and—if you can get past the “sine” puns and fraction jokes—you’ll likely find us griping about precisely this phenomenon. Our students lack persistence. Give them a recipe, and they settle into monotonous productivity; give them an open-ended puzzle, and they panic.
Students want the Method, the panacea, the answer key. Accustomed to automaticity, they can’t accept being stuck.
…
“What I fight against most,” said Wiles, naming an unlikely enemy, “is the kind of message put out by—for example—the film Good Will Hunting.”
When it comes to math, Wiles said, people tend to believe “that there is something you’re born with, and either you have it or you don’t. But that’s not really the experience of mathematicians. We all find it difficult. It’s not that we’re any different from someone who struggles with maths problems in third grade…. We’re just prepared to handle that struggle on a much larger scale. We’ve built up resistance to those setbacks.”
If you have walked past a rack of popular non-fiction books in the past decade, you are thinking “not another lecture on grit or growth mindset please”. Ben doesn’t go there. In fact, he’s quick to affirm how we often overplay the “grit “ hand:
Recently, the currency of “grit” has fallen among teachers. It’s not that the idea lacks psychological validity. It’s more the weight of its educational connotations. Grit has become an excuse to romanticize poverty as “character-building.” It has devolved into a vague catch-all at best, and at its paradoxical worst, a reason to write kids off as lost causes.
Orlin proposes a 3rd idea:
Wiles is no educational theorist, of course, but I find that he offers a resonant and compelling third path. For him, perseverance is neither about personality (as with grit) nor belief (as with mindset).
Rather, it’s about emotion.
Fears and anxieties come to us all. You can be a nimble mathematician, a model of grit, and a fervent believer in the human potential for growth—but still, getting stuck on a math problem may leave you deflated and disheartened.
Wiles knows that the mathematician’s battle is emotional as much as intellectual. You need to quiet your fear, harness your joy, and cope effectively with the doubt we all feel when stuck on a problem.
Giles offers some counterintuitive ideas as well:
On the value of forgetfulness
“I think it’s bad to have too good a memory if you want to be a mathematician,” Wiles said. “You need to forget the way you approached [the problem] the previous time.”
It goes like this. You try one strategy on a problem. It fails. You retreat, dispirited. Later, having forgotten your bitter defeat, you try the same strategy again. Perhaps the process repeats. But eventually—again, thanks to your forgetfulness—you commit a slight error, a tiny deviation from the path you’ve tried several times. And suddenly, you succeed.
Wiles has a nifty analogy for this: it’s like a chance mutation in a strand of DNA that yields surprising evolutionary success.
“If you remember all the false, failed attempts before,” said Wiles, “you wouldn’t try. But because I have a slightly bad memory, I’ll try essentially the same thing again, and then I’ll realize I was just missing this one little thing.”
Wiles’ forgetfulness is a shield against discouragement. It neutralizes the emotions that would push him away from productive work.
Coming back to the parent survey…how did I reply?
I want Zak to build the muscle of persisting through drawn-out problems.
This skill is more valuable in a holistic, psychological sense than just being a technique. It’s hard to feel truly empowered unless you become familiar with the pattern of feeling stuck and the emotional reward of chipping your way out of it. If you find success too quickly, you’ll fear that you can’t repeat it. You’ll feel like an imposter. You’ll be imbalanced — with a bias towards protection, not growth. Coddling your ego or hating on others when you should be prepping for your next climb from a new valley.