How a World-Famous Mathematician Overcomes Mental Blocks

Even the most accomplished mathematicians spend great swaths of their careers pushed to the limits of their abilities. But being stumped isn’t cause for despair. Quite the opposite: It’s usually a sign that you’re on the right track. And continuing to fight with problems you don’t think you can solve is an essential aspect of learning. The following tips can help you surmount your steepest logical challenges, whatever they may be.

Jump Right In
Stop worrying and take a stab at it. Sure, there’s a chance that you won’t land on an answer at first. But putting in the effort could give you ideas that lead to success down the line—or prime your brain for solving future problems.

Simplify, Simplify, Simplify
In mathematics, this might entail using smaller numbers, removing or adding restrictions, and combining like terms by addition or subtraction. In life, it could involve breaking large problems into small chunks, listing what you don’t understand, and trying to take a bird’s-eye view of your tasks.

Build Yourself Up
Recall the problems you do know how to solve and see if you can apply the knowledge you gained to the dilemma in front of you. You’ve done a lot thus far in your life, no doubt. You’ve probably even solved problems similar to the one you’re currently facing.

Don’t Lament Time Spent
The Danish physicist Niels Bohr supposedly said that an expert is someone “who has found out by his own painful experience all the mistakes that one can make in a very narrow field.” This concept helps Terence remind himself that there’s no such thing as wasted time, so long as you’re learning: The goal isn’t just to solve a problem quickly or efficiently, but to enjoy yourself and draw lessons from the process.

Cheat (Ethically)
In this context, cheating means approaching a novel problem with tools you already possess. Like a video game’s “cheat code,” which allows you to skip over some tasks or stages, math cheats can get you further into a problem faster. Terence, for example, will sometimes take a curve and make it a straight line to simplify a problem—a mathematical tool called linearization.

“There is a certain way in which mathematicians approach problems. We abstract them. We break them up into pieces. We make analogies. We try to find connections with other problems.“ —Terence

Try a New Approach
When Terence finds himself in a rut, sometimes it’s because he’s been looking at a problem and thinking, I must solve it this specific way. To get past this mental dead end, he tries to let go of his preconceived beliefs. He says that ideas formed in desperation can be your friend in these moments: “Sometimes they can jar you out of one thought process and into a better one.”

Collaborate!
The more people working on a single problem, the better. Maybe one member of the team is an expert in an obscure mathematical field and another has read a piece of arcane-yet-relevant literature. Good! Terence also loves solving problems with collaborators because it heightens the joy of finding a solution. “When you and your collaborator are both standing at the blackboard...and everything checks out...that’s a great experience and more fun than if you’re working on your own.”