“Equations written in chalk on a worn-out blackboard” by Roman Mager on Unsplash

Andrew Wiles: How to Do the Impossible


Andrew Wiles isn’t like most people. He always had a strange childhood dream.

When he was 10 years old, Wiles had come across The Last Problem. It was a book written by Eric Temple Bell, and it recounted the history of a famous mathematical formula that had remained unsolved for over three centuries. We know it as Fermat’s Last Theorem.

The story behind the problem begins in the 17th century. Pierre de Fermat had been studying an ancient Greek text when he began to play around with a few of the numbers.

He manipulated these numbers to create his theorem and then built a mathematical proof to solve it. Before sharing the proof, however, he ended the text with the following sentence:

“I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.”

Naturally, this created immense intrigue in the mathematical community. It was the ultimate challenge, and for 300 years, the greatest minds on the planet struggled to find this proof.

Bell predicted in his book that civilization would come to an end before a solution was found.

Yet, for some reason, a 10-year-old British kid decided that this was his calling.

Over the years, Wiles completed a PhD in mathematics and eventually become a professor at Princeton University. Much of his subsequent work led him in the direction of his dream. He spent years isolated, failing, and struggling to come up with a comprehensive proof.

Then, in 1995, just as he was on the verge of giving up, he made mathematical history.

The Value of Doing Difficult Things

Having solved the theorem, Wiles received all kinds of prestigious awards and prizes over the following years and decades. But to him, it was about much more than that.

“It’s more rewarding than anything imaginable. Having solved this problem there’s certainly a sense of loss, but at the same time there is this tremendous sense of freedom.”

That’s from a BBC documentary covering his quest. But why? What part of us is it that craves a sense of pursuit even when things are difficult? Why work to solve hard problems?

For Wiles, it was a yearn, a passion. He developed an emotional connection at a young age.

Another way to look at it is through the lens of time. Many of us live quite long lives. As we age, we experience more, and we understand more. We begin to get desensitized to many of the day to day things that felt new and exciting to us in younger days. We get too comfortable.

Although comfort has its benefits, over time, it becomes stagnating and mundane.

At its core, in one way or another, what keeps life interesting is growth. There are very few among us who don’t strive to be at least somewhat better tomorrow than we are today.

This kind of growth can come in many ways, but the most substantial way is also the most counterintuitive — through adversity, discomfort, challenge, and ultimately, difficulty.

With a few exceptions, it’s no coincidence that many people that suffer unimaginable pain will often look back on those same periods as some of the most meaningful in their life.

In our bodies, when a muscle is strained and pushed, it begins to tear. It’s anything but comfortable. But it’s precisely this tear that allows that muscle to get stronger and better.

We don’t do difficult things in spite of them being difficult. We do them because they are.

The Only Secret Is Obsession

Although Wiles worked towards Fermat’s Last Theorem, in one way or another, for most of his adult life, the last eight years leading up to 1995 was when he really switched into high gear.

He worked in complete secrecy during that time, and the only person who knew what he was up to was his wife. He stopped attending conferences, he reduced the hours he spent teaching and tutoring, and he eliminated everything else that didn’t align with his goal.

Wiles quite literally had an obsession and that was partly the reason that he managed to come up with a proof when so many other great minds before him had failed.

In order to do difficult things, the most important part of the equation is elimination. And not just elimination of the inessential, but also elimination of things that appear essential. Difficult and worthy pursuits often take a long time, and they require immense focus.

This doesn’t mean that you can’t have a personal life, but it does mean that you have to choose. We all have a list of stuff we want to do or accomplish. Many of these are fun and interesting. Well, it’s precisely these fun and interesting things that should be eliminated.

Most of these things only provide the illusion of importance when, in fact, they are largely distractions. Before you say “yes” to one thing, you have to say “no” to a lot of other things.

The growth that comes from difficulty is a result of pushing boundaries, and pushing boundaries isn’t easy. By definition, it requires a commitment beyond selective dedication.

The only way to do the really important stuff well is to give up on the kind of important stuff. It’s the sacrifice that earns the reward.

All You Need to Know

The proof of Fermat’s Last Theorem is to the field of mathematics as the discovery of the DNA helix structure was to biology and the Large Hadron Collider project was to physics.

On a practical level, the solution doesn’t really do much to enhance our place in the world.

That wasn’t really what it was about either. It was about the culmination of effort exerted by generations of mathematicians, and more than anything, it was about human ingenuity.

On a personal level, Wiles lived up to the expectations of his 10-year-old self. He had the rare luxury that few get. He was able to take a childhood passion and bring it to fruition.

In the process, however, he reminded us of why we do difficult things. It isn’t always out of necessity or need, but because they lead us through to a journey of growth and meaning.

When we choose to do hard things, we say “no” before we say “yes,” and we eliminate the good so that we can choose an obsession. That’s what fuels real, valuable accomplishment.

The idea of comfort and ease is alluring; seductive even. And yet, it’s quick to lose its charm.

Nobody makes progress by standing still. The beauty is in the push, and it’s never easy.


The internet is noisy

I write at Design Luck. It’s a free high-quality newsletter with unique insights that will help you live a good life. It’s well-researched and easy-going.

Join 16,000+ readers for exclusive access.