Learning Perseverance
. . . from someone in a completely different field?
I was never good at math, but it was from that subject — or more precisely, from a great mathematician — that I learned lasting lessons about perseverance, lessons that guided my work during TTG’s long development.
The story: After years of work, Andrew Wiles in 1994 solved a problem that had vexed mathematicians around the world for more than three centuries.
Through long days and years of working alone, he was able to take everything relevant he could find and weave it into his own intellectual breakthroughs in order to solve a problem of worldwide interest.
Wiles’ experience intrigued me when in the late 1990s I started working on the problem I call the “Digital Dilemma”:
“How do we decide which visual images we can trust now that we can no longer believe our eyes?”
Inspired by Wiles’ approach, I have returned time and again to four of his practices, learned habits that cultivate perseverance when working on a long-term problem:
I was never good at math, but it was from that subject — or more precisely, from a great mathematician — that I learned lasting lessons about perseverance, lessons that guided my work during TTG’s long development.
The story: After years of work, Andrew Wiles in 1994 solved a problem that had vexed mathematicians around the world for more than three centuries.
Through long days and years of working alone, he was able to take everything relevant he could find and weave it into his own intellectual breakthroughs in order to solve a problem of worldwide interest.
Wiles’ experience intrigued me when in the late 1990s I started working on the problem I call the “Digital Dilemma”:
“How do we decide which visual images we can trust now that we can no longer believe our eyes?”
Inspired by Wiles’ approach, I have returned time and again to four of his practices, learned habits that cultivate perseverance when working on a long-term problem:
1. “Care” about the problem you choose
A. Internally, if the problem is going to be your constant companion for days, months, or years, it should be a problem you want to live with over time. As Andrew Wiles noted, “One thing that I've learned is that it is important to pick a problem based on how much you care about it. Always try the problem that matters most to you.”
B. Externally, the solution to a big problem often depends on sticking with it long enough — which can be for long years and through seasons when a solution is by no means guaranteed. What is expressed as “perseverance” can largely reflect “caring so much that giving up is not an option.”
B. Externally, the solution to a big problem often depends on sticking with it long enough — which can be for long years and through seasons when a solution is by no means guaranteed. What is expressed as “perseverance” can largely reflect “caring so much that giving up is not an option.”
2. “List” your progress on the problem
As a mathematician building a proof, Wiles’ main task was, of course, to compile a “list” — a list of his progress, logical steps he had confirmed that would build upon each other to produce a conclusion.
But there are two ways that such progress lists — not “to-do” lists but “have done” lists — can be helpful for non-mathematical problems too:
A. As a reminder of discoveries and accomplishments. When chipping away at a mountain of a problem — on many days feeling like there’s nothing to show for it — noting how much cumulative progress has been made can be a source of reassurance, motivation, and direction.
B. As a means of finding helpful patterns. In explaining how he went about constructing his colossal proof on a day-to-day basis, Wiles reflected, “I used to come up to my study and start trying to find patterns.” What seem like discrete accomplishments can, when viewed in concert with each other, reveal shared characteristics that cast the problem — and the solution — in a new light.
But there are two ways that such progress lists — not “to-do” lists but “have done” lists — can be helpful for non-mathematical problems too:
A. As a reminder of discoveries and accomplishments. When chipping away at a mountain of a problem — on many days feeling like there’s nothing to show for it — noting how much cumulative progress has been made can be a source of reassurance, motivation, and direction.
B. As a means of finding helpful patterns. In explaining how he went about constructing his colossal proof on a day-to-day basis, Wiles reflected, “I used to come up to my study and start trying to find patterns.” What seem like discrete accomplishments can, when viewed in concert with each other, reveal shared characteristics that cast the problem — and the solution — in a new light.
3. “Live” with the problem
A. Even when day-to-day life includes such things as a job and loved ones, the “Problem” or “Project” can be a go-to mental exercise at any moment there is downtime. Andrew Wiles recalled, “I was thinking about [the math problem] all the time — when I woke up in the morning, when I went to sleep at night—and that went on for eight years.”
B. “Living with the problem” also means viewing other things through the lens of that problem. Creative cross-pollination can occur when going about the day and dealing with other matters: studying solutions to unrelated challenges can lead to solutions to “The Big Problem.” One of the greatest scientific problem-solvers of all time, Isaac Newton, described himself as “someone who could mix and combine disparate fields to stimulate creative breakthroughs.”
B. “Living with the problem” also means viewing other things through the lens of that problem. Creative cross-pollination can occur when going about the day and dealing with other matters: studying solutions to unrelated challenges can lead to solutions to “The Big Problem.” One of the greatest scientific problem-solvers of all time, Isaac Newton, described himself as “someone who could mix and combine disparate fields to stimulate creative breakthroughs.”
4. “Walk” around (and step back)
A. The value of combining walking with problem-solving has been known by great thinkers for centuries; an extensive body of literature extols the virtues of thinking while walking. This was true for Andrew Wiles’ problem-solving regimen as well: “When I got stuck and I didn't know what to do next, I would go out for a walk.”
B. Regularly stepping back also helps to address the biggest danger of working on a problem alone: losing perspective. It may be impossible to view dispassionately your own passion, but any grand lapses in logic have a better chance of being revealed when viewed from a distance of a few yards than from a distance of a few inches.
B. Regularly stepping back also helps to address the biggest danger of working on a problem alone: losing perspective. It may be impossible to view dispassionately your own passion, but any grand lapses in logic have a better chance of being revealed when viewed from a distance of a few yards than from a distance of a few inches.
There Are No Shortcuts
. . . and no previous paths to follow when sailing in uncharted waters.
Andrew Wiles shared that “perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark, unexplored mansion. You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark.”
Early on I realized that the “Digital Dilemma” would take a long time to solve. That realization prompted focus not just on the problem but also on how to stick with it long enough solve it — how to persevere.
The four principles above are necessarily nonspecific; each person must tailor these practices to the problem they take on and to their personal challenges. But considering that for most people summoning traits like “perseverance” and “persistence” are daily challenges, the example of Andrew Wiles can be inspiring. It certainly was for me.
Andrew Wiles shared that “perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark, unexplored mansion. You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark.”
Early on I realized that the “Digital Dilemma” would take a long time to solve. That realization prompted focus not just on the problem but also on how to stick with it long enough solve it — how to persevere.
The four principles above are necessarily nonspecific; each person must tailor these practices to the problem they take on and to their personal challenges. But considering that for most people summoning traits like “perseverance” and “persistence” are daily challenges, the example of Andrew Wiles can be inspiring. It certainly was for me.
Source of the Andrew Wiles quotes above