There’s a math concept that I keep seeing in real life. It’s a weird one: the asymptote.
An asymptote is a line that a graph curves towards but never reaches. The graph gets closer and closer, but it can never get there.
It’s a cool concept in math, to be sure. Well, cool if you’re a math nerd like me. But that’s not the point. And math is never really about math, anyway.
No, asymptotes are interesting because life is full of them. And by understanding asymptotes, we develop a better understanding of how many of the most important things in life actually work.
Mastery
One that I’ve touched on before is that mastery of any skill is an asymptote. As you move along the mastery path, your skills improve. But there’s no point at which you can say you’re “done.” Whether you’re an expert pianist, a brilliant basketball player, or a chess champion, there’s always more room to grow. Complete mastery can never be reached, only approached.
Knowledge
Knowledge works the same way. It’s impossible to know everything about a subject. Whether you practice medicine, study history, or research physics, there’s no point at which you can say you have total knowledge of your subject. Everything you learn moves you toward completely knowing your subject, but total knowledge is an ideal that can never be reached.
Perfection
The concept of an asymptote is good to keep in mind if you’re struggling with perfectionism. Perfection is an asymptote: it’s an ideal you can move toward, not a destination you can reach. As Tal Ben-Shahar advises, think of perfection like a guiding star rather than an island. It’s a direction to travel, not a place you’ll ever visit.1
Health and Fitness
Health and fitness are also asymptotes. No matter how healthy you are, you could always be a little healthier. Mental health works this way, too. No one has perfect mental health. You can approach it incrementally, but the work is never finished.
Thinking of fitness like an asymptote reminds you that you can always benefit from exercise, even if you’re already in great shape. It’s another version of everything counts. But, at the same time, it helps you see that perfect fitness is unattainable, reminding you to be kind to yourself when you fall short of your ideal vision.
The asymptote is both a motivation to keep working on self-improvement and a reminder to give yourself permission to be human.
Love and Kindness
Being kind and loving are asymptotes too. There’s always room for growth in how well you treat others, how you talk to your family, and how you engage with your friends. The same goes for being kind and loving toward yourself.
Wisdom
In Ryan Holiday’s book Wisdom Takes Work, he writes that wisdom is “a kind of asymptote. … There is always more to learn, more to know, more to understand about the world and yourself.”2
Later, he writes that:
“We can get wiser, but never wise.
Smarter but never smart.
Closer but never there.”2
1Ben-Shahar, Tal. The Pursuit of Perfect. McGraw Hill, 2023.
2Holiday, Ryan. Wisdom Takes Work. Portfolio, 2025.
Chris Loper has been working as a tutor and academic coach since 2014, racking up over 13,000 hours of experience supporting students.
Along with Greg Smith, Chris is the co-creator of Parenting for Academic Success, a series of classes that create empowered parents, confident students, and harmonious families.
Chris writes the popular self-improvement blog Becoming Better, where he also offers habit coaching, helping busy adults with habit formation and productivity.
Chris’s most recent endeavor combines his academic and habit-formation expertise to help students thrive in college. Visit SmartCollegeHabits.com to learn more.
In 2021, he published a humorous memoir titled Wood Floats and Other Brilliant Observations, a book that blends crazy stories with practical life lessons.
He lives in Issaquah, WA, where he is the owner of South Cove Tutoring.