Ultralearning, in my opinion, often works well because it compresses the frustration barrier to a shorter period of time. ​ Whenever we, as human beings, sense a comparative disadvantage, it’s as if our brain immediately tries to avoid practicing the skill. ​ One-on-one tutoring immediately removes the “I’m the worst in the class” feeling. It also removes the “I’m the best in the class” laziness that can afflict high-performing students. Woah, hadn’t thought of it this way. À la the more “single-player games” tendency I’ve been leaning into.

Andrew Wiles, one of the world's most renowned mathematicians, wonderfully describes research like exploring a big 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. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of, and couldn't exist without, the many months of stumbling around in the dark that precede them. ​ But more often than not you'll find that by the time you revisit a problem you've literally grown so much (mathematically) that it's trivial.

I became well-rehearsed in failed attempts, and so much more patient as a result. ​ As a result, my tolerance for frustration is so much higher. I’m convinced that the seeds of patience and resilience were planted and sprouted in those math notebooks. ​ The art lies in knowing which tool to grab ​ And just because I arrived at an answer, didn’t immediately make it the right one. ​ Answering that question directly is a mistake. When are you going to need to factor a polynomial in the “real world”? Maybe never, kid. Especially not with that attitude. But when are you going to face a problem that requires focusing for more than 30 seconds? All the goddamn time. ​ I needed that bottom row of math textbooks. They were my anchor. The bedrock. The foundation for much of what I’ve learned, and a sturdy base for everything still to come. ​ At times, I hated math. And yet, six years later, I’m so grateful that I studied it. The reasons have nothing to do with numbers and everything to do with life.