Understanding is the base

More than ever, it is easier to pass a class without understanding its content. And even if you spend time with the content, it is much easier to convince yourself you have learned the content than to really learn it.

When I came to Stanford, one of the nicest things I learned was how rigorous you can be. Take Lean as an example: in a language like Lean, each piece of the puzzle must for sure hold on its own, and only then can the sum of the parts be true. In first quarter, when I saw Alex do math, it opened my eyes. I had never done proof-based math before, and as a competitive programmer, I was used to relying on my intuition to solve problems. I watched him go through many proofs, squashing out every bug and possible ambiguity, and wondered if I had been learning wrong my entire life.

A common theme I've noticed while learning these things, whether competitive programming or debate, is that understanding is the primary objective. When you can hold an idea clearly in your mind, manipulate it, tinker with it, and freely draw connections from it, only then is that idea truly yours to use. Anything else, and I feel this grey fog, this mist of unusability and uncertainty, that I have come to enjoy clearing up.