My biggest realization about doing hard things is that I needed to let go of my intellectual entitlement. Just because something is (or seems) effortless to others, doesn't mean it will be the same for me.
Part of this entitlement stemmed from a (now eroded by bitter experience) belief that I'm somehow a faster learner than normal, that _I_ don't have to do the work.
For example, about seven years ago I wanted to learn Calc I-III on my own. I went down the usual, lazy, intellectually-entitled route of watching lectures and YouTube videos online without doing a single exercise.
A year later, guess what? I couldn't remember jack-shit. Moreover, I couldn't solve problems, which is basically the reason I was learning math anyway. Any bystander could have predicted this outcome, but I was blinded by my own entitlement.
Now, after being humbled (here and elsewhere, e.g. in learning to play music by ear), I realize that there's honor, even long-term efficiencies in following every step the great teachers of the past have laid out, in moving slowly albeit with rigor and confidence.
I resumed my math study with Geometry 101, the absolute basics, using a book of 5000 (short) exercises. It probably took me three times as long as Calc I-III lectures combined. But I realized something — I found more joy in doing the exercises, in doing things the _right_ way, than I ever had in watching lectures.
Part of this entitlement stemmed from a (now eroded by bitter experience) belief that I'm somehow a faster learner than normal, that _I_ don't have to do the work.
For example, about seven years ago I wanted to learn Calc I-III on my own. I went down the usual, lazy, intellectually-entitled route of watching lectures and YouTube videos online without doing a single exercise.
A year later, guess what? I couldn't remember jack-shit. Moreover, I couldn't solve problems, which is basically the reason I was learning math anyway. Any bystander could have predicted this outcome, but I was blinded by my own entitlement.
Now, after being humbled (here and elsewhere, e.g. in learning to play music by ear), I realize that there's honor, even long-term efficiencies in following every step the great teachers of the past have laid out, in moving slowly albeit with rigor and confidence.
I resumed my math study with Geometry 101, the absolute basics, using a book of 5000 (short) exercises. It probably took me three times as long as Calc I-III lectures combined. But I realized something — I found more joy in doing the exercises, in doing things the _right_ way, than I ever had in watching lectures.