It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the…
Right. >Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. This is so true. I was exactly like the author. I could not understand any math beyond algebra. Trigonometry was way beyond my ability. But one day, I found an old trig book lying around when I went…
One analogy I've come up with to justify this method is that you should not measure your progress by distance covered when traversing terrain of varying elevation. Some days you will be walking up hill, and others downhill. To lament that you covered two miles today but ten yesterday without regard for the energy required to traverse each day's path is often the type of thinking that makes students give up on their math or technical abilities.
Often times when learning something technical, I will spend as much time on one sentence, one line of the proof, as the rest of it. Being honest with my own understanding makes it harder and makes these roadblocks more frequent - but the unquestioning mastery of the topic after the fact is well worth it.