I wrote this for the personal diary, but I believe itās also appropriate here.
As I have finished a textbook on the beginnings of the naiive set theory... let's summarize, and embrace the bigger picture. Ā 1. school math very much $\ne$ all other (normal? decent?) math, and I love that, though am also terrified (pleasantly so); Ā Ā 1.1 which may also have to do with what someone has said on MSE, something in the fashion of 'set theory is highly abstract, more so than some other areas of mathematics'; Ā 2. commutation and associativity can be entrusted no longer; Ā 3. all in all, MSE and math.hashcode.ru are nice and valuable resources (though, as any other streams of constant new materials, can tap into the neural pathways in a destructive, wearing-out-of-the-reward-circle manner; also, I just don't understand a proof written in a foreign language sometimes); Ā 4. feeling blessed given access to the very foundations of the queen of all sciences... something a wanted to do a long time ago... peeking under the math's skirt; Ā 5. unfortunately, I lack persistence/tenacity/intelligence to understand some concepts/proofs and do half of the problems; Ā 6. using MathJax and LaTeX feels very rewarding, think I could work as a typesetter and never complain, haha; Ā 7. I feel like I could write something technical (did you know R can be well-ordered? how do you feel about Zorn's lemma? P(n)=>P(lim ord), anyone?); feels wrong at the same time, like if that would mean I'm showing off--math is not about learning half-understood theorems by heart, it's about solving problems in a logically correct, rigourous, elegant manner (which to me was hard, I don't do enough problems!). Ā All in all, let's //choose// the following summarizing one-liner: Ā Ā the attempt to learn elementary set theory INCREASED my MATHEMATICAL MATURITY, while at the same time DECREASING my INTELlectual abilities/problem solving skills/whatever you call that. I don't know how much sense that makes. Are these mutually exclusive? Am I deluding myself? Have you ever felt after a long time of [procrastination/doing nothing/not burdening your mind with intellectual work] strictly physically like if the connections in your brain are starting to disconnect, and are gradually fading away, leaving you stupider/dumber than you were? That's how I feel right now. I am also grateful I was exposed to proofs that use 80% human words and 20% mathematical notation--a complete reverse of what they do in school. I don't know why I am still keeping a diary on a dead platform, where nobody is reading this. Perhaps. Okay, bye!
