Why ain'tcha better at math
I feel like one response people might have, if they hear that I think I have a new and exciting way to learn math, is to ask why I personally am not the best at math. There are a couple of responses to this:
- Math is pretty interesting, but it's not my main interest. People who are into math enough to become mathematicians are really into math in a way that I am not. I am too much of a generalist to ever become a mathematician. Just in terms of time invested, I've probably only spent one year full-time doing math (mid 2018 to mid 2019); in all the other years of my life, math has not been a singular focus for me.
- I'm more interested in the psychological aspects of math than in pushing the field forward. I like to think about pedagogical and foundational stuff (like how to best teach something, or how to look at very basic stuff in a new way) more than I like pushing forward into the most advanced thing I can get my hands on, or proving a theorem that nobody else has ever proved before. I spend time writing solutions manuals for newcomers, writing wikis about the psychological aspects, experimenting with Anki, writing expository pieces, etc. So even within math, the parts that I like don't involve me going super deep into the most advanced stuff.
- My baseline ability/raw processing power isn't as high compared to people who are really good at math (e.g. people who win math contests, get into top PhD programs, win professional prizes).
I think the basic point is a good one, however. If my method has any merit, then the person who is using it should be able to learn and retain non-trivial stuff. I actually have this criticism about people who are seriously into productivity/life hacking stuff: if your note taking method/learning method/to-do list system/life style/whatever is so good, then where is the output? Where are the things you have done with it? So I do feel that I need to demonstrate that I am good/passable at math, not necessarily in the usual ways but at least in some idiosyncratic way that I am satisfied with and that a reasonable person would be satisfied with.