# Remembering mathematics

From Learning

## Notes

My own experience learning math is that I often forget a lot of what I learn even if I read everything and do plenty of exercises. It's quite discouraging to forget so much, and one thing I want to understand better is how much is "normal" to forget, how to forget less, etc.

From Tao's *Analysis I*:

The subject matter [real analysis] is too vast to force the students to memorize the definitions and theorems, so I would not recommend a closed-book examination, or an examination based on regurgitating extracts from the book. (Indeed, in my own examinations I gave a supplemental sheet listing the key definitions and theorems which were relevant to the examination problems.)

There were many occasions early in my career when I read, heard about, or stumbled upon some neat mathematical trick or argument, and thought I understood it well enough that I didn’t need to write it down; and then, say six months later, when I actually needed to recall that trick, I couldn’t reconstruct it at all. Eventually I resolved to write down (preferably on a computer) a sketch of any interesting argument I came across – not necessarily at a publication level of quality, but detailed enough that I could then safely forget about the details, and readily recover the argument from the sketch whenever the need arises.

When I first worked through this book, it didn’t result in long-term retention of the material (I’m sure some people will be able to manage, just not me, not without meditating on it much longer than it takes to work through or setting up a spaced repetition system).

https://twitter.com/michael_nielsen/status/960583071845163008 (and the tweets after this one)