Some interesting observations by Mike Kayser :
- Patience. Math is hard. It takes time. Try to make progress today, but also know it will be there for you tomorrow
- Humility. Related to the above. Math will surpass your abilities on some days. That’s fine. It does that to everyone sometimes.
- Intellectual honesty. You won’t get anywhere until you admit to yourself what you don’t know.
- Zen like mental calm. It is impossible to do math if you are feeling overly emotional. To study math is thus in some sense to rehearse inner stillness.
- An aesthetic appreciation for rationality. This is harder to explain. For me, math can be an almost spiritual experience, like an interaction with pure abstract beauty. One could almost compare it to “talking to God.” You know that in some sense it will always be beyond you, but the slow, steady accretive work of understanding one piece at a time has its deep, life-long satisfactions.
- Willingness to tolerate bad explanations. Changing gears, a lot of pedagogy in math is terrible, perhaps because people generally don’t understand math all that well, or just don’t know how to talk about it clearly. By wading through bad explanations, you can learn how to mentally translate something complex into something that makes sense to you. This is a useful skill in other domains too.
- An appreciation for complexity and for the limits of our ability to understand things. I guess this is the same as humility above, but doing math makes you realize that most people, most of the time, probably don’t know what they are talking about. Math, like programming, chess, or most complex pursuits, is an antidote to human BS because BS doesn’t get you anywhere in trying to figure out something mathematical.