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One thing that worked for me was to have a community of fellow mathematicians to study with. There's a lot of cultural stuff that is kind of hard to osmose from

One thing that worked for me was to have a community of fellow mathematicians to study with. There's a lot of cultural stuff that is kind of hard to osmose from books, such as for example, how to pronounce things that you read. Mathematical notation is meant to be read out loud. It's shorthand for English, or whatever your natural language is. You should be comfortable seeing a sigma sign and thinking in your head, "the sum as ehn goes from one to infinity of eff of ecks squared times ..." That's just the basic part of it. There's lots of cultural shorthands that are just kind of osmosed, seldom overtly acknowledged (for example, the precise meaning of "without loss of generality"). Maybe you can acquire them by watching videos, but if you can find people that you can hang out with that can teach you the cultural aspects of mathematics, that would help a lot. Picking up a book and reading and working through it and understanding it gets a lot easier once you have the culture down.

throwawaymath 8y ago
That is also part of the loosely defined term, “mathematical maturity.” When you’ve reached it, you can generally grasp the basics of unfamiliar math quickly. Failing that, you can find out what you need to study to understand it and do so on your own. You don’t typically obtain that kind of maturity until graduate school, maybe upper undergrad if you’re quite good.
- jordigh 8y ago
  Yeah! There's that whole thing where you understand how a work is structured, you know what part to pay attention to, what part to skim or read later, where you're required to do your own calculation to fill in something... People complain a lot that books and presentations don't do everything and that mathematics has a bad "user experience". They may have a point, but the complaining alone won't fix it and will leave most people still feeling like frustrated outsiders.

throwawaymath 8y ago

That is also part of the loosely defined term, “mathematical maturity.” When you’ve reached it, you can generally grasp the basics of unfamiliar math quickly. Failing that, you can find out what you need to study to understand it and do so on your own. You don’t typically obtain that kind of maturity until graduate school, maybe upper undergrad if you’re quite good.

jordigh 8y ago
Yeah! There's that whole thing where you understand how a work is structured, you know what part to pay attention to, what part to skim or read later, where you're required to do your own calculation to fill in something... People complain a lot that books and presentations don't do everything and that mathematics has a bad "user experience". They may have a point, but the complaining alone won't fix it and will leave most people still feeling like frustrated outsiders.