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Can you offer any empirical evidence that it is not difficult? The vast majority of people I've encountered who are entirely self-taught beyond typical high sch

by kd0amg 7y ago

Can you offer any empirical evidence that it is not difficult? The vast majority of people I've encountered who are entirely self-taught beyond typical high school (or college freshman) material have been quite bad. They repeatedly make fundamental errors of the sort I would expect to be swiftly corrected in undergrad coursework, even in topics they (claim to) have studied for years. I don't think I've met anyone who learned to write a good proof without significant human instruction. That is probably something to be expected because much of what makes a "good" proof is social expectations, but I see a lot more cases of unjustifiable leaps of logic than excessive, obvious detail.

empath75 7y ago
What does it mean to ‘learn math’? I feel like there’s a value to learning enough math that you understand the general concepts and vocabulary and having an intelligent conversation with a mathematician about, for example, how group theory might apply to some problem you’re working on, without having an actual working knowledge of group theory yourself. I feel like it’s relatively easy to learn a lot _about_ math, as a self learner, without knowing a lot about how to _do_ math. I’m mostly set taught, and I know the notation, I know the vocabulary, and I can follow along with a lot of math papers without too much of looking up terminology and I’ve adapted things I’ve read in math papers into working code, but I’m also well aware of my limitations —- I don’t know how to evaluate whether any of these papers are valid, I don’t have any sort of working knowledge of the tools of proofs to be able to do anything outside of fairly elementary calculus, etc. I know about higher math, but I wouldn’t say I know higher math. But even without that working knowledge, I wouldn’t say that what I know is valueless.
Koshkin 7y ago
Difficult or not, people - programmers, engineers, scientists - keep learning mathematics all the time. True, it may be difficult if you have little background, but for the vast majority of people with a high school diploma it should be no problem, especially given the amount of materials available.

by kd0amg 7y ago

empath75 7y ago

What does it mean to ‘learn math’? I feel like there’s a value to learning enough math that you understand the general concepts and vocabulary and having an intelligent conversation with a mathematician about, for example, how group theory might apply to some problem you’re working on, without having an actual working knowledge of group theory yourself. I feel like it’s relatively easy to learn a lot _about_ math, as a self learner, without knowing a lot about how to _do_ math. I’m mostly set taught, and I know the notation, I know the vocabulary, and I can follow along with a lot of math papers without too much of looking up terminology and I’ve adapted things I’ve read in math papers into working code, but I’m also well aware of my limitations —- I don’t know how to evaluate whether any of these papers are valid, I don’t have any sort of working knowledge of the tools of proofs to be able to do anything outside of fairly elementary calculus, etc. I know about higher math, but I wouldn’t say I know higher math. But even without that working knowledge, I wouldn’t say that what I know is valueless.

Koshkin 7y ago

Difficult or not, people - programmers, engineers, scientists - keep learning mathematics all the time. True, it may be difficult if you have little background, but for the vast majority of people with a high school diploma it should be no problem, especially given the amount of materials available.