I disagree. Generally speaking students aren't able to teach themselves mathematics on their own until they hit the graduate level. That's not a hard rule, it j

I disagree. Generally speaking students aren't able to teach themselves mathematics on their own until they hit the graduate level. That's not a hard rule, it just depends on mathematical maturity. But everyone I know who is able to teach themselves math without lectures or a professor still does the exercises in the textbook. Math isn't a spectator sport, it's really important to do active learning.