>Finding a teacher isn't at all mandatory I firmly disagree. What a teacher can give you is perspective that you, not knowing the subject, cannot have -- and

>Finding a teacher isn't at all mandatory I firmly disagree. What a teacher can give you is perspective that you, not knowing the subject, cannot have -- and augmenting any particular viewpoint expressed in a book. If people could learn everything from texts, we wouldn't have universities (for students) and conferences (for working mathematicians). In theory, one can write a Great Text that explains an Idea. In practice, it's damn hard to do that, and it's far easier to impart understanding in a conversation, filling in any blank spots the audience might have on the spot, and guiding the way in the jungle. That's why all texts are kind of bad. Either they are too narrow to give a wide perspective, or too huge to be absorbed! As one of my advisors said: mathematics, like food, is best shared. Don't go into it alone; and whether you have or don't have a mentor, try to find someone else to join you on your journey (a friend who wants to learn the same subject).