The situation is even trickier than that because you can keep on looking up these terms, one after another, but it's going to take a lot more than their particu

The situation is even trickier than that because you can keep on looking up these terms, one after another, but it's going to take a lot more than their particular definitions before things begin 'coming together' for someone. I think this largely comes down to the fact that there's no place people can go to learn what it is mathematics is, what it's about, how it works, etc.—and consequently, what mathematicians are interested in and why they have their particular quirks of formulation, and why certain points (which can seem utterly uninteresting to an outsider) are emphasized. Of course you can get this by doing a math degree (and maybe graduate work), but I'm just trying to describe the difficulty in teaching oneself. At least in the U.S., our exposure to mathematics in formal education (pre-university), gives exactly all of the wrong answers to those questions above, so that when you try to start teaching yourself you never know what direction to search in in order to resolve ambiguities.