if you wanted to educate yourself to graduate level in mathematics, but didn't actually want to go to university, what would you do?
If you want to really learn the stuff, and you're not outlandishly talented, it'd still take you at least a couple of years of full-time effort, likely more (and correspondingly even more in part-time effort), assuming you don't trip up and go in a wrong direction (e.g. form shallow understanding of advanced topics instead of building reliable foundation). This is unlikely to be achieved if you aren't led step-by-step by a college system, don't enjoy the process, and don't have something to protect.
This will not be a long post; I have a simple question to ask: if you wanted to educate yourself to graduate level in mathematics, but didn't actually want to go to university, what would you do? I would ask for text-book recommendations, but I don't want to limit your responses (however, bear in mind that the wikipedia articles on, say, cardinality or well-ordering go over my head – they may skim my hairline, but over they go). Also bear in mind that while I personally have A-levels (British qualifications) in both Maths and Further Maths (which is to say, I know some calculus at least), there are probably plenty of people on lesswrong who don't and who desire the same information – so assume as much ignorance as you feel necessary (it's a shame, actually, that there isn't a sequence here on lesswrong for maths). What do you advise (if you think the query ill-defined, I would like to know that as well)?