When learning anything you need feedback. In many cases you don't need feedback from humans, and then self-teaching is possible: if you learn chess, you can see if you win more games and if your ELO goes up; if you learn to draw, you can appreciate quite objectively if the apple you drew today looks more realistic than the one you drew one month ago. If you learn programming, you can see if your web page renders or not, or if your sql query returns duplicate records. In machine learning, you can see your AUROC score, is it improving? Is your kaggle ranking breaking the top 100, or you are stuck to 5000 ?
In math, what you deliver is proofs. It's very difficult to "debug" your own proofs, as logical lapses that you might have had when you put together the proof are very easy to persist when you do the self-verification. Sure, mathematicians have developed all sorts of heuristics to flesh out bugs in proofs, but these heuristics come with experience, so for an aspiring self-thought mathematician, this is Catch-22 situation.
What about Ramanujan, or maybe Gauss, or some other historical figures? I don't have a very good explanation, I'm inclined to say they are the exceptions that prove the rule. What I can say for today's day and age is that if someone says they know a self thought mathematician, my reaction would be "extraordinary claims require extraordinary evidence".