Not a very interesting article imo, but the topic of self teaching mathematics is a pretty interesting one. There's a few challenges with self teaching math. First, math is inherently about communication. If you cannot communicate your proof, you're not doing math–you're doing mysticism. For instance, the supposed proof of the ABC conjecture by Mochizuki is not verifiable because other mathematicians have not been able to read and vouch for it in its entirety. More mundanely, if you have a proof for the first Sylow theorem in your head with hand waves and loose intuition based arguments, that's extremely different from a proof with tight logic, well defined lemmas and carefully detailed phrasing. Basically if you're self teaching, you have to do problems and have their solutions verified by another mathematician with a degree of rigor.

Second, it's quite easy to convince yourself that you understand a topic. I don't know what it is about math, but there's so many people, myself included, who fall into the trap of thinking they understand a topic, when in fact they don't at all. For instance, there's a multitude of people who can recite verbatim the quadratic formula, or the power rule for differentiation. But ask them to explain why this is true, or give them variants on the power rule (what if we redefine derivatives to be based on multiplication? How does the power rule change?), and they won't be able to give you satisfactory answers. This goes back to my first point; the only way to truly understand math is to do problems and have them checked.