If he was learning physics and that stuff about topology came up, he'd notice his definitions weren't adding up and fix it. If he never saw it again then the maybe didn't need to learn it to accomplish his goal.
This is very optimistic. I watch people fail to learn things all the time without noticing, especially if they do not have the tools to be honest with themselves, which is a thing that is almost exclusively learned through formal training. Sure, not everyone arrives at that state, but they are much more likely to with guidance.
I'm inclined to be very optimistic, because the guy is fifteen years old and the opportunity cost is League of Legends. :-)
But more to the point you're addressing, physics tends to be easier to grade than math because there is a big focus on calculation, and there you can have answers in the back with no subtle questions about things like whether a student's proof skipped a step because they thought it was obvious or because they didn't know it was necessary. That is not to say physics doesn't have those questions, just that a lot of times the answer is clearer-cut. If the whole thing had been about topology it'd be different.
I disagree. Moreover, it is rather unfortunately the case that the comments section here has decided to throw a party for the death of formal higher education. I'm here to piss in the punch at that party.
