Very soft question I admit, but it's something that's been bothering me for a while.
I've been thinking that being self taught has the problem of accreditation. You can't evaluate a mathematician in a vacuum. You need an accredited mathematician to decide whether or not someone else is also a mathematician worthy of accreditation. Well, who evaluated the other mathematician? Other accredited mathematicians. It's sort of like becoming a member of an exclusive club.
We put the job of accreditation on our universities. But what if some person was discovered, off-the-grid so to speak, who had taught themselves mathematics from library textbooks.
How could such a person evaluate themselves? How do you know if you're making progress when you study?
It's tricky. It's like language learning. Do I speak German more fluently now than I did yesterday? I've no idea. Who can say?
It's like playing with Lego. How do you know if you're getting better with Legos? You build more complicated things. But who's to say one person's Lego helicopter is better than another's Lego Enterprise? What's the goal with Legos? Is there one? Should there be one?
I know already that this question will be deleted almost immediately, but I think these are important questions and many people visiting this site are in fact self-taught and I'm sure these questions show up as massive roadblocks.
Thanks for reading.