In a loose sense this is the accepted purpose of a degree, not just as an education center (theoretically motivated peers in addition to the teachers), but as a

In a loose sense this is the accepted purpose of a degree, not just as an education center (theoretically motivated peers in addition to the teachers), but as a stamp of "we have given you education in X and deemed that you learned/retained enough of it". I don't know that many school do it well, but some universities can claim that they have much more rigorous programs than others and so students going there will come out better educated (I studied abroad and the mathematics standards at my host school were just nonexistent). Anyone can pick up a math book and start teaching themselves, there's no doubt about it - but any form of third-party verification of this is very high effort on a case-by-case basis.