Mmmh, here's what I think he means by limit...
He has perfected the practice of magic so much, that it bores him.
To feel excitement again for a discipline he once adored, he learns "new" magic from this era, or by proxy through real students.
I put "new" between quotes, because he probably can already cast all those spells better, more efficiently and more powerfully than what they can teach him.
I don't think he's looking to better himself. I don't think he CAN get better. Not because of his magic power, knowledge or capacity, but because there is nothing better to learn appart from what he already knows.
From what we could gather from the story, all of the magically strong living beings throughout the world are dwarfed by his power... And that was before he spent 200 years learning everything.
I really want to see him pissed off, but I don't think he can do that anymore. He's lived so long that almost anybody he knew died of old age, and he learned literally everything there is to learn, so the fact that he isn't a nihilistic mess, but seems pretty happy-go-lucky, makes me believe that nothing other than himself can radically change his mood.