AFAIK, smoke rings and elastic vibrations aren’t prerequisites for a lot of physics (maybe @alanforr or @lmf knows more about this). They are things which are taught in schools, so you’re socially expected to know them.
And then he mentions a number theory course. And I think what he means is he had gaps in his knowledge of advanced math, not that he had errors in his understanding of arithmetic or algebra.
And then in the next quote, he’s talking about how much (advanced) math he learned, not how well he learned the basics.
And there are different things you can be great at besides math in order to contribute to physics. But being really good at math is one of the paths that can work. But you can’t tell from what Oppenheimer says here how good he was at math.
lol @ reading Principia Mathematica. i now suspect he was quite good at math.
I have no opinion about whether Oppenheimer was a great physicist. But I don’t see any contradiction to it in these quotes.