> The take away is that it's very easy to fool yourself into thinking you've learned a lot from a math book when you're reading it like a novel. In practice, though, if you aren't doing the exercises (or if they don't exist, working through your own), then you probably aren't actually engaging with the material in any deep and significant way.
Agreed. That doesn't mean he didn't read it and glean a little from it though.
> I actually think this is in line with many of his other claims: he seems to be a person who seems to believe he has learned everything important about a field in a relatively short amount of research time, without having a deep background in it already, either through reading a single textbook or by spending a few hours/days/weeks researching and reading. I think most of his claims should probably be considered in that light.
Agreed, it just smacked of elitism to say that it's not possible to read a textbook without interpretation or instruction. That sort of doctrinaire thinking is just bad policy.
I agree that he may have gleaned something (possibly even a substantial something) from it. As I pointed out, it's easy to learn the applied parts of differential geometry in a day or two: curvature, fundamental forms, etc. are fairly simple, fairly intuitive ideas for someone with a good grasp of multivariate calculus and differential equations, particularly when you're restricting yourself to three dimensional manifolds.
I'd note that that's different from having a rigorous understanding of arbitrary dimension differential geometry, and being able to rigorously show new (if simple/uninteresting) results.
I wasn't trying to imply that you can't read a textbook (or any math text, for that matter) and not learn the material at as deep a level as anyone who's main reference is that text. It's a bit like reading someone's code after very heavy optimization, though: it's easy to miss little parts of how or why the algorithm works, and if you go over it once, without trying possible inputs/etc., then you're likely to miss something.
Instruction and interpretation are like comments in code when you're dealing with specific proofs (they make it easier, but it isn't impossible without them). The thing that is harder (but not impossible) to get without some sort of feedback is a deep understanding of when a proof is rigorous and mathematical aesthetics.
Agreed. That doesn't mean he didn't read it and glean a little from it though.
> I actually think this is in line with many of his other claims: he seems to be a person who seems to believe he has learned everything important about a field in a relatively short amount of research time, without having a deep background in it already, either through reading a single textbook or by spending a few hours/days/weeks researching and reading. I think most of his claims should probably be considered in that light.
Agreed, it just smacked of elitism to say that it's not possible to read a textbook without interpretation or instruction. That sort of doctrinaire thinking is just bad policy.