I find this post very encouraging, but I can’t shake a particular concern about the approach that it recommends.
From extrapolating past experiences, it seems like every time I try (or even succeed) at something ambitious, I soon find that somebody else already did that thing, or proved why that thing can’t work, and they did it better than I would have unless I put in ten times as much effort as I did. In other words, I struggle to know what’s already been done.
I notice that this happens a lot less often with mathematics than it used to. Perhaps part of it is that I became less ambitious, but I also think that part of it was formal education. (I finished a BS in math a few years ago.) I do think one of the major benefits of formal education is that it gives the student a map of the domain they’re interested in, so that they can find their way to the boundary with minimal wasted effort.
I find this post very encouraging, but I can’t shake a particular concern about the approach that it recommends.
From extrapolating past experiences, it seems like every time I try (or even succeed) at something ambitious, I soon find that somebody else already did that thing, or proved why that thing can’t work, and they did it better than I would have unless I put in ten times as much effort as I did. In other words, I struggle to know what’s already been done.
I notice that this happens a lot less often with mathematics than it used to. Perhaps part of it is that I became less ambitious, but I also think that part of it was formal education. (I finished a BS in math a few years ago.) I do think one of the major benefits of formal education is that it gives the student a map of the domain they’re interested in, so that they can find their way to the boundary with minimal wasted effort.