Do you think that theory-building and problem-solving maps at all to your hammers and nails dichotomy? One would be about becoming a hammer that can hit all the nails, and the other is more about really understanding each particular nail.
I think it’s more about the nature of the hammers. Theory-building hammers are legible: they’re big theorems, or maybe big messes of definitions and then theorems (the term of art for this is “machinery”). Problem-solving hammers are illegible: they’re a bunch of tacit knowledge sitting inside some mathematician’s head.
I mostly agree. By the end of the hammers and nails post I realized the real dichotomy was between systematic (including both hammers and nails) and haphazard, and this is a different dichotomy from all the others mentioned in this thread because I will actually make a value judgment that systematic is just better.
Then again, these are just two stages of development and you can extrapolate there’s some third stage that’s even better than systematic that looks like haphazard genius from the outside.
Do you think that theory-building and problem-solving maps at all to your hammers and nails dichotomy? One would be about becoming a hammer that can hit all the nails, and the other is more about really understanding each particular nail.
I think it’s more about the nature of the hammers. Theory-building hammers are legible: they’re big theorems, or maybe big messes of definitions and then theorems (the term of art for this is “machinery”). Problem-solving hammers are illegible: they’re a bunch of tacit knowledge sitting inside some mathematician’s head.
I mostly agree. By the end of the hammers and nails post I realized the real dichotomy was between systematic (including both hammers and nails) and haphazard, and this is a different dichotomy from all the others mentioned in this thread because I will actually make a value judgment that systematic is just better.
Then again, these are just two stages of development and you can extrapolate there’s some third stage that’s even better than systematic that looks like haphazard genius from the outside.