Being told to ‘show your work’ and graded on the steps helps you learn the steps and y default murders your creativity, execution style.
I acutely empathize with this, for I underwent similar traumas.
But putting on a charitable interpretation: what if we compare this to writing proofs? It seems to me that we approximately approach proofs this way: if the steps are wrong, contradictory, or incomplete the proof is wrong; if they are all correct we say the proof is correct; the fewer steps there are the more elegant the proof, etc.
It seems like proofs are just a higher-dimensional case of what is happening here, and it doesn’t seem like a big step to go from here to something that could at least generate angles of attack on a problem in the Hamming sense.
Yes because the proof itself works that way, no because when a mathematician is looking for a proof their thinking involves lots of steps that look very different from that, I think?
I feel like I have the same implied confusion, but it seems like a case where we don’t need it to record the same kind of steps a mathematician would use, so much as the kind of steps a mathematician could evaluate.
Although if every book, paper or letter a mathematician ever wrote on the subject of “the steps I went through to find the proof” is scanned in, we could probably get it to tell a story of approaching the problem from a mathematician’s perspective, using one of those “You are Terry Tao...”-style prompts.
I acutely empathize with this, for I underwent similar traumas.
But putting on a charitable interpretation: what if we compare this to writing proofs? It seems to me that we approximately approach proofs this way: if the steps are wrong, contradictory, or incomplete the proof is wrong; if they are all correct we say the proof is correct; the fewer steps there are the more elegant the proof, etc.
It seems like proofs are just a higher-dimensional case of what is happening here, and it doesn’t seem like a big step to go from here to something that could at least generate angles of attack on a problem in the Hamming sense.
Yes and no?
Yes because the proof itself works that way, no because when a mathematician is looking for a proof their thinking involves lots of steps that look very different from that, I think?
I feel like I have the same implied confusion, but it seems like a case where we don’t need it to record the same kind of steps a mathematician would use, so much as the kind of steps a mathematician could evaluate.
Although if every book, paper or letter a mathematician ever wrote on the subject of “the steps I went through to find the proof” is scanned in, we could probably get it to tell a story of approaching the problem from a mathematician’s perspective, using one of those “You are Terry Tao...”-style prompts.