Mathematicians and scientists have vague folk theories of what math and science are that both are blurred ancestral memories of pre-WWII logical positivism.
These theories are totally wrong, but do little *direct* harm because they are mainly ignored in practice.
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"Improved"? You can improve traffic safety by speed limiting all cars to 3 miles per hour. But it would have some other disadvantages. I'm not against formally checkable proofs, but it does seem like focusing on the 17th most significant bit.
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Oh, to be clear, I am not advocating for computer proof checking. I hope it can be made useful but that’s not what I had in mind in today’s tweets at all. Rather, an upgrade in social processes, as in the psychology re-credibilizing movement.
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Need to separate issues of verifiability from failures of replication/reproducibility due to failure of generalizability.
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When it comes to undergraduate/MSc level maths, I read the proof to find out if it's true. When it comes to research maths, I try to read the proof, and then if necessary I start opinion polling. Should it really be like this? Is this inevitable?
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