David Marr on two types of information-processing problems
I found an essay written by David Marr called Artificial Intelligence -- a personal view that I thought was fairly insightful. Marr first discusses how information processing problems are generally solved: > The solution to an information processing problem divides naturally into two parts. In the first, the underlying nature...
Your account of "proof" is not actually an alternative to the "proofs are social constructs" description, since these are addressing two different aspects of proof. You have focused on the standard mathematical model of proofs, but there is a separate sociological account of how professional mathematicians prove things.
Here is an example of the latter from Thurston's "On Proof and Progress in Mathematics."
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