do you know many sources that talk about "the mathematical wilderness"? i made up the phrase in this post but it has to be a thing people already think about
i'll see if i can summarize the point if you wanna skip the post
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with many problems that are NP-hard we have heuristic algos that do a suitable job for day to day tasks
this seems to point at the og problem wasn't what you cared about
like, you think you care about the traveling salesman problem, but you actually care about a specific subset
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it seems like there's lots of mathematics where "most" of the entities in some grouping are going to be meaningless/incomprehensible wild objects, and there's room to figure out a formalism that gets a much smaller but much more meaningful subset of problems
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this kind of thing is indirectly a thing in manifold learning, where you recognize that the set of all data you care about is a tiny low-dimensional submanifold of the manifold of all possible data, but haven't heard anyone apply it to mathematical objects