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are there known mathematical entities/subsystems about which people are searching for more information or certainty, where they are failing explicitly because of this idea of incompleteness? the general idea is that godel ruined the unified theory of math, but that's a vague statement. i'd understand this better if there was an example. (i mean beside his highly abstract proof.) i've been reading this, which seems like one: https://www.nature.com/news/paradox-at-the-heart-of-mathematics-makes-physics-problem-unanswerable-1.18983 but there's a missing link in the description of turing's work with undecidable algorithms. i guess that's the peril of science journalism: at some point you just need to learn the subject.