No matter how many articles I read on this subject I cannot comprehend how it proves what it proves. I do well with words and rhetorics, philosophy and science – but as soon as you add numbers my mind goes blank. Not very helpful when those fields often rely on equations and models for explanations and proof. I can somewhat understand equations if explained in a simple or cohesive way – but if at all possible analogies or just word-centric explanations would be very helpful.
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Gödel proved in an extemely abstract way that there are limits to what statements any logical/symbolic system (like math) can make *about itself*, so there are statements in math that fundamentally cannot be proven or disproven (although we do not know which those are).
Gödel developed his theorem during a time where some mathematicians worked on a big project to prove that basically all maths is consistent and “true” (to its own rules). Gödel proved that their project was fundamentally doomed.
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