this post was submitted on 27 May 2025
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I don't know much about this, but I can't help but think that "complete" and "consistent" are doing a lot more work in that sentence than my current understanding of the terms would lead me to believe.
I am sure there was a typo, it's Gödel's incompleteness theorem which proves that consistent systems are incomplete.
Consistency means likely what you expect: it's that you cannot reach contradiction from very axioms.
The result is insane in my opinion, it means any sensible math system with basic arithmetic has a proposition that you cannot prove. AND you cannot also prove that the system is contradiction-free.
It is completionist's worst nightmare.
Stated more precisely, it has true propositions that you cannot prove to be true. Obviously it has false propositions that can't be proven, too, but that's not interesting.