Theorem: Any lay explanation of Gödel's incompleteness theorems is either incomplete or inconsistent.
Proof: :made-it-the-fuck-up:
I'm only sour about these because it's one of those things like string theory or "0.999...=1" that attracts almost exclusively cranks who want to use whatever details they internalized from the NATOpedia page and use it to explain why orgones are real or whatever.
I know I'd need to do a deep dive to actually understand the theorem, so I've trained myself to actively reject any information about it because I assume it would be wrong.
Are you familiar with the Metamath project? https://us.metamath.org/mm.html
They don't have a complete proof of Godel's incompleteness theorems yet but I feel like I must plug them anyway lol
It's an ongoing attempt to express and formalize all of mathematics via a massive collection of theorems defined as rules to rewrite the basest axioms of formal mathematics into the theorems to be proved (although in practice you usually start with your theorem and work backwards in Metamath). For any theorem in the database you want to get an understanding of, you can look at the rewriting rules which are expressed as a series of steps to understand why a theorem is true. Or if something is hard to believe you can at least look at the computer-verified proof and safely accept a theorem as true by the rules of the system :3
Has been rly useful to me as someone interested in learning about abstract math but not having a place to start
For example here are the proofs for 0.999 = 1 and 2 + 2 = 4
Theorem: Any lay explanation of Gödel's incompleteness theorems is either incomplete or inconsistent.
Proof: :made-it-the-fuck-up:
I'm only sour about these because it's one of those things like string theory or "0.999...=1" that attracts almost exclusively cranks who want to use whatever details they internalized from the NATOpedia page and use it to explain why orgones are real or whatever.
I know I'd need to do a deep dive to actually understand the theorem, so I've trained myself to actively reject any information about it because I assume it would be wrong.
Are you familiar with the Metamath project? https://us.metamath.org/mm.html
They don't have a complete proof of Godel's incompleteness theorems yet but I feel like I must plug them anyway lol
It's an ongoing attempt to express and formalize all of mathematics via a massive collection of theorems defined as rules to rewrite the basest axioms of formal mathematics into the theorems to be proved (although in practice you usually start with your theorem and work backwards in Metamath). For any theorem in the database you want to get an understanding of, you can look at the rewriting rules which are expressed as a series of steps to understand why a theorem is true. Or if something is hard to believe you can at least look at the computer-verified proof and safely accept a theorem as true by the rules of the system :3
Has been rly useful to me as someone interested in learning about abstract math but not having a place to start
For example here are the proofs for 0.999 = 1 and 2 + 2 = 4
https://us.metamath.org/mpeuni/0.999....html
https://us.metamath.org/mpeuni/2p2e4.html
This is cool, I'll check it out