Thanks for the further detail!
Comment on What are the most mindblowing fact in mathematics?
parrottail@sh.itjust.works 1 year ago
Godel’s incompleteness theorem is actually even more subtle and mind-blowing than how you describe it. It states that in any mathematical system, there are truths in that system that cannot be proven using just the mathematical rules of that system. It requires adding additional rules to that system to prove those truths. And when you do that, there are new things that are true that cannot be proven using the expanded rules of that mathematical system.
"It’s true, we just can’t prove it’.
cll7793@lemmy.world 1 year ago
Reliant1087@lemmy.world 1 year ago
Incompleteness doesn’t come as a huge surprise when your learn math in an axiomatic way rather than computationally. For me the treacherous part is actually knowing whether something is unprovable because of incompleteness or because no one has found a proof yet.