Yes. From a quick scan of the paper, it includes a formal proof in Lean4. That said, it is very long and complicated, with lots of steps in the chain (as you might expect) so it would need to be checked carefully to ensure it proves what it claims to prove.
Lean uses Curry-Howard correspondence, so how proofs work is you declare your propositions as types and then your proof is actually a recipe that goes from things that have already been established and finishes by instantiating that type. The guarantees there are very strong - if you succeed in instantiating the type you have definitely proved something. The question is whether you have proved the thing you said you have. So here scanning the proof (it’s like 100 pages and I am sick so definitely sub-par intellectually) they use category theory to embed the problem, so the proof is actually a proof of the properties of this embedding. So if there is a problem with the proof, my guess would be that it would lie in the embedding not being exactly representative of the problem somehow.
It seems a pretty serious attempt though- it’s not just some random crank paper.
Thank you! This is the kind of comment I hoped to see.
I'm betting it was published in a hurry. I know I would hit "publish" within 24 hours of creating such a result, and would hope it would go wide. I'd publish to arxiv before getting clearance to release the code. I bet that's what happened here.
I appreciate your explanation of the Curry-Howard correspondance. I was familiar with it, but not with Lean in particular. I'd heard of Lean, but didn't know how it worked.
seanhunter|4 months ago
Lean uses Curry-Howard correspondence, so how proofs work is you declare your propositions as types and then your proof is actually a recipe that goes from things that have already been established and finishes by instantiating that type. The guarantees there are very strong - if you succeed in instantiating the type you have definitely proved something. The question is whether you have proved the thing you said you have. So here scanning the proof (it’s like 100 pages and I am sick so definitely sub-par intellectually) they use category theory to embed the problem, so the proof is actually a proof of the properties of this embedding. So if there is a problem with the proof, my guess would be that it would lie in the embedding not being exactly representative of the problem somehow.
It seems a pretty serious attempt though- it’s not just some random crank paper.
rescrv|4 months ago
I'm betting it was published in a hurry. I know I would hit "publish" within 24 hours of creating such a result, and would hope it would go wide. I'd publish to arxiv before getting clearance to release the code. I bet that's what happened here.
I appreciate your explanation of the Curry-Howard correspondance. I was familiar with it, but not with Lean in particular. I'd heard of Lean, but didn't know how it worked.
Thank you again!
krackers|4 months ago
rescrv|4 months ago
beanshadow|4 months ago
https://github.com/comphomology/pvsnp-formal