Comment by GPerson
12 hours ago
I’m not sure about this. Anthropic’s AI constructed complex structures on S^6 and wrote a 108 page paper about it, and a few days later there was already a 250k line lean program claiming to verify it.
12 hours ago
I’m not sure about this. Anthropic’s AI constructed complex structures on S^6 and wrote a 108 page paper about it, and a few days later there was already a 250k line lean program claiming to verify it.
an obvious question would be if 250k loc is what is required for the proof or if it can be shortened massively, is this essentially going to be AI trying to search for a smaller proof or is it that a human being would be beneficial in that loop.
It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.
I guess it could be AI turtles checking and summarizing all the way down, but is that any more credible than a single AI checking it? I doubt it.
> It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.
Generally you only need to look at 10-100 lines (unless you have a highly novel theorem that essentially invents a new field of math or builds on a field that has never been worked on in Lean before) of the 250k to verify what it claims. This is why there is excitement around formal verification. The rest of it is perhaps useful to read to figure out why the proof works, but is not necessary for checking.
Human verification of the Lean program only requires verifying that the theorem itself is represented correctly. The theorem will only make up a very small part of the entire Lean program.