Has anyone verified any of the proofs produced by OpenAI or is everyone just assuming that it just be true because the Lean code checks out? Couldn’t the Lean code just be formulated incorrectly?
For example, the statement of e.g. Fermat's last theorem in Lean should be understandable to anyone who played The Natural Number Game [0] and knows a bit of mathematics and programming. For the proof, you trust the compiler.
The statement of other theorems can be much more delicate, and the Lean formalization may require an extensive introductory section which will need to be carefully checked.
Then there are the cases where no Lean formalization is currently available, and all we have right now is an often impenetrable pdf in the OpenAI repo. I would not at all be surprised if some of those contained logical gaps.
Time will surely tell, but there are certainly doubts and lots people are very busy checking these results.
> In this process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully.
I'm however puzzled by the number of proof claims without lean proofs. How does OpenAI have confidence in those, especially if, as noted in the blog posts, the papers are very hard to read?
In other words, they save effort by wasting the effort of others.
I believe so, even with all the usual safeguards properly in place: https://news.ycombinator.com/item?id=49672339
> is everyone just assuming that it just be true because the Lean code checks out?
Kinda? It's only been 24 hours since they dumped 722 manuscripts on the world, most of which are apparently basically unreadable, and only some of which come with a Lean proof, which in itself is not a joy to read afaik.