This was initially "completed" in the 80s. You can see the timeline for cleaning up the proof in e.g. this mathoverflow answer
https://mathoverflow.net/questions/114943/where-are-the-seco...
it's something that some people have been waiting decades for, and is not yet completed.
No we cannot. LLMs do not, by their very nature, understand a single thing. You are giving far too much credence to hype and marketing.