I was thinking about trying this exact problem with AI. I missed that it had already been solved. It's not that surprising that someone else already tried it. What's surprising is that open problems get solved so quickly now that it's impossible to keep up with them all.
Unless you have access to the same compute limits as the guy at Anthropic, and the internal model they use, you probably would just have spent a lot of tokens without success. So you can take solace in that.
I understand the spirit of what you're saying, but "unassisted humans" isn't a good yardstick. There's hardly anything "unassisted" humans understand today... We require plenty of assistance from computer tools in most scientific discoveries.
This is based on a 108 page prose paper that the repository links to. Of course, that's a very difficult paper as well, I don't know how many people would be qualified to read and digest it, but they do exist.
We understand the proof (most math from all of history) -> We understand how the proof was made (computer-assisted proofs like the four-color theorem) -> We have to trust the computer's explanation for how the proof was made (some LLM proofs)
Oh wow, I'm fairly impressed. I wouldn't have expected AI to solve a problem this hard just now.
There have been claims of complex structures on s6 (or absence of them) quite a few times over the last 15 years. Some by acclaimed mathematicians.
There was some discussions on HN a few days ago:
Surprisingly the (a, since multiple things have this name) Hopf conjecture was solved by human mathematicians around the same time. It’s the statement that S^2 x S^2 admits a positive sectional curvature Riemannian metric.
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[ 149 ms ] story [ 348 ms ] threadI looks like we are breezing past the point where unassisted humans can understand any of this
for all intents an purposes, the paper as well as the lean repo could be full LLM output with zero human involvement
We understand the proof (most math from all of history) -> We understand how the proof was made (computer-assisted proofs like the four-color theorem) -> We have to trust the computer's explanation for how the proof was made (some LLM proofs)
There have been claims of complex structures on s6 (or absence of them) quite a few times over the last 15 years. Some by acclaimed mathematicians. There was some discussions on HN a few days ago:
https://news.ycombinator.com/item?id=49412947