It’s fine that OpenAI posted their findings. It’s not fair to claim these problems have been solved. Not until someone can understand and verify the proof and then communicate the core, novel methodological element to someone else.
It’s fine that OpenAI posted their findings. It’s not fair to claim these problems have been solved. Not until someone can understand and verify the proof and then communicate the core, novel methodological element to someone else.
So yeah, probably we should stop saying "X has been solved", and instead say, "A Lean proof for X (or !X) has been generated". That doesn't change the fact that incentives are currently on finding the proof, and once the proof is generated by an AI, there's not currently a good mechanism / incentive structure to move that into the mathematical community. AI is here, so we need to find a new mechanism.
Convenient. To verify my shovel works you must buy…more shovels!
Possibly yes such a representation is possible. But it doesn’t mean it’s certain there is a "best compressed representation". And even less one that encompass everything important and that is understandable by any human brain, even the most exceptionally brilliant ones sponsored by a whole society to reach their best possible achievable performance on that goal through full dedication on that sole task.