1) is probably phrased wrongly. I think it isn't even research for the AI labs, it's just an inevitable byproduct of how they train and verify their models. That goes perhaps to the heart of how the mathematicians feel about it: what they thought was a crowning achievement of the human intellect is now a byproduct of a mechanical-industrial process. But that also means the AI labs can't just stop, because they need ever harder puzzles to be part of the training.