Actually I may take back my previous thought. While I don't think there's curiosity, I think it could be mimicked pretty well by a reward function similar to so

Actually I may take back my previous thought. While I don't think there's curiosity, I think it could be mimicked pretty well by a reward function similar to social media bots. Initially it will explore specifically what mathematicians ask. Then it will start producing intermediate results. It can learn what intermediate results are interesting by standard engagement models. Once that gets good enough, it may start to understand how to explore deeper questions without being prompted. At that point someone may decide to fund it just to continuously explore on its own and report anything interesting. Eventually it'll get so good at this that human mathematicians won't be able to keep up. IDK what happens after that.