Author here! My impression is that it's customary in the mathematical community to take responsibility for the result with your name, regardless of whether it came from LLM etc (as long as you disclose LLM usage). I am perfectly fine calling it "LLM's proof" or somehow else, but it's "my" in the sense that "if there is a mistake in it, it is my mistake".

Someone had to choose the problem, steer the model, and check the output - it's clearly taken a lot of time. That's authorship with a powerful tool, same as it's always been.

I don't understand your comment. At first it seems like you think the LLM should get credit for the work. But then you mock the author for asking about the LLM's mood, which makes me think you believe the LLM is just a tool and not capable of receiving credit (FWIW I would agree.)

When you use a drill to put a hole in the wall, do you take credit for it, or do you credit the drill? Without intent, a tool, whether it be a drill or an LLM, is just an inert object.

They still needed to invest time and other resources into this. It's listed clearly in the 2nd paragraph. Mathematicians, or anyone for that matter, don't figure out everything from scratch. They lean on the work that others have done before them to save time. How is this any different?

LLMs need a lot of help to get to any kind of complicated proof, really. And yes, they get in moods. I spent 3 weeks trying to prove something and frequently had to try and convince Claude that it wasn't impossible and that it could really do it.