I run such tests since a long time at chorasimilarity open notebook.
I always used guest non login accounts.
As a mathematician I was able to check two plagiates (by humans) with even such primitive means.
But I have to mention that some things irk me in this conversation about math or science and AI.
First, I see lots of attribution and other related problems, with certain impact for the researcher proffesion.
But I don't see the most natural question: wouldn't you like to know the answer to _open-problem_ ?
I mean, is research now only about publishing and solving famous problems?
From this point of view I think the links from this recent post are depressing
https://terrytao.wordpress.com/2026/09/10/crowdsourcing-a-li...
Second, I think very relevant that the original meaning of "encyclopedia" is "recurrent education".
So I arrived to think that the present and future forms of AI in mathematics and sciences should be seen as modern day encyclopedic efforts.
Once we pass over the flurry of solving famous open problems (and wouldn't you like to know?) the next natural step is an audit of the ehole corpus of mathematics and sciences accumulated until now.
And then pass further on a saner basis and damn about problem solvers and unhappy publishers and management.