Instead of writing that the results in this paper have been obtained using AI, we could write that the results in this paper could not be proved by AI. This can be used as a proof of non-triviality or novelty that could facilitate the evaluation of the paper. Practically, one can share a conversation with the model.
This goes back to something that I’ve always been interested in: how to define banality. My definition was in terms of kolmogorov complexity, so something is banal if it has low kolmogorov complexity given all the rest that is out there. Here, I’m also referring to novels, movies, music, etc., not just math. Naturally this definition is impractical, and it is interesting that large language models can give a practical definition of something similar.
In some communities, compressors like ZIP are used as a proxy for Kolmogorov complexity. It would be interesting to try to use large language models instead or in combination with compressors.
Thoughts 
Related thought: Now that all of my friends and non-theory colleagues have learned that AI can do serious maths, they’ll surely be very impressed if I tell I proved something that AI wasn’t able to prove.
Indeed! This may be the future. Rather than trying to beat each other, we can try to beat the various AIs.
It would be interesting to see which AI one chooses for this, since this is effectively the continuous anomaly-detection approach: a deviation from something the AI can easily predict/solve is essentially the “novelty” score. A well-trained Mathematics AI may consider a Differential Geometry problem generally more novel than a Number Theory problem, for instance, just because of the regularisation used during training.
Thanks for the comment. I agree it’s an interesting aspect. It would obviously be time-sensitive because as soon as the result is published, AI will scrape it, unless we choose to starve it, as I mentioned in the previous post. I am not sure there will be many different AIs. Perhaps there will be very strong AIs that can do pretty much everything because, unlike for humans, it is not hard to combine all the knowledge into a single AI. I see evidence of this right now in the breadth of ChatGPT, for example.