I’m an applied math master student at a top european university, and while doing a research internship, we ran into a missing lemma in a proof. We had no idea whether the specific quantity we needed even existed, so before spending days trying to prove something that might be false, I asked ChatGPT to run a quick numerical check, to just have an idea if the existence of what I needed was blatant, or if I needed to look for specific conditions, finer inequalities, etc. The numerical results would just give me an extremely vague direction (If I didn't have chatgpt, I would probably still have implemented it btw).
Instead, it produced what appears to be a complete analytical proof on the spot, introducing several intermediate lemmas and using results I wasn’t even aware of.
My supervisor is fully aware that I use LLMs for coding, simulations, and implementation work, as long as I understand everything they produce. This situation feels different though.
What would you do next ? How would you go about verifying and using a result like this in research ? And, more importantly, with the rapid progress of AI in maths, is it even worth doing a PhD considering that in 2 to 3 years, ChatGPT could be able to write my whole thesis in a day ?