Another AI-assisted proof. This time in optimal transport / convex analysis by @AdilSlm
This report details the interactions with the LLM and is a very informative case study on how to work together with ChatGPT.
100% agree on the productivity boost. One just needs patience to correct mistakes, which are more subtle than before imo.
I had a nice interaction with GPT-5-pro while proving a convex analysis lemma: arxiv.org/abs/2510.26647
The model didn’t write the full proof, but the interaction was interesting enough for me to write a short report about it. The report illustrates both the productivity gain and the need for careful proof-checking. The model’s contributions are in blue, and the full chat is in the Appendix. You will see my prompts and how I think, so, no judgement please :)
The problem itself has an history in optimal transport (see intro) and comes from a question I was discussing with some UCLA math professors last summer. Simpler than @ErnestRyu's recent result imo, but still very useful in optimal transport!
Oct 31, 2025 · 8:54 PM UTC








