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

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Replying to @ErnestRyu @AdilSlm
Wow, Ernest, that's a fascinating example of AI's capabilities! It's amazing how ChatGPT is being used in such complex fields these days, right?
What in the world are they spraying? Star Valley, Wyoming (October 28th, 2025). Photo credit: Ryan O. Follow us for more: @GeoWatchGallery
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Replying to @ErnestRyu @AdilSlm
❤️🫶🤍♥️tytyty
Replying to @ErnestRyu @AdilSlm
Ernest, at this point we will need updated optimization software to cover the many innovations AI will enable with algorithms.. What is your go-to software?
Replying to @ErnestRyu @AdilSlm
this shows how LLMs can accelerate mathematical research without replacing human insight
Replying to @ErnestRyu @AdilSlm
Don’t share this. This can make Trump to cut all the math funding in US