In very vague, rough terms, the Langlands program gives a way of understanding certain types of maps between two specific types of groups that are related in a particular way. One way I like to think about it is that it gives mathematicians a template for conjectures of such “correspondences” which are likely to be true. Around 20-30 years ago, I was very interested specifically in the metaplectic covers of SL(2,F), where F is a p-adic field. I seems to have roped a number of victims into thinking and talking about such things with me. My colleagues Courtney Moen (who has retired from mathematics) and Jason Levy (who seems to have also left academia) are two examples.

Around 2004, with Jason, I wrote down a form of the correspondence that I thought the Langlands program template gave me as a conjectural “correspondence” between SL(2) over a p-adic field and the 2-fold cover. It’s very technical to write up, yes, but technically complicated and original are completely different things. I want to be clear, the notes/conversations had nothing original – we were writing down this template due to Robert Langlands in the case we wanted to investigate. I vaguely remember knowing that the conjectural guess was false, but it was just a template and I knew I’d have to sculpt it, like an artist, into a correct one. Sadly, my brain did not have the sharpness needed for the job, and I gave up.

That would have ended it forever if not for the facts that (a) I typed up notes of the template conjecture (or my version of how I remembered them) and, (b) now in 2026 20-something years later, AI is being used to prove the quasi-Riemann hypothesis. So, can it fix the false template guess I made long ago?

Thanks to both Opus-Claude and Sol-ChatGPT, the answer is yes. The AI-written paper The Satake Isomorphism, the Fundamental Lemma, and Transfer of Orbital Integrals for the Metaplectic Double Cover of SL(2, F) is the result. Basically, I tag-teamed one AI agent against another, one acting as the researcher and the other as the referee, and I would be adding or subtracting material at each stage to increase readability, preserve topicality, and maintain correctness. This went through 7 rounds of revision and the pdf above is the result.

The real work was done by AI, not Jason, not me. I think the reason it was so much fun working with that AI team in this way was solely because it taught me something new and interesting. I don’t like to give up on a problem. No one does. This helped me finish the job I gave up on in 2004.