Terence Tao: "As an experiment, I recently t…" - Mathstodon

As an experiment, I recently tried consulting #GPT4 on a question I found on #MathOverflow prior to obtaining a solution. The question is at https://mathoverflow.net/questions/449361/elegant-recursion-for-a301897 and my conversation with GPT-4 is at https://chat.openai.com/share/53aab67e-6974-413c-9e60-6366e41d8414 . Based on past experience, I knew to not try to ask the #AI to answer the question directly (as this would almost surely lead to nonsense), but instead to have it play the role of a collaborator and offer strategy suggestions. It did end up suggesting eight approaches, one of which (generating functions) being the one that was ultimately successful. In this particular case, I would probably have tried a generating function approach eventually, and had no further need of GPT-4 once I started doing so (relying instead on a lengthy MAPLE worksheet, and some good old-fashioned hand calculations at the blackboard and with pen and paper), but it was slightly helpful nevertheless (I had initially thought of pursuing the asymptotic analysis approach instead to gain intuition, but this turned out to be unnecessary). I also asked an auxiliary question in which GPT-4 pointed out the relevance of Dyck paths (and some related structures), which led to one of my other comments on the OP's question. I decided to share my experience in case it encourages others to perform similar experiments.