A recent experience with ChatGPT 5.5 Pro

We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to which I am fortunate to have been given access, producing a piece of PhD-level research in an hour or so, with no serious mathematical input from me. The background is that, as has been widely reported, LLMs are now capable of solving research-level problems, and have managed to solve several of the...