I have played a little bit with OpenAI's new iteration of GPT, GPT-o1, which performs an initial reasoning step before running the LLM. It is certainly a more capable tool than previous iterations, though still struggling with the most advanced research mathematical tasks. Here are some concrete experiments (with a prototype version of the model that I was granted access to). In https://chatgpt.com/share/2ecd7b73-3607-46b3-b855-b29003333b87 I repeated an experiment from https://mathstodon.xyz/@tao/109948249160170335 in which I asked GPT to answer a vaguely worded mathematical query which could be solved by identifying a suitable theorem (Cramer's theorem) from the literature. Previously, GPT was able to mention some relevant concepts but the details were hallucinated nonsense. This time around, Cramer's theorem was identified and a perfectly satisfactory answer was given. (1/3)