The topic of Terence Tao using GPT-4 for mathematical research began with Tao's own article on Microsoft Unlocked, titled "Embracing Change and Resetting Expectations". In the article, he mentions:

…… I could feed GPT-4 the first few PDF pages of a recent math preprint and get it to generate a half-dozen intelligent questions that an expert attending a talk on the preprint could ask. I plan to use variants of such prompts to prepare my future presentations or to begin reading a technically complex paper. Initially, I labored to make the prompts as precise as possible, based on experience with programming or scripting languages. Eventually the best results came when I unlearned that caution and simply threw lots of raw text at the AI ……

This passage indicates that Tao is using GPT-4 to assist in reading papers, and his experience suggests that the simpler and more straightforward the prompts, the better. GPT-4 already possesses a very good text comprehension ability. In addition to reading papers, Tao also points out:

…… The 2023-level AI can already generate suggestive hints and promising leads to a working mathematician and participate actively in the decision-making process. When integrated with tools such as formal proof verifiers, internet search, and symbolic math packages, I expect, say, 2026-level AI, when used properly, will be a trustworthy co-author in mathematical research, and in many other fields as well ……

Tao's viewpoint on the above content is based on his practical experience. He shared a case on his main social media platform https://mathstodon.xyz/@tao, where he used GPT-4 to assist in solving a mathematical problem (see https://mathstodon.xyz/@tao/110601051375142142 for details).

This problem is named Elegant Recursion for A301897. Instead of asking the AI to directly answer the question, Tao's approach was to have it play the role of a collaborator, providing strategic suggestions. The AI offered eight methods, one of which (generating functions) was ultimately verified as a viable approach. In this specific case, Tao found the AI helpful because he initially considered using asymptotic analysis to gain intuition, but it turned out to be unnecessary. Additionally, GPT-4 pointed out the relevance of Dyck paths (and some related structures), which gave Tao some inspiration. Tao shared the detailed conversation process, which can be viewed through https://chat.openai.com/share/53aab67e-6974-413c-9e60-6366e41d8414.