AI‑Assisted Proof‑of‑Concept Tool for Verifying Asymptotic Estimates by Tao Zhuoxuan

In a May Day post, Fields Medalist Tao Zhuoxuan described how he spent the holiday building a proof‑of‑concept software tool that checks whether a given asymptotic estimate (e.g., X≲Y or X≪Y) holds for any positive real parameters, using only basic arithmetic operations.

The motivation stemmed from a discussion with his former student Bjoern Bringmann about the lack of symbolic‑math tools capable of automatically validating such estimates, especially when functions or sequences are involved.

Tao implemented the tool in Python with heavy assistance from ChatGPT, iterating through prompts to create classes for symbolic expressions, overload operators, and generate verification code; the entire interaction was captured and shared via screenshots.

The project, hosted at https://github.com/teorth/estimates , can automatically prove simple inequalities like the weak arithmetic‑mean–geometric‑mean inequality, handling the multiplicative constant loss denoted by the “~” symbol.

Tao emphasized that while the tool is not an elegant mathematical proof, its automation showcases the practical power of large language models in research, and he encouraged collaboration between mathematicians and professional programmers.

Following the technical description, the article shifted to promotion: Tao announced a paid AI community (“DeepSeek场景实操合集”), offering exclusive resources, ChatGPT accounts, tutorials, and a discounted membership price, along with links to related AI‑related products and services.

He also referenced his earlier predictions that AI would become a trusted co‑author in mathematics by 2026, and invited readers to join his groups, purchase the offered packages, and explore further AI applications.