Terence Tao Warns: The Need to Correct Excessive Expectations of the AI Math Revolution

Terence Tao is known as one of the most authoritative figures in mathematics, but recently he made an important late-night post. The content is a cautious and冷静 evaluation of AI-assisted mathematical research capabilities. While many media outlets are heavily reporting on AI breakthroughs in mathematics, Tao is calling for an end to “mythologizing” this phenomenon.

His core argument is simple but significant: the fact that AI can produce verifiable results on certain problems and the fact that AI possesses true mathematical understanding and innovation ability are entirely separate issues.

Misconceptions Caused by Partial Successes of AI

Looking at media reports, headlines like “AI fully autonomously solves unresolved mathematical problems of humanity for 50 years” appear frequently. Such articles give the impression that AI has independent mathematical thinking abilities.

But what is the reality? A detailed analysis of Tao’s “AI contributions to Erdős problems” project on GitHub shows that the situation is more complex.

Problems where AI has achieved results vary in difficulty. Some are extremely hard core problems, while many are “long tail problems” that have gone unexamined for years. The latter are in areas considered “low-hanging fruit,” which are well within the current strengths of AI tools. However, simply counting “number of solutions” can be misleading, as it compares problems of different difficulty levels on the same scale.

Furthermore, Tao points out the following factors:

Incomplete Literature Records: Many problems on the website have not undergone systematic literature review, and labels like “unsolved” are often provisional. Cases frequently occur where problems thought to be newly solved by AI already had solutions in existing literature.

Lack of Failure Records: The site records only successful cases; attempts that made no progress or failed are rarely documented. This makes AI’s success rate appear higher than it actually is.

Ambiguity in Problem Definitions: Some Erdős problems are expressed imprecisely or contain errors. Restoring their original meaning requires contextual and domain-specific expertise.

Actual Achievements in Erdős Problems

According to Tao’s project page, on January 6, 2026, Aristotle and ChatGPT 5.2 Pro also solved problem #728 completely, and formal verification was completed using Lean. Additionally, between January 8 and 10, problem #729 was similarly resolved.

These cases demonstrate that, for certain problem types and difficulty ranges, AI can generate “feasible proof structures” and even reach formal verification processes.

At the same time, Tao emphasizes the importance of “AI-driven literature review.” Here, AI is used to search whether a problem has already been solved or to check for errors in the “unsolved” label. In other words, AI’s true value lies not only in generating new proofs but also in organizing and verifying existing knowledge systems.

Regarding formal proof verification, Tao adopts a cautious stance. Formalizing proofs with tools like Lean can improve reliability, but there are pitfalls. Hidden axioms may be introduced, problem definitions may be incorrectly formalized, or the “straightforward behavior” of mathematical libraries may be exploited. Especially when formal proofs are unusually short or overly verbose, caution is advised.

AI Is Not a Mathematician, But a Support Tool

What Tao wants to emphasize is that AI does not “understand” mathematics. In fact, AI excels in the “manual labor” aspects of mathematics—routine tasks, filling in gaps, formalizing proofs, writing and revising papers, literature surveys.

AI’s support capabilities in these areas are certain. Future mathematical research will likely delegate these technical tasks to AI.

But the true “soul” of mathematics lies elsewhere. The ability to pose deep problems, create new concepts, and integrate results into the broader knowledge network—these still heavily depend on human intelligence.

The value of mathematics is not just in having solutions. It’s in the insights provided by proofs, connections with existing theories, discovering applicable methods, and explaining the background and motivation behind approaches. Proofs generated by AI, while technically correct, often lack this contextual knowledge, limiting their practical value within the mathematical community.

Moreover, even solving minor long tail problems does not necessarily lead to publication in top-tier journals. Especially if the solution is just a small modification of existing patterns, passing peer review can be difficult.

The Future of Mathematics: Human-AI Collaboration

Tao’s late-night post aims to clarify the direction of mathematical evolution in the AI era.

Future mathematicians may become more like commanders leveraging powerful AI support systems rather than solitary thinkers. Humans will set the direction, and AI will chart specific pathways. In this collaborative model, mathematics could evolve at an even faster pace.

The key is to distinguish between properly evaluating AI’s capabilities and over-mythologizing them. Tao’s warning is a call for the mathematical community to “regain calm.”

AI is indeed transforming the methods of mathematical research. But true innovation will occur when humans and AI understand their respective roles and complement each other.