Terence Tao Sounds Alarm in Mathematics: Harshly Criticizes Excessive Evaluation of AI

Recently, there have been a series of bold headlines claiming that “AI has independently solved long-standing mathematical problems that humans couldn’t crack for decades.” As the influence of such reports grows daily, an unexpected figure has voiced dissent: Terence Tao. Given his active use of AI in mathematical research, his warning carries particular weight. Tao is not outright rejecting AI itself but is calling for an end to the media and public mythologizing of its capabilities.

Why Does the Illusion of an “AI Math Revolution” Spread?

You’ve probably seen sensational headlines like “AI Fully Solves 50-Year-Old Math Problems—Is the Era of Mathematician Unemployment Coming?” For those dreaming of artificial general intelligence (AGI), such headlines seem like a beacon of hope. For researchers committed to preserving human intellectual dignity, they can be a source of anxiety.

In reality, behind these sensational reports lies a fragmented understanding of information. Misinterpreting individual successes as representing overall capability, treating unverified results as established facts—these misconceptions accumulate, forming the so-called “AI invincibility in mathematics” narrative.

Terence Tao raised his voice late at night to bring these exaggerated expectations back to reality. On his updated GitHub page, “AI contributions to Erdős problems,” he details what to watch out for when evaluating AI’s contributions to unresolved Erdős problems.

The Pitfalls in Evaluating AI’s Performance, as Highlighted by Tao

Tao’s cautions may seem to dismiss AI’s achievements at first glance, but in fact, they are redefining what constitutes true success.

Overlooking the difficulty spectrum: Erdős problems range from core issues that are extremely hard to solve, to “long tail” problems that have been neglected for years. AI excels at the latter, but judging its performance solely by the number of problems solved can grossly misrepresent its actual capabilities.

The label “unsolved” is itself uncertain: Many problems listed online haven’t undergone systematic literature review. Some are marked “Open” but have already been solved in past papers. It’s not uncommon for AI to appear to solve a problem that was actually resolved decades ago.

Only successes are highlighted: Records tend to showcase successful AI attempts. Failed trials or research with no progress are rarely documented. This selection bias inflates AI’s perceived ability.

Problems with ambiguous or flawed statements: Some Erdős problems lack rigorous precision or contain errors, requiring deep domain knowledge to interpret correctly. Surface-level loopholes can be exploited to claim solutions.

Mathematical value isn’t just about correctness: While a proof’s validity is crucial, the true value of mathematics lies in how it connects with existing theories and what insights it offers to other fields. Human researchers naturally include context, motivation, and literature connections in their papers. As Tao points out, AI-led proofs often lack this depth of knowledge.

Many problems can’t be formalized: Solving a minor Erdős problem doesn’t guarantee publication in top journals. If the solution involves only minor modifications of existing methods, it’s even less likely.

The pitfalls of formal verification: Formalizing AI-generated proofs using tools like Lean may seem to enhance reliability, but it can also introduce hidden axioms, misinterpret problem statements, or rely on subtle behaviors of the formal system. Especially suspicious are proofs that are unusually short or overly verbose.

The True Role of AI: From “Manual Labor” to “Bridging Knowledge”

In January 2026, the Erdős problem #728番と#729 was fully solved by AI and verified with Lean. This demonstrates that, in certain problem domains, AI can generate “computationally feasible proofs” and carry out formal verification.

So, what is AI actually doing in mathematical research? Tao categorizes AI’s contributions into several roles:

• Generating complete solutions
• Recognizing problems already solved
• Assisting in literature searches
• Formalizing existing human proofs into systems like Lean

Of particular interest is “AI-driven literature review,” where AI verifies whether prior results exist or whether a problem is truly unsolved—essentially conducting “preliminary investigations.”

In summary, Tao emphasizes that AI excels at routine tasks: filling in gaps, formalizing proofs, writing and editing papers, and literature surveys. However, the core of mathematics—posing deep questions, creating new concepts, integrating results into the broader knowledge system—still heavily relies on human ingenuity.

The Future of Mathematics: Human Leadership and AI Execution

Tao’s late-night warning is not about underestimating AI but about understanding its true nature. The future mathematician may no longer be a solitary thinker but a commander leading a legion of silicon intelligence. Humans will chart the course; AI will pave the way and build bridges. This division of labor represents the ideal future of mathematical research.

Let’s refrain from overly glorifying AI’s achievements. At the same time, we must recognize the transformative power it holds in changing how we pursue truth. Tao’s message illuminates a path of calm realism, revealing new possibilities while maintaining a grounded perspective.