## AI in Mathematics: Between Myth and Reality, Terence Tao Pulls the Brake

The mathematical community has been bubbling for weeks. Sensational headlines proclaim that artificial intelligence has solved problems deemed unsolvable for decades, fueling theories about the imminent obsolescence of mathematicians. But someone had to slow down this inflated narrative, and that someone has been precisely one of the most enthusiastic researchers at the intersection of AI and mathematics: Terence Tao.

In a proactive move that reflects urgency, Tao has updated his documentation on GitHub to critically question how AI achievements are interpreted. His message is clear: do not confuse "producing verifiable results" with "mastering mathematics." The distinction is vital but often overlooked.

### The problem of decontextualized interpretation

When AI solves Erdős problems, there is a natural tendency to magnify the achievement. However, Tao points out that this simplistic view hides fundamental complexities. First, Erdős problems are not all equally difficult. While some pose extreme challenges, others are "low-hanging fruit" that current tools can relatively easily reach. Comparing "number of problems solved" without calibrating for complexity is like measuring achievements by numbers without context.

Another critical factor is that many problems labeled as "unsolved" on public platforms lack thorough literature review. When AI "solves" one of these, it often turns out that a solution already existed somewhere in the scientific corpus. The narrative of the "first discovery by AI" collapses under scrutiny.

### A scenario biased by visibility

Public records mainly capture successful cases. Failures, attempts without progress, dead-end exploration routes of AI are not recorded. This asymmetry of information inevitably distorts our perception of actual capabilities.

Furthermore, when Tao analyzes how a proof is formalized in assistants like Lean, he identifies subtle traps: additional axioms introduced, misinterpreted statements, exploitation of peculiar behaviors of mathematical libraries. A formally verified proof does not always imply genuine conceptual validity.

### Beyond the correct answer

Here Tao touches the core of what it means to be a mathematician. Being a mathematician is not simply providing a verifiable answer, but weaving that answer into the broader network of disciplinary knowledge. A human proof typically includes context, historical motivation, comparisons with previous work, scope, and limitations of the method.

AI-led proofs, by contrast, often lack this "halo of meaning." They are technically correct but epistemologically poor for the community that receives them.

### What AI really does

Tao is cautious but fair in his assessment. AI excels as a composite tool: literature search, rewriting arguments, formalizing existing proofs, automatic review, routine tracking. In specific cases, problems like #728 y el #729 obtained complete verified solutions in Lean by early January 2026, demonstrating that in certain niches, AI can indeed generate "executable proof structures."

But this does not equate to comprehensive mathematical capability. AI is not a mathematician; it is a sophisticated component in the chain of tools.

### The future without idolatry

The mathematics of the future will probably not be the work of solitary thinkers but of commanders orchestrating armies of synthetic intelligence. Humanity formulates deep questions, establishes novel concepts, and intuitively perceives meaningful connections. AI excavates, formalizes, verifies, accelerates.

Tao’s call is for balance: neither demonize nor deify. Recognize the transformative potential of AI without falling into mythology fueled by isolated cases, without allowing exaggeration to replace rigorous analysis.