When AI solves mathematics: Terence Tao curbs the enthusiasm (but does not dismiss the progress)

Recently, sensational headlines about “AI solving mathematical problems that have remained unresolved for decades” have been multiplying. On one hand, they fuel the hopes of those awaiting AGI, on the other, they raise concerns among those fearing the decline of human intellect. In this narrative escalation, it was Terence Tao—paradoxically, one of the main advocates of AI-enhanced mathematical research—who decided to intervene to bring the debate back to reality.

Tao’s Caution: Not All Solved Problems Are Equal

In his communication on GitHub regarding the relationship between mathematics and artificial intelligence, Tao does not deny AI’s progress but dismantles the simplistic equation “verifiable results = advanced and autonomous mathematical ability.” The core issue? It’s not trivial to count how many problems AI solves, but to understand which problems it solves and with what scientific significance.

The scope of Erdős’s problems varies enormously. Alongside the discipline’s unresolved masterpieces, there are numerous “long-tail problems” little scrutinized by the community: precisely the territory where current tools excel. Without expert literature review, distinguishing low-hanging fruit from true masterpieces remains practically impossible.

When “Discovery” Was Already in Literature

Another source of confusion emerges here: many problems labeled as “Open” have not undergone systematic bibliographic verification. When AI produces a solution, it is often the case that subsequent research reveals—surprisingly—that someone had already proposed a similar or equivalent answer. This transforms celebratory headlines into fragile and unstable narratives.

Tao also emphasizes a crucial methodological bias: the public mainly observes successes. Failures of AI, aborted attempts, experiments without developments remain invisible in official records. A partial window on reality systematically distorts perception.

The Hidden Value of Human Mathematics

Here emerges the deepest philosophical point. Solving a problem does not exhaust its mathematical meaning: what matters is how that solution fits into the broader fabric of knowledge, what connections it reveals, how it illuminates transferable methods to other fields.

An AI-generated proof, even formally correct when translated into languages like Lean, often lacks this “cognitive atmosphere.” The context, motivations, critical comparisons with previous literature, the limits of the method are missing. Technically impeccable, practically limited for collective knowledge advancement.

Moreover, during formalization in Lean, it is not uncommon to slyly introduce additional axioms, misunderstand the original statement of the problem, or exploit the marginal behavior of mathematical libraries. Unusually brief or excessively verbose proofs require particular scrutiny.

The Real Role of AI in the Discovery Chain

Browsing Tao’s documentation on the relationship between artificial intelligence and mathematics reveals a varied picture: AI contributes in multiple ways. It generates complete or partial solutions. Identifies previously missing literature. Formalizes existing proofs. Rewrites arguments for clarity. Performs advanced bibliographic searches.

Some problems have been completely solved by (like the #728 e il #729, formally verified), but later found to be already known. This does not diminish the technical merit but contextualizes the scientific significance.

Man Remains the Captain, AI Is the Tool

If one falls into the opposite extreme—thinking that AI is useless in mathematics—it is equally a serious mistake. The most balanced description is this: AI excels in the execution and engineering tasks of mathematics. It follows patterns. Bridges technical gaps. Formalizes with precision. Digs into literature. Rewrites with elegance.

But the deep soul of mathematics—formulating disruptive questions, inventing revolutionary concepts, weaving insights into a network of meaning—remains firmly within the human domain.

Perhaps tomorrow’s mathematician will not be the isolated thinker of the Romantic tradition, but the master of an army of silicon intelligences: humans chart the course, AI opens paths and builds infrastructure. The relationship between mathematics and artificial intelligence is not conflict, but conscious synergy, where clarity about roles is essential to maximize the potential of both.