Tao Warns AI Is Exhausting Math's Best Open Problems

Terence Tao's Warning: AI Is Non-Renewably Mining Mathematics' Best Open Problems

In a series of posts on Mathstodon, Fields Medalist Terence Tao issued a stark warning: artificial intelligence is rapidly depleting the supply of what he calls "good, fruitful open problems" in mathematics. These aren't just any unsolved questions—they are the ones that have historically driven the field forward, revealing deep connections and spawning new sub-disciplines.

Tao's argument is subtle and counterintuitive. The set of mathematical problems is infinite, so how could we ever run out? He offers a powerful analogy: a region can face a critical drinking water shortage while surrounded by an ocean. The vast majority of open problems, like computing the 10^10^10th digit of pi, are mathematically valid but mathematically sterile—they offer no insight, no connection to other questions, and no meaningful challenge relative to known techniques.

The Flattening of the Difficulty Landscape

Identifying which problems are actually worth pursuing is, according to Tao, a "lengthy, deliberate, and subjective process." Mathematicians rely on a deep understanding of what he calls the "difficulty landscape" of their field—knowing which questions are trivial, which are challenging but tractable, and which are effectively impossible with current methods. This landscape guides researchers toward the most fertile ground.

However, every new mathematical advance—whether a new technique, a new technology, or new infrastructure like better libraries—flattens this landscape. It makes previously hard problems easier, which is generally good. But it also erodes the subtle gradients that point toward promising new questions. Tao notes that normally, this effect is counterbalanced by the tool's ability to expand the "sphere of results" one can reach, creating new frontiers to explore.

The AI Era: No Clear Frontiers

The current AI era is different, Tao argues, because there are no definitive boundaries separating "AI-feasible" from "AI-hard" problems. While AI tools have flattened the difficulty landscape in many areas, they haven't created clear new frontiers. This is partly due to the technology's rapid evolution, but it's also compounded by AI companies' refusal to disclose negative results or the process behind their solutions.

This lack of transparency is critical. It means mathematicians can't learn from AI's failures, and they can't even fully understand its successes. The result is that the very act of identifying a promising problem has become the scarce and precious resource. Tao observes that even the rumor of someone working on a problem can trigger a massive AI-powered effort to "flatten" it before the original researcher can develop the insights it was meant to generate.

The Threat to Open Science and Early-Career Researchers

This dynamic is creating a perverse incentive: researchers may stop sharing promising directions with the broader community, reversing centuries of open science tradition. Tao warns this would do "serious long-term damage to the future of the field." The fear is not just about being scooped, but about the entire ecosystem of mathematical discovery collapsing.

The impact is already being felt, particularly by early-career mathematicians. As noted in the Hacker News discussion and by commenter abelc on Tao's post, publication inflation and uncertainty about how research will be evaluated are creating immense anxiety. Young researchers question whether their work has value, and the threat of being outpaced by AI solutions before they can develop their ideas is driving some out of the field entirely. A generational gap could be the most damaging long-term consequence.

Proposal: Designating Problems for Careful Analysis

Tao isn't advocating for a ban on AI in mathematics, which he admits would be technically infeasible. Instead, he proposes a more nuanced approach: designating certain classes of problems as "desirous of a careful analysis." This would mean that solving the problem isn't enough—the solution process must also yield insights about the difficulty landscape and connections to nearby problems. Raw solutions without such analysis would be considered of "negligible or even negative value" for these purposes.

He draws an analogy to modern food donation drives, which no longer accept arbitrary edible items but instead maintain explicit, socially accepted standards for what contributions are actually sought. This would create a cultural shift in how the mathematical community values work, emphasizing insight over mere result.

Debate and Counterarguments

Tao's thesis has sparked significant debate. On X (formerly Twitter), Nilesh Trivedi argued that the worries are misplaced, suggesting that because open problems are infinite, AI solutions are inherently valuable. He frames mathematics as a tool for technological progress, where any solution, even without deep insight, is a step forward.

However, others, like Scott Neville, point out that Tao's argument is precisely about the choice of artifacts and systems. The value of a solution isn't intrinsic; it's determined by the ecosystem we build around it. A raw solution to a deep problem might advance a narrow goal but do nothing to sustain the broader culture of mathematical inquiry.

Commenter Sulfide_Sleuth added a practical perspective, noting that AI can now recreate a literature survey that once took four months in under 20 minutes. While efficient, this bypasses the deep reading and thinking that built understanding. The speed of publication is outpacing the ability to read and synthesize, leading to a world where papers are written by AI for AI.

Why This Matters Now

The urgency of Tao's warning is underscored by recent events. As noted in the Hacker News thread, his posts are a direct response to multiple Navier-Stokes results appearing within the last 24 hours—a sign that AI is now tackling problems that were once considered the pinnacle of mathematical difficulty.

The core issue is not whether AI can solve problems, but what mathematics is for. If the goal is to produce insights that deepen our understanding of the universe, then a solution without insight is a hollow victory. If the goal is merely to produce answers, then AI will indeed make much of human mathematics obsolete.

Tao's warning serves as a critical call to action for mathematicians, AI companies, and policymakers alike. The challenge is to build a future where AI augments human mathematical creativity rather than extinguishing the very conditions that make it possible.