Terence Tao, the Fields Medalist and UCLA professor, has published a comprehensive summary of his evolving stance on AI in mathematics, predicting that AI will function as a "trustworthy co-author" in research. This forecast, originally made in mid-2023 regarding "2026-level AI," has reportedly come in "almost exactly [on] schedule," with current tools now contributing at a level "on par with... a junior human co-author." The document, hosted on his personal website and curated with assistance from Claude, synthesizes nearly a decade of Tao’s public statements, lectures, and interviews, offering a rare, detailed look at how a top-tier mathematician integrates large language models (LLMs) into high-level problem solving.

Verification Is the Key Differentiator

Tao argues that mathematics is uniquely positioned to benefit from AI because of the field’s inherent verifiability. Unlike other disciplines where AI hallucinations are often undetectable, mathematical proofs can be checked by formal verification systems. He describes this relationship using a hydraulic analogy: traditional math is a "water tap" producing a trickle of reliable output, while AI is a "firehose of low-quality water." Formal verifiers act as "water filters," allowing mathematicians to harness the AI’s speed without accepting its errors. This distinction leads to his core rule of thumb: use AI only where you can independently red-team its output. If you cannot verify the result or explain it without further AI assistance, the tool should not be part of your workflow.

From 'General Intelligence' to 'General Cleverness'

Rejecting the hype around Artificial General Intelligence (AGI), Tao proposes the concept of "artificial general cleverness." He defines this as the ability to solve broad classes of problems through ad hoc, stochastic, and often uninterpretable means. While humans correlate cleverness with intelligence, machines decouple them. Tao notes that LLMs are "unreliable but powerful" probability kernels that excel at data-scarce reasoning only when paired with strong verification. He emphasizes that AI’s competence is "spiky," capable of superhuman feats in specific domains while making "hilarious" basic errors elsewhere. This unpredictability necessitates a shift in how developers and researchers interact with these tools, moving away from "push-a-button" automation toward interactive, conversational workflows where the human remains the primary director.

The OpenAI Friction and Industrial-Scale Collaboration

Despite his optimism about the technology, Tao’s relationship with industry has grown strained. He disclosed that he no longer sees a way to engage constructively with OpenAI, citing a retrospective disagreement over how his interview was used in advertising after an IPAM workshop sponsored by the company. However, his vision for the future of mathematical collaboration remains robust. He highlights the use of proof assistants to enable "industrial-scale mathematics," where trust is replaced by compilation. A prime example is the formalization of the Polynomial Freiman–Ruzsa conjecture, a 33-page paper broken into independent nodes and completed by twenty people in three weeks. In this model, an idea from an unknown researcher or even an amateur can be taken seriously if it passes formal verification, potentially blurring the lines between human and AI contributors.

Key Takeaways

  • Tao predicts AI will be a reliable junior co-author in math research by 2026, a forecast he now believes has been met.
  • Formal verification is the critical infrastructure that makes AI usable in mathematics, filtering out hallucinations.
  • Tao introduces the concept of "artificial general cleverness" to describe AI’s specific, non-human mode of problem-solving.
  • Proof assistants enable "trustless" collaboration, allowing large groups to work on complex proofs without personal reputation as a barrier.

The Bottom Line

Tao’s evolution from skeptic to pragmatic collaborator offers a blueprint for developers: treat AI as a high-volume generator that requires rigorous, human-led verification pipelines, rather than a black-box oracle.