Terence Tao, widely considered the greatest living mathematician, posted a new paper to arXiv on March 23 that contains a quiet bombshell buried in its exposition: one of its key inequalities was proved by ChatGPT.
The paper, "Local Bernstein theory, and lower bounds for Lebesgue constants," tackles a problem originally posed by Paul Erdős about Lagrange interpolation. Most of it is standard Tao: elegant modifications of classical arguments by Bernstein, Boas, Duffin, and Schaeffer. But one bound resisted him. In the accompanying blog post, Tao explains he had reduced the problem to a toy inequality involving trigonometric polynomials, confirmed numerically by Google's AlphaEvolve that sinusoids appeared to be the extremizer, but couldn't find a rigorous proof.
So he fed it to ChatGPT Pro. The model identified the problem as an approximation theory question and returned a duality-based proof built on the Fourier expansion of the square wave. Tao then adapted this proof to functions of global exponential type, replacing Fourier manipulations with contour-shifting arguments, and eventually completed the paper.
What the AI actually did
It's worth being precise here, because the story is more interesting than "AI solves math problem." ChatGPT didn't prove the main theorem. It solved one specific inequality that Tao had already isolated as a self-contained subproblem, one where the key insight was recognizing which technique to apply rather than inventing new mathematics. Tao says as much on his blog: the AI's main value was in quickly confirming his approach was numerically plausible and in recognizing the right technique to solve one part of the toy problem he had isolated.
The second half of his toy problem, a matching lower bound, resisted ChatGPT entirely. Tao switched to pen and paper, played with contour integrals and the residue theorem, and solved it himself. So the picture is mixed: ChatGPT cracked one piece, failed on another of comparable difficulty, and the mathematician assembled everything into a coherent whole.
From "mediocre grad student" to daily tool
Tao's evolving relationship with AI tools has become a story in itself. In September 2024, he compared working with AI to advising "a mediocre, but not completely incompetent, graduate student." By early March 2026, the assessment had shifted considerably. At an IPAM conference called "Accelerating Math and Theoretical Physics with AI," Tao said current models are now "ready for primetime" because in math and theoretical physics, AI now saves more time than it wastes, according to an OpenAI Academy writeup of the talk.
He now routinely uses AI for literature search, code generation, plotting, and testing whether an approach is worth pursuing. The lower cost of exploration, he says, lets him try "crazier things." But he's careful to distinguish between AI as a capable search-and-match engine and AI as a source of deep original ideas. The former works. The latter, not yet.
The verification problem
Tao has spent the past year pushing hard on formal verification, the practice of writing proofs in Lean, a programming language that checks every logical step mechanically. His concern is practical: as AI generates more proposed solutions to open problems, the risk of plausible-looking but subtly wrong proofs grows. AI can produce arguments that look polished while hiding the weak step.
This is where tools like Gauss come in. Developed by Math, Inc., Gauss is an autoformalization agent that translates human-readable proofs into Lean code. It completed a formalization of the strong Prime Number Theorem in three weeks, a project that had stalled human experts for over 18 months. More recently, Gauss formalized Maryna Viazovska's sphere-packing proof in both 8 and 24 dimensions, even catching a typo in the published paper along the way.
The pattern emerging is a division of labor. LLMs like ChatGPT generate candidate proofs and identify techniques. Formal verification tools like Lean confirm or reject the results. Humans set the direction, decompose problems, and handle the parts that require genuine novelty.
Is this the future or a party trick?
A reasonable skeptic might note that recognizing an inequality as an approximation theory problem and applying duality is not exactly the stuff of Fields Medal citations. It's clever pattern matching. Tao himself would probably have found the proof eventually, maybe in hours, maybe in days. The AI compressed that timeline.
But compression matters. The Erdős problems community has seen a similar dynamic play out over recent months, with GPT-5.2 and other models chipping away at decades-old conjectures. Most of the "solved" problems turned out to be ones where existing proofs already lurked in the literature, or where the AI's main contribution was connecting known techniques to known problems. The genuinely novel solutions remain rare.
Tao expects AI to keep clearing the backlog of problems where standard techniques suffice but nobody had bothered to apply them. The hard problems, the ones requiring new concepts and structures, still belong to humans. For now.
The paper is on arXiv, tagged under math.CA and math.CV. Tao notes he also used AI for "several other secondary tasks, such as literature review, proofreading, and generating pictures," adding that these applications have matured to the point where using them is almost mundane.
