The Pulse
Researchers Credit ChatGPT in a Concurrent Math Discovery
Five researchers say ChatGPT-6 Astra helped produce a proof of the strong secretary conjecture for linear matroids. Their paper appeared one day after another team published an essentially identical result using a similar approach.
AI.info Team ·
A 1/e guarantee arrives twice in 24 hours
A proof tied to ChatGPT-6 Astra appeared on arXiv on September 17, one day after another research team published an essentially identical result. The result establishes a 1/e guarantee for the matroid secretary problem on linear matroids, settling the strong secretary conjecture for that class.
The authors of The Strong Secretary Conjecture is True for Linear Matroids say the proof's central argument emerged during a conversation with ChatGPT-6 Astra at 1:02 a.m. Pacific time on September 15. They then checked the argument, prepared the manuscript and discovered, while finalizing the submission, that Hamed Abdi, Kiarash Banihashem, MohammadTaghi Hajiaghayi and Danny Mittal had already posted a paper containing the same result.
The disclosure makes the paper an unusually direct account of AI involvement in a mathematical result. It also separates the model's contribution from the researchers' responsibility for the finished proof: the authors say they verified the argument in full and are responsible for its final presentation.
What the strong secretary conjecture asks
The matroid secretary problem generalizes the familiar secretary problem, in which candidates arrive in random order and a decision-maker must select the best one without being able to revisit earlier choices. In the matroid version, each arriving element carries a weight, and the algorithm must choose an independent set rather than a single item.
A matroid is called linear when its elements can be represented by vectors, with independence corresponding to linear independence. The strong secretary conjecture asks whether an algorithm can select every element of an optimal basis with probability at least 1/e, the same bound that is optimal in the classical rank-one secretary problem.
The new paper proves that guarantee for linear matroids in two settings. The matroid may be known in advance, or its vector representation may be revealed as elements arrive over a finite field. The authors also extend the result to a broader class of matroids that admit a finitary modular extension.
ChatGPT suggested the proof's key move
The paper's algorithm tracks the expected dimension of the intersection between the span of accepted vectors and every relevant subspace. Acceptance probabilities are selected through a family of finite linear programs designed to preserve those dimension bounds while giving each improving element the required chance of selection.
The authors say ChatGPT-6 Astra identified the supermodularity of a function governing those constraints and proposed the uncrossing argument used to prove that the linear programs are feasible. Uncrossing is a standard method in combinatorial optimization that replaces crossing structures with nested ones, often simplifying a proof without changing the underlying bound.
The researchers do not claim that their construction has a polynomial-time implementation. The algorithm maintains distributions over possible spans and solves large linear programs, so the result is a mathematical existence theorem rather than a ready-to-deploy procedure.
“The proof of the main result in this manuscript was obtained in a conversation with ChatGPT-6 Astra on Tuesday, September 15, 2026 at 1:02 AM PDT.”
Kristóf Bérczi, Shaddin Dughmi, Vasilis Livanos, José A. Soto and Victor Verdugo, arXiv authors
Two teams, one result
The concurrent paper, On the Strong Matroid Secretary Conjecture and Beyond, was submitted to arXiv on September 16. Its authors prove the conjecture for every linear matroid and also present results for prophet algorithms and arbitrary matroids, including a 1/64-competitive secretary algorithm obtained through a reduction.
The first paper says the two manuscripts use an “essentially identical approach,” but it does not suggest that either group copied from the other. The ChatGPT-assisted team says it learned of the earlier manuscript only during the final stages of its own submission.
The timing is central to the disclosure. The researchers began working on their manuscript after the model conversation on September 15 and intended to upload it on September 17. The other group had already submitted its paper on September 16, making the episode a case of simultaneous discovery in which an AI system participated in one of the efforts.
Credit belongs to more than the model
The paper treats ChatGPT-6 Astra as a source of a proof idea, not as an author. Its authors describe their own work as including the mathematical verification, the formal exposition and the responsibility for the final result. That distinction matters because the paper's theorem depends on a chain of definitions, feasibility arguments and reductions that extends well beyond the model's reported suggestion.
The disclosure also records that the researchers had been working on ideas in the project since 2024. They say the basic strategy of assigning acceptance probabilities equal to k/(i−1) predates their use of generative AI, while the linear-programming formulation drew on earlier published work.
Both papers now sit on arXiv as public records of the same mathematical advance. One documents an AI-assisted proof conversation; the other provides an independent account of the result without a comparable AI disclosure. The theorem is the 1/e guarantee for linear matroids, and the unresolved question is how much of the proof should be credited to the model's proposed argument versus the researchers who established that the argument works.