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Terence Tao Proposes an AI-Assisted Challenge to Revisit a Classical Problem of Gauss Terence Tao has announced a collaborative mathematical challenge that connects recent AI-generated arguments concerning Landau–Siegel zeros with a classical problem in number theory dating back to Carl Friedrich Gauss. Instead of asking artificial intelligence to solve another open conjecture, Tao proposes a different experiment: using AI to examine, compare, and strengthen mathematical arguments for a theorem that has already been established. The problem concerns nine positive integers associated with imaginary quadratic fields whose rings of integers have unique factorization: 1, 2, 3, 7, 11, 19, 43, 67, 163. Gauss studied these exceptional cases, but the question of whether a tenth integer existed remained unsolved for more than a century. In 1952, Kurt Heegner established that the list was complete, although his proof gained wider acceptance only after subsequent work clarified its validity. Tao's new challenge approaches this classical result from a different direction. He invites researchers to investigate whether recent arguments excluding Landau–Siegel zeros, a particularly elusive possibility involving zeros of Dirichlet L-functions, can yield explicit upper bounds for a hypothetical tenth discriminant without invoking Heegner's theorem. Earlier approaches have produced bounds as strong as d ≤ e⁵⁵. The aim is to determine whether newer techniques can improve these estimates, reveal connections between apparently different proofs, or ultimately lead to an independent argument that could be formally verified using Lean. The project is open to mathematicians and AI researchers, who are encouraged to share their calculations, arguments, and proofs publicly. AI assistance is permitted, provided its contribution is clearly disclosed and the resulting mathematics is carefully checked. What makes Tao's proposal distinctive is its emphasis on understanding rather than merely obtaining a result. Since the theorem is already known, the experiment offers an opportunity to evaluate how AI-assisted mathematical reasoning performs when correctness can be assessed against established mathematics. The challenge therefore places collaboration, reproducibility, and rigorous verification at its centre, treating artificial intelligence not simply as a means of discovering new theorems, but as a potential instrument for understanding why existing theorems are true.

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How often do ArXiv papers contain errors in the main theorems they claim to prove? Using GPT-6.1 Sol to identify such mistakes, it finds: - 6% of papers before 08/2026 contain main theorems that are false. - Only 1.5% contain similar mistakes in the last two months.