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Terry Tao discusses a recent counterexample to the Heil-Ramanathan-Topiwala (HRT) conjecture in harmonic analysis, explaining the structure of time-frequency shifts and the conjecture's status.
A new arXiv paper disproves Maxwell's 1873 conjecture by presenting a configuration of five point charges with at least 24 non-degenerate critical points, exceeding the conjectured bound. The construction was suggested by OpenAI's GPT-5.6 Sol, with the authors verifying the mathematics.
The article discusses how AI models like Anthropic's Fable and ChatGPT have been used by mathematicians to disprove famous conjectures, suggesting a new paradigm of brute intelligence in fields with verifiable answers.
Terry Tao explains a counterexample to the Jacobian conjecture in three dimensions, discovered with the help of Fable AI.
Number theorists discovered a counterexample to the Jacobian conjecture in three-dimensional space using the AI model Fabel. After 87 years, the conjecture was disproved, but the planar version remains open.
AI systems, including ChatGPT and OpenAI's Sol, have disproved and fully formalized the Erdős Unit Distance conjecture, marking a milestone in AI-assisted mathematics. The article discusses the process and implications for the future of mathematical proof verification.
An AI model named Fable discovered a counterexample to the Jacobian conjecture, a long-standing open problem in mathematics, by finding a polynomial function that meets the special conditions but is not invertible.
Claude, an AI model, reportedly found a counterexample to the long-standing Jacobian Conjecture, verified by multiple LLMs, sparking debate about AI's role in mathematical discovery.
A tweet claims that the AI model Claude Fable produced a counterexample to the Jacobian Conjecture, providing an explicit polynomial map that is not injective despite having constant nonzero Jacobian determinant.
A mathematician reports that Grok 4.5 discovered a novel counterexample to hypercontractivity on the 4-sphere, potentially marking the first instance of original mathematical research by an AI, pending peer review.
Kyle Kabasares claims to have used OpenAI's ChatGPT-5.5 Pro to generate a candidate counterexample to an open problem from Don Knuth's The Art of Computer Programming, and requests verification.