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Gromov Hypothesis Solved The Gromov hypothesis on the growth of space volume has been claimed to be solved in three mathematical manuscripts. Two of these manuscripts reveal the role of AI in the proofs, which were published on arXiv on 13-14 August. In two of the manuscripts, the authors describe the role of generative models in finding the proof. In 1986, Mikhail Gromov asked if the geometry at each point could limit the growth of an infinite space as a whole. He considered spaces where two mathematical indicators of how space is curved around a point satisfy strict conditions: one is nowhere negative, the other is everywhere positive. For a sphere of radius R in n dimensions, Gromov expected an upper bound of the volume to be C·Rⁿ⁻². Usually, the volume in n dimensions grows like Rⁿ; here the power of the radius is less by two. The works of Jian Ge, Joacchino Antonelli, and Bochao Kong and Xinyu Zhu all claim this bound. The path from local curvature to volume goes through the spread of heat in space in Ge's work. Antonelli obtains this estimate as a special case of a more general theorem on intermediate curvature. Kong and Zhu relate mass transfer to the volume of spheres of large radius. The three works arrive at the same estimate by different methods. In two of the manuscripts, the authors separately describe the role of generative models in finding the proofs, citing arXiv and referencing their own work, as well as the assistance of GPT and ChatGPT 5.6 Sol Ultra and Codex in exploring the proof and writing the manuscript. 🔗 Read original →