Extremal descendant integrals on spaces of curves: inequality proved with AI (arxiv.org)

In a groundbreaking advancement at the intersection of mathematics and artificial intelligence, researchers have proven a significant inequality related to extremal descendant integrals on moduli spaces of curves. The study investigates the pure $\psi$-class intersection numbers, revealing how these numbers are influenced by choices of parameters that yield extremal values. Notably, the proof leverages the properties of nefness of the $\psi$-classes alongside Khovanskii–Teissier log-concavity, highlighting that minimal values occur for powers of a single $\psi$-class while maximal values emerge from balanced vectors. What sets this work apart is its collaborative effort between human mathematicians and AI models, including GPT-5 and Gemini 3 Pro, which not only contributed to the formulation of the proof but also drafted significant portions of the paper. By openly documenting the use of various AI tools, this study not only advances mathematical knowledge but also serves as a model for the future of research involving AI in mathematical proofs. This collaborative approach hints at transformative possibilities for the AI/ML community, emphasizing the potential of AI to enhance complex problem-solving in theoretical mathematics.