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Unsolved Problem by Fields Medalist Breached by Two High School Students
In a remarkable breakthrough, two high school students from Oak Park High School, Aayush Bathija and Prince Rohatgi, with guidance from UCLA postdoctoral researcher Daniel Soskin, have solved an open problem related to the theory of Lorentzian polynomials—a field pioneered by Fields Medalist June Huh. Their 75-page paper, "Bounded Ratios for Lorentzian Polynomials," is now available on arXiv. The research investigates the constraints on coefficient ratios within Lorentzian polynomials, extending prior work that characterized bounded ratios for quadratic polynomials to polynomials of arbitrary degree. The core challenge was determining which coefficient ratios have a universal upper bound across all polynomials in the class and identifying the optimal bounds. The students heavily utilized AI assistants, specifically Claude Opus 5 and GPT-5.6 Sol, for computational exploration, proof idea generation, and editing. They emphasize that while AI provided helpful suggestions, some were misleading, and all calculations and arguments were independently verified. This achievement is particularly notable as it follows a recent open letter signed by 25 Fields Medalists, including June Huh, expressing concerns about AI's impact on mathematical rigor. The students' work demonstrates how AI can lower barriers to entry, enabling talented pre-university researchers to engage with advanced mathematical frontiers.
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