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.

Can you believe it?

They haven't even started university, yet their research has connected with the work of a "Fields Medalist".

Just today, stunning news spread through the UCLA mathematics community—

Two high school students, Aayush Bathija and Prince Rohatgi, under the guidance of a postdoctoral researcher, have solved a problem that mathematician June Huh never managed to crack.

Even more eye-catching is that this proof was completed with heavy assistance from AI!

One was Claude Opus 5, the other GPT-5.6 Sol.

Currently, the paper titled "Bounded Ratios for Lorentzian Polynomials" has been published on arXiv, spanning 75 pages.

Paper: https://arxiv.org/pdf/2609.05341

The names of the two high school students and one postdoc are written right there in the author list.

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