High school students Aayush Bathija and Prince Rohatgi from Oak Park High School have published a 75-page paper titled 'Bounded Ratios of Lorentzian Polynomials' on arXiv. The research addresses a mathematical problem involving Lorentzian polynomials, a field previously studied by Fields Medalist June Huh.
The students, both AIME qualifiers, conducted the research under the guidance of UCLA mathematics postdoctoral fellow Daniel Soskin. The project utilized AI models, specifically Claude Opus 5 and GPT-5.6 Sol, to assist with calculations, proof strategies, and editing.
The paper introduces a 'main structure theorem' that extends findings from quadratic Lorentzian polynomials to polynomials of arbitrary degree. It establishes a set of discrete convexity conditions to determine whether specific coefficient ratios possess a uniform upper bound.
The research process involved integrating AI into the mathematical workflow to identify potential derivation paths. The authors noted that while AI provided useful suggestions, it also generated misleading information, requiring human verification to ensure the validity and completeness of the proofs.
This achievement occurs amid a broader debate in the mathematical community, highlighted by a recent open letter from 25 Fields Medalists expressing concerns regarding the impact of AI on mathematical rigor and research integrity.
