A stunning development from the UCLA mathematics community has captured global attention: two high school students have reportedly solved a problem that Fields Medalist June Huh could not crack. Aayush Bathija and Prince Rohatgi, with guidance from a postdoctoral researcher, completed a proof with significant assistance from artificial intelligence systems. The paper, titled "Bounded Ratios of Lorentzian Polynomials," has been published on arXiv and spans an impressive 75 pages, listing the two students and their postdoc mentor as authors.
The backstory begins with June Huh, a Korean mathematician who won the Fields Medal in 2022 after a remarkable personal journey that included dropping out of high school to pursue poetry before transitioning to pure mathematics. His landmark work from 2020, establishing the theory of Lorentzian polynomials, forms the foundation of this new research. These polynomials are special because their coefficients must satisfy strict mathematical constraints, creating a complex web of relationships that connects combinatorial mathematics with geometry and inequalities.
The fundamental question investigated in this new paper concerns how strong these constraints truly are. When you multiply certain coefficients and divide by others, is there always a limit to how large that ratio can grow? While computing a specific ratio is straightforward, determining whether all possible ratios remain bounded across infinitely many valid polynomials is far more challenging. If bounds exist, researchers must then discover the most precise limit possible.
Previous work by Huh and his collaborators mapped out which ratios are bounded in quadratic Lorentzian polynomials and found optimal bounds for three-variable cases. However, extending these findings to cubic, quartic, or even higher-degree polynomials remained an open problem. The complexity increases dramatically with degree, making direct extrapolation impossible. This gap became the target for the two high school students, who successfully generalized the theory to arbitrary degrees through their main structural theorem, establishing that a discrete convexity condition can completely determine whether a coefficient ratio has a universal bound.
To understand the core idea, consider a simple quadratic polynomial where coefficients must satisfy specific balance conditions. If you have endpoints of 4 and 9, the middle coefficient must be at least 6 to maintain the Lorentzian property. These constraints are what make the ratios potentially bounded. While some ratios have clear limits, like the example that can never exceed 1, reversing the fraction creates a scenario where values can grow without bound as the middle coefficient increases. The research systematically addresses which combinations of multiplied and divided coefficients remain bounded across all valid polynomials.
Both student researchers attend Oak Park High School in California and participate in the UCLA Olga Radko Math Circle (ORMC). Bathija is a sophomore who earned AIME qualification, while Rohatgi is a junior who also achieved AIME status and teaches an AMC 10/12 course within the math circle. Their collaboration with AI, guided by UCLA postdoc Daniel Soskin, compressed what typically requires five to eight years of university and doctoral training into a rapid research campaign.
The proof strategy deeply integrated AI with formal computational tools. By examining how ratios behave at extreme values, the researchers transformed complex numerical relationships into simpler exponential forms. Setting a parameter t approaching zero allows coefficients to be expressed as powers of t, converting multiplication and division into addition and subtraction of exponents. The sign of these exponents instantly reveals whether a ratio shrinks or explodes. This "tropicalization" approach builds on existing Lorentzian polynomial theory, which shows that valid power patterns follow M-convexity rules. The critical proof step demonstrates that if any ratio can grow unboundedly, a path with these characteristic features must exist, turning the examination into a complete criterion using tools from semi-algebraic geometry.
The authors openly acknowledge in their paper's acknowledgments that Claude Opus 5 and GPT-5.6 Sol were core tools used for computation, proof ideas, and editorial assistance during this research. The "proof ideas" contribution is particularly noteworthy, marking a shift toward using AI for genuine explorative mathematics rather than merely verification. However, the authors also candidly note that while some AI suggestions proved helpful, others were misleading. They state they have independently verified all calculations and take full responsibility for the paper's content, underscoring that rigorous verification remains essential even when AI assists with ideas and exploration.
The timing of this announcement adds an ironic twist. Just one day before this research appeared, 25 Fields Medalists had issued a joint public letter warning that AI threatens to destroy mathematics itself. June Huh was among the signatories. The juxtaposition of these events highlights a genuine tension within the mathematical community: while leading experts worry about preserving rigor and purity in research, this demonstration suggests AI can also lower barriers to entry, granting talented individuals access to frontiers that were previously unreachable without decades of training.
This story suggests a shifting landscape where high school students with AIME qualifications, working with AI assistance and professional guidance, can touch mathematical territory that eluded Fields Medalists. Five years ago, such an achievement would have been virtually impossible. Whether this represents progress or peril for mathematics will likely remain a subject of intense debate within the community for years to come. The door, however, has unquestionably been cracked open.