More Like this

1. Inequality Ranking and Inference System (IRIS): Giving Mathematical Conjectures Numerical Value

   Davila, Randy; De_Loera, Jesus A; Eddy, Jillian; Fang, Ethan X; Lu, Junwei; Yang, Zini (August 2025, ICML Workshop of AI for Math)

   We introduce IRIS, a geometric and heuristic-based scoring system for evaluating mathematical conjectures and theorems expressed as linear inequalities over numerical invariants. The IRIS score reflects multiple dimensions of significance—including sharpness, diversity, difficulty, and novelty—and enables the principled ranking of conjectures by their structural importance. As a tool for fully automated discovery, IRIS supports the generation and prioritization of high-value conjectures. We demonstrate its utility through case studies in convex geometry and graph theory, showing that IRIS can assist in both rediscovery of known results and proposal of novel, nontrivial conjectures. 

   more » « less
2. A Note on Directed Analogues of the Sidorenko and Forcing Conjectures

   https://doi.org/10.37236/11675  

   Fox, Jacob; Himwich, Zoe; Mani, Nitya; Zhou, Yunkun (July 2025, The Electronic Journal of Combinatorics)

   We study analogues of Sidorenko’s conjecture and the forcing conjecture in oriented graphs, showing that natural variants of these conjectures in directed graphs are equivalent to the asymmetric, undirected analogues of the conjectures. 

   more » « less
3. The stability problem for extremal black holes

   https://doi.org/10.1007/s10714-025-03394-1  

   Dafermos, Mihalis (March 2025, General Relativity and Gravitation)

   Abstract I present a series of conjectures aiming to describe the general dynamics of the Einstein equations of classical general relativity in the vicinity of extremal black holes. I will reflect upon how these conjectures transcend older paradigms concerning extremality and near-extremality, in particular, the so-called “third law of black hole thermodynamics”, which viewed extremality as an unattainable limit, and the “overspinning/overcharging” scenarios, which viewed extremality as a harbinger of naked singularities. Finally, I will outline some of the difficulties in proving these conjectures and speculate on what it could mean if the conjectures turn out not to be true. 

   more » « less
4. A Case of a Computational Setting Facilitating Empirical Re-Conceptualization

   De_Chenne, Adaline; Lockwood, Elise (February 2023, RUME XXV Conference Proceedings)

   The use of computer programming is ubiquitous for research mathematicians, and two common practices are facilitation of experimentation and testing of conjectures. These practices align with empirical re-conceptualization, which is the process where empirical data is used to identify patterns, form related conjectures, and then re-interpret the conjectures from a structural perspective. However, literature on empirical re-conceptualization has only examined student work done by hand. We present case study data of one student, Allen, using the programming language Python to facilitate empirical re-conceptualization as he found the closed-form solution for binomial coefficient C(n,k). We discuss why the computational environment was productive for empirical re-conceptualization and provide avenues for future research. 

   more » « less
5. Geometric Langlands Duality for Periods

   https://doi.org/10.1007/s00039-025-00702-4  

   Feng, Tony; Wang, Jonathan (April 2025, Geometric and Functional Analysis)

   Abstract We study conjectures of Ben-Zvi–Sakellaridis–Venkatesh that categorify the relationship between automorphic periods andL-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some low-rank examples, by using derived Fourier analysis and the theory of chiral algebras to categorify the Rankin-Selberg unfolding method. 

   more » « less