A research team of mathematicians and computer scientists has used machine learning to reveal new mathematical structure within the theory of finite groups. By training neural networks to recognise simplicity in algebraic data, the team discovered and proved a new theorem on the necessary properties of generators of finite simple groups. This work demonstrates how artificial intelligence can assist in formulating and even proving conjectures in pure mathematics. The 2-generator representation furthers earlier work of one of the authors with M. Kim using Cayley Tables, showing that simplicity has interesting data structure.

A University of Massachusetts Amherst study has found that gerrymandering in North Carolina resulted in reduced access to healthcare services. As states across the country grapple with politically charged redistricting efforts, the finding could ultimately offer a new strategy to fight gerrymandering in the courts, the researchers say.

In many modern sciences, data often exist on curved geometric spaces rather than flat planes, posing challenges for traditional statistical tools. These curved spaces are called Riemannian manifolds. Researchers from Pusan National University and Seoul National University have developed the “Huber mean,” a new method for robustly analyzing data on Riemannian manifolds. This study offers a powerful way to calculate averages that remain accurate even when data contain noise or outliers.

In a study published in SCIENCE CHINA Earth Sciences, researchers from Nanjing Normal University developed a unified mathematical model and a six-category classification system for coastal tipping points. By integrating land-sea interactions and multi-scale processes, the framework analyzes 91 global cases, highlighting spatial heterogeneity and urging advances in data fusion, modeling, and adaptive management to address irreversible shifts in these vulnerable systems.