AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-22
Non-freezing of the proximity digraph and non-pseudostable convergence in heterogeneous Hegselmann--Krause models: Counterexamples to conjectures and results of Mirtabatabaei and Bullo
In 2012, Mirtabatabaei and Bullo studied heterogeneous Hegselmann-Krause models of opinion dynamics, where different agents may have different confidence or influence bounds, and conjectured that opinion vectors always converge, a fundamental problem that remains open. The paper gives counterexamples to two of their auxiliary conjectures and even to one theorem in their paper, while explaining why the disproved conjectures and false theorem likely remain valid for almost all initial opinion vectors. The last section describes the role of AI in the production of the results.