Solving a 31-year-old grand challenge in mathematics – the KLS conjecture

Fundamental scientific breakthrough: Researchers resolved the Kannan-Lovász-Simonovits (KLS) conjecture, a 31-year-old problem widely regarded as one of the central open questions in high-dimensional geometry, with implications for statistics, optimization, algorithms, and computer science. A universal geometric principle: The result establishes a universal geometric principle for log-concave distributions, showing that simple flat cuts can capture their narrowest bottlenecks within a fixed factor, regardless of dimension. Human-AI collaboration: The breakthrough emerged from a human-directed agentic research process in which AI systems explored mathematical possibilities while researchers evaluated, pruned, and redirected the search. Independent confirmation: Multiple independent researchers have validated this research, identifying its central criterion as the key breakthrough, followed by a machine-checked formal verification. For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted…