Microsoft researcher and collaborator combine new mathematical ideas with human-directed AI to resolve a central problem in high-dimensional geometry and probability

At a glance

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,…