{
  "id": 15912762,
  "title": "Solving a 31-year-old grand challenge in mathematics – the KLS conjecture",
  "url": "https://urgent.news/2026/10/21/solving-a-31-year-old-grand-challenge-in-mathematics-the-kls",
  "topic": "ai",
  "section": "AI",
  "published": "2026-10-21T16:00:00.000Z",
  "source": {
    "name": "Microsoft Research",
    "slug": "microsoft-research",
    "url": "https://www.microsoft.com/en-us/research/blog/solving-a-31-year-old-grand-challenge-in-mathematics-the-kls-conjecture/"
  },
  "original_language": "en",
  "account": "For three decades, mathematicians have grappled with the Kannan-Lovász-Simonovits (KLS) conjecture, a central open question in high-dimensional geometry that questioned the effectiveness of flat cuts in high-dimensional probability distributions. A team of Microsoft researchers, collaborating with human-directed AI, finally resolved the conjecture, establishing a universal geometric principle that simplifies the understanding of high-dimensional spaces. The breakthrough, published in October 2026, showed that simple flat cuts can capture the narrowest bottlenecks within a fixed factor, regardless of the number of dimensions. This result has significant implications for statistics, optimization, algorithms, and computer science, confirming that high-dimensional spaces are less complex than previously believed. The research combined human insight with AI exploration of mathematical possibilities, marking a significant shift in how complex problems can be tackled in the modern era.",
  "summary": "For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing. The Kannan–Lovász–Simonovits (KLS) conjecture was proposed in 1995. It asks whether, for a broad class of…",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}