{
  "id": 9130644,
  "title": "Mathematicians use AI to find mysterious symmetries, solving decades-old problem",
  "url": "https://urgent.news/2026/09/22/mathematicians-use-ai-to-find-mysterious-symmetries-solving-decades",
  "topic": "science",
  "section": "Science",
  "published": "2026-09-22T11:00:00.000Z",
  "source": {
    "name": "Scientific American",
    "slug": "scientific-american",
    "url": "https://www.scientificamerican.com/article/mathematicians-use-ai-to-find-mysterious-symmetries-solving-decades-old-problem/"
  },
  "original_language": "en",
  "account": "Mathematicians have utilized artificial intelligence to uncover hidden symmetries, ultimately resolving a perplexing mathematical conundrum that has puzzled experts for decades. The breakthrough emerged from a collaboration between human ingenuity and AI's computational capabilities.\n\nThe inverse Galois problem, first posed by 19th-century mathematician Évariste Galois, asks whether it is possible to find a polynomial equation for any given set of symmetries, known as a Galois group. While many Galois groups can be systematically derived from polynomials, certain sporadic groups elude this pattern, posing a challenge in finding corresponding polynomials.\n\nIn May, mathematicians gathered at California Institute of Technology to brainstorm solutions to the inverse Galois problem. One notable participant, Rachel Pries, proposed a particularly promising candidate. Within months, a team of researchers, comprising Pries, Poonen, Huang, Jackson, Lee, and Zhang, employed AI to rapidly explore potential solutions on a scale beyond human capability.\n\nBy analyzing seven surfaces and refining their numerical approximations through AI-driven techniques, the team discovered an explicit equation that generates the M23 sporadic group, a long-sought solution to the inverse Galois problem. The breakthrough, described in a preprint server paper, marks a significant milestone in the field, opening new avenues for understanding the intricate relationships between polynomials and symmetries.",
  "summary": "In parallel, a race by amateurs and mathematicians has found all 25,000 cases of one “inverse Galois problem”",
  "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."
}