{
  "id": 13187517,
  "title": "Two Futures for LLMs in Mathematics",
  "url": "https://urgent.news/2026/10/09/two-futures-for-llms-in-mathematics",
  "topic": "ai",
  "section": "AI",
  "published": "2026-10-09T17:23:45.000Z",
  "source": {
    "name": "Lobsters",
    "slug": "lobsters",
    "url": "https://wiredream.com/llm-two-futures/"
  },
  "original_language": "en",
  "account": "Two distinct approaches have emerged in the application of Large Language Models (LLMs) to the domain of mathematics and theoretical computer science. Anthropic, a company known for its advanced AI models, collaborated with researchers Josh Alman and Virginia Williams, who have previously made significant strides in improving matrix multiplication efficiency. This partnership resulted in a research paper that demonstrated a method to further optimize matrix multiplication algorithms, specifically targeting the exponent ω, which currently stands at 2.371177. The novel approach outlined in the Anthropic paper achieved a reduction to 2.25 or 9/4, representing the most substantial improvement in the field since the 1981 reduction by Schönhage. This accomplishment not only pushes the boundaries of matrix multiplication but also has a cascading effect on related computational problems, such as the 3SUM conjecture, for which the new technique provided a significant breakthrough, offering a sub-quadratic time solution for the first time in decades.\n\nIn contrast, OpenAI took a different route by releasing a comprehensive collection of over 700 PDF documents related to diverse mathematical theories, proofs, and conjectures. The repository includes various works with accompanying Lean proofs—formal verification systems that rigorously validate mathematical statements—while others lack such substantiation. Some of the claimed results within the OpenAI repository are notably impressive, such as the one claiming a reduction in the exponent ω for matrix multiplication to 2.25. However, these assertions have been met with skepticism and criticism, as multiple papers have already been withdrawn due to discovered errors. The writing style of the OpenAI PDFs has been described as \"AI-sloppy,\" with unclear notations, convoluted explanations, and inconsistencies that hinder human comprehension. The authors' approach seems to prioritize quantity over clarity, resulting in a text that is more challenging for non-experts to navigate and understand. The contrast between the meticulously crafted research paper by Anthropic and Williams and the seemingly haphazard compilation by OpenAI highlights the divergent paths that LLMs are taking in advancing mathematical knowledge.",
  "summary": null,
  "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."
}