{
  "api_version": "1",
  "updated": "2026-11-10",
  "latest_event": "2026-11-09",
  "rights": "© Frontier Log, all rights reserved.",
  "story": {
    "slug": "ai-math-discoveries-2026",
    "title": "AI Math Discoveries in 2026",
    "description": "Four AI companies made 11 announcements on open math problems this year. Nine credit a model the public could not use that day.",
    "url": "https://frontierlog.ai/stories/ai-math-discoveries-2026",
    "date": "2026-11-09",
    "image": "https://frontierlog.ai/og/story-ai-math-discoveries-2026.png",
    "event": "2026-10-26-openai-three-discoveries",
    "tags": [
      "math",
      "science",
      "reasoning"
    ],
    "steps": [],
    "tables": [],
    "records": [
      {
        "date": "2026-02-11",
        "party": "Google",
        "what": " says its Aletheia agent, powered by Gemini Deep Think, solved four open Erdős problems on its own",
        "by": "Google DeepMind",
        "source": "https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/",
        "quote": "including autonomous solutions to four open questions listed there"
      },
      {
        "date": "2026-05-20",
        "party": "OpenAI",
        "what": " says an internal model disproved Erdős's unit-distance conjecture",
        "by": "OpenAI",
        "source": "https://openai.com/index/model-disproves-discrete-geometry-conjecture",
        "quote": "An internal OpenAI model has disproved this longstanding conjecture"
      },
      {
        "date": "2026-07-20",
        "party": "Anthropic",
        "what": "'s Levent Alpöge posts that the Jacobian conjecture is false, crediting Fable",
        "by": "Levent Alpöge",
        "source": "https://x.com/__alpoge__/status/2079028340955197566",
        "quote": "the jacobian conjecture is false",
        "also": [
          {
            "by": "Anthropic",
            "source": "https://www.anthropic.com/research/discovering-cryptographic-weaknesses"
          }
        ]
      },
      {
        "date": "2026-08-01",
        "party": "OpenAI",
        "what": " shares ten results on long-standing open problems from an internal version of Astra",
        "by": "OpenAI",
        "source": "https://openai.com/index/ten-advances-in-mathematics",
        "quote": "The results were achieved by an internal version of Astra, our next major model."
      },
      {
        "date": "2026-08-10",
        "party": "Anthropic",
        "what": " says an unreleased Claude raised the lower bound for Riemann zeta zeros on the line from 41.6% to 67.2%",
        "by": "Anthropic",
        "source": "https://www.anthropic.com/research/riemann-zeta",
        "quote": "An unreleased research version of Claude has improved on a longstanding lower bound"
      },
      {
        "date": "2026-09-08",
        "party": "OpenAI",
        "what": " shares a solution to the Navier–Stokes Millennium Prize Problem with a Lean proof",
        "by": "OpenAI",
        "source": "https://openai.com/index/navier-stokes-solution",
        "quote": "we used an internal model that is significantly more capable than GPT‑6 Astra"
      },
      {
        "date": "2026-09-21",
        "party": "OpenAI",
        "what": " says the same model has resolved more than 100 long-standing open problems",
        "by": "OpenAI",
        "source": "https://openai.com/index/advisory-group-on-mathematics-and-ai",
        "quote": "this model has now resolved more than 100 long-standing open problems across most areas of mathematics"
      },
      {
        "date": "2026-10-06",
        "party": "OpenAI",
        "what": " publishes 722 manuscripts from an internal model on GitHub",
        "by": "OpenAI",
        "source": "https://openai.com/index/sharing-ai-progress-in-mathematics",
        "quote": "We’re releasing a broad range of new mathematical results produced by an internal frontier model.",
        "also": [
          {
            "by": "OpenAI",
            "source": "https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/README.md"
          }
        ]
      },
      {
        "date": "2026-10-26",
        "party": "OpenAI",
        "what": " announces results on the Kakeya conjecture, the Exponential Time Hypothesis and Yang–Mills existence",
        "by": "OpenAI",
        "source": "https://openai.com/index/building-scientific-understanding-with-academic-communities",
        "quote": "Surprisingly, our system has recently proved that the ETH is false"
      },
      {
        "date": "2026-10-27",
        "party": "Anthropic",
        "what": " publishes a refutation of the Exponential Time Hypothesis by an internal Claude model",
        "by": "Anthropic",
        "source": "https://hexagonmath.org/2610.00577v1",
        "quote": "The core algorithm was found on October 16 by an internal Claude research model",
        "also": [
          {
            "by": "Anthropic",
            "source": "https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth"
          }
        ]
      },
      {
        "date": "2026-11-06",
        "party": "PSI",
        "what": " says its research system proved the Aaronson–Ambainis conjecture using a non-public Anthropic model",
        "by": "Physical Superintelligence",
        "source": "https://psi.inc/research/aaronson-ambainis/",
        "quote": "Instances of a non-public Anthropic model were used in the run.",
        "also": [
          {
            "by": "Physical Superintelligence",
            "source": "https://github.com/physical-superintelligence/aaronson-ambainis"
          }
        ]
      }
    ],
    "cites": [
      {
        "url": "https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/",
        "by": "Google DeepMind",
        "medium": "blog post",
        "date": "2026-02-11"
      },
      {
        "url": "https://openai.com/index/model-disproves-discrete-geometry-conjecture",
        "by": "OpenAI",
        "medium": "research post",
        "date": "2026-05-20"
      },
      {
        "url": "https://x.com/__alpoge__/status/2079028340955197566",
        "by": "Levent Alpöge",
        "medium": "X post",
        "date": "2026-07-20"
      },
      {
        "url": "https://www.anthropic.com/research/discovering-cryptographic-weaknesses",
        "by": "Anthropic",
        "medium": "research post",
        "date": "2026-07-28"
      },
      {
        "url": "https://www.anthropic.com/news/redeploying-fable-5",
        "by": "Anthropic",
        "medium": "news post",
        "date": "2026-06-30"
      },
      {
        "url": "https://openai.com/index/ten-advances-in-mathematics",
        "by": "OpenAI",
        "medium": "publication post",
        "date": "2026-08-01"
      },
      {
        "url": "https://www.anthropic.com/research/riemann-zeta",
        "by": "Anthropic",
        "medium": "research post",
        "date": "2026-08-10"
      },
      {
        "url": "https://openai.com/index/navier-stokes-solution",
        "by": "OpenAI",
        "medium": "research post",
        "date": "2026-09-08"
      },
      {
        "url": "https://openai.com/index/advisory-group-on-mathematics-and-ai",
        "by": "OpenAI",
        "medium": "company post",
        "date": "2026-09-21"
      },
      {
        "url": "https://openai.com/index/sharing-ai-progress-in-mathematics",
        "by": "OpenAI",
        "medium": "research post",
        "date": "2026-10-06"
      },
      {
        "url": "https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/README.md",
        "by": "OpenAI",
        "medium": "GitHub README",
        "date": "2026-10-06"
      },
      {
        "url": "https://github.com/openai/math/blob/4eaee87548250b2682affda7d05d947c05554bae/history.md",
        "by": "OpenAI",
        "medium": "GitHub release history",
        "date": "2026-10-29"
      },
      {
        "url": "https://openai.com/index/building-scientific-understanding-with-academic-communities",
        "by": "OpenAI",
        "medium": "research post",
        "date": "2026-10-26"
      },
      {
        "url": "https://hexagonmath.org/2610.00577v1",
        "by": "Anthropic",
        "medium": "paper on Hexagon",
        "date": "2026-10-27"
      },
      {
        "url": "https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth",
        "by": "Anthropic",
        "medium": "GitHub repository",
        "date": "2026-10-27"
      },
      {
        "url": "https://psi.inc/research/aaronson-ambainis/",
        "by": "Physical Superintelligence",
        "medium": "research post",
        "date": "2026-11-06"
      },
      {
        "url": "https://github.com/physical-superintelligence/aaronson-ambainis",
        "by": "Physical Superintelligence",
        "medium": "GitHub repository",
        "date": "2026-11-06"
      }
    ],
    "sources": [
      "https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/",
      "https://openai.com/index/model-disproves-discrete-geometry-conjecture",
      "https://x.com/__alpoge__/status/2079028340955197566",
      "https://www.anthropic.com/research/discovering-cryptographic-weaknesses",
      "https://www.anthropic.com/news/redeploying-fable-5",
      "https://openai.com/index/ten-advances-in-mathematics",
      "https://www.anthropic.com/research/riemann-zeta",
      "https://openai.com/index/navier-stokes-solution",
      "https://openai.com/index/advisory-group-on-mathematics-and-ai",
      "https://openai.com/index/sharing-ai-progress-in-mathematics",
      "https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/README.md",
      "https://github.com/openai/math/blob/4eaee87548250b2682affda7d05d947c05554bae/history.md",
      "https://openai.com/index/building-scientific-understanding-with-academic-communities",
      "https://hexagonmath.org/2610.00577v1",
      "https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth",
      "https://psi.inc/research/aaronson-ambainis/",
      "https://github.com/physical-superintelligence/aaronson-ambainis"
    ],
    "updates": [],
    "body": [
      {
        "figure": "main"
      },
      {
        "p": "OpenAI, Anthropic, Google and the startup Physical Superintelligence (PSI) each announced results on open math problems in their own posts this year. Of the 11 announcements since Feb 11, nine credit a model that had no public release that day. The latest came on Nov 6, when [PSI said](https://psi.inc/research/aaronson-ambainis/) its system proved the Aaronson–Ambainis conjecture using “instances of a non-public Anthropic model”."
      },
      {
        "h": "Two claims credit a public model"
      },
      {
        "p": "On Feb 11, Google DeepMind [wrote about](https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/) Aletheia, a research agent powered by Gemini Deep Think. Google described a “semi-autonomous evaluation” of 700 open Erdős problems that included “autonomous solutions to four open questions”. Deep Think has been a mode in the Gemini app since [Aug 1, 2025](https://frontierlog.ai/event/2025-08-01-deep-think-in-the-gemini-app). Google [upgraded it](https://frontierlog.ai/event/2026-02-12-gemini-3-deep-think-upgrade) the next day, Feb 12. Google said it claims no “Major Advance” among these results."
      },
      {
        "p": "On Jul 20, Anthropic’s Levent Alpöge [posted a counterexample on X](https://x.com/__alpoge__/status/2079028340955197566). He wrote that “the jacobian conjecture is false” and credited “fable”. Anthropic’s [Jul 28 research post](https://www.anthropic.com/research/discovering-cryptographic-weaknesses) links to that post. It says “we announced that Claude Fable 5 resolved the Jacobian Conjecture”. [Claude Fable 5](https://frontierlog.ai/model/claude-fable-5) was public then. Anthropic [made it available again](https://www.anthropic.com/news/redeploying-fable-5) to users globally on Jul 1, after suspending access for all users in June."
      },
      {
        "h": "OpenAI’s claims all credit internal models"
      },
      {
        "p": "OpenAI made six announcements. On May 20 it [said](https://openai.com/index/model-disproves-discrete-geometry-conjecture) an internal model disproved Erdős’s unit-distance conjecture, and that outside mathematicians checked the proof. On Aug 1 it [shared](https://openai.com/index/ten-advances-in-mathematics) ten results on long-standing open problems, including Erdős problems 146, 180 and 183, from “an internal version of Astra, our next major model”. Each came with a Lean certificate. [GPT-6 Astra](https://frontierlog.ai/model/gpt-6-astra) launched on Sep 3."
      },
      {
        "p": "On Sep 8, OpenAI [shared](https://openai.com/index/navier-stokes-solution) a solution to the Navier–Stokes Millennium Prize Problem with a Lean proof. It came from “an internal model that is significantly more capable than GPT‑6 Astra”. The same post reports a disproof for the Euler equations with no external force. It also credits Anthropic’s Levent Alpöge and NYU’s Tristan Buckmaster with a resolution of the forced Euler problem “using an internal Anthropic model”, and recognizes “the priority of their work on forced Euler”. OpenAI began training its internal model on Aug 28. On Sep 21 it [said](https://openai.com/index/advisory-group-on-mathematics-and-ai) the model “has now resolved more than 100 long-standing open problems”."
      },
      {
        "p": "On Oct 6, OpenAI [released](https://openai.com/index/sharing-ai-progress-in-mathematics) a GitHub repository of results from an internal model. Its [README](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/README.md) counted 722 manuscripts in 372 families, from about 4,000 problems posed. The next day OpenAI withdrew three manuscripts after finding a sign error, and its [history](https://github.com/openai/math/blob/4eaee87548250b2682affda7d05d947c05554bae/history.md) put the share of top-line results formalized in Lean at 300 of 719. On Oct 26 it [announced](https://openai.com/index/building-scientific-understanding-with-academic-communities) three more results. OpenAI says its models proved the local smoothing conjecture, which resolves the Kakeya conjecture in all dimensions. It says its system proved the Exponential Time Hypothesis (ETH) false. It also says its models produced an existence proof for Yang–Mills theory and quantum chromodynamics. OpenAI says it formalized the Kakeya, ETH and Yang–Mills proofs in Lean. Outside groups will examine the ETH and physics results, and the physics group is holding back the AI output for now."
      },
      {
        "h": "Anthropic’s internal Claude and PSI’s run"
      },
      {
        "p": "On Aug 10, Anthropic [said](https://www.anthropic.com/research/riemann-zeta) “an unreleased research version of Claude” raised the lower bound for the share of Riemann zeta zeros on the critical line from 41.6% to 67.2%. Claude and an Anthropic staff member produced a Lean formalization. Two outside experts, Brian Conrey and Dan Goldston, examined the paper. On Oct 27, Anthropic [published](https://hexagonmath.org/2610.00577v1) its own refutation of ETH, found on Oct 16 “by an internal Claude research model”, with a [Lean proof](https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth). The [ETH Refutation Timeline](https://frontierlog.ai/stories/two-labs-refute-eth) covers how the two labs’ ETH claims unfolded."
      },
      {
        "p": "PSI’s Nov 6 post says its own system ran on PSI’s infrastructure, and that Lean accepted its first complete proof and the final version after two improvements. The Lean files are on [GitHub](https://github.com/physical-superintelligence/aaronson-ambainis). Stanford’s Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan are reading the proof. PSI does not name the Anthropic model. Anthropic has published no post on the result as of Nov 9."
      },
      {
        "table": {
          "cols": [
            "Date",
            "Party",
            "Problem",
            "Model credited",
            "Public model"
          ],
          "rows": [
            [
              "Feb 11",
              "Google",
              "[Four Erdős problems](https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/)",
              "Gemini Deep Think",
              "Yes"
            ],
            [
              "May 20",
              "OpenAI",
              "[Unit-distance conjecture](https://openai.com/index/model-disproves-discrete-geometry-conjecture)",
              "Internal model",
              "No"
            ],
            [
              "Jul 20",
              "Anthropic",
              "[Jacobian conjecture](https://www.anthropic.com/research/discovering-cryptographic-weaknesses)",
              "Claude Fable 5",
              "Yes"
            ],
            [
              "Aug 1",
              "OpenAI",
              "[Ten open problems](https://openai.com/index/ten-advances-in-mathematics)",
              "Internal version of Astra",
              "No, launched Sep 3"
            ],
            [
              "Aug 10",
              "Anthropic",
              "[Riemann zeta zeros](https://www.anthropic.com/research/riemann-zeta)",
              "Unreleased Claude",
              "No"
            ],
            [
              "Sep 8",
              "OpenAI",
              "[Navier–Stokes](https://openai.com/index/navier-stokes-solution)",
              "Internal model",
              "No"
            ],
            [
              "Sep 21",
              "OpenAI",
              "[100+ open problems](https://openai.com/index/advisory-group-on-mathematics-and-ai)",
              "Internal model",
              "No"
            ],
            [
              "Oct 6",
              "OpenAI",
              "[722 manuscripts](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/README.md)",
              "Internal model",
              "No"
            ],
            [
              "Oct 26",
              "OpenAI",
              "[Kakeya, ETH, Yang–Mills](https://openai.com/index/building-scientific-understanding-with-academic-communities)",
              "Internal model",
              "No"
            ],
            [
              "Oct 27",
              "Anthropic",
              "[Exponential Time Hypothesis](https://hexagonmath.org/2610.00577v1)",
              "Internal Claude",
              "No"
            ],
            [
              "Nov 6",
              "PSI",
              "[Aaronson–Ambainis conjecture](https://psi.inc/research/aaronson-ambainis/)",
              "Non-public Anthropic model",
              "No"
            ]
          ]
        }
      }
    ],
    "events": [
      "2025-08-01-deep-think-in-the-gemini-app",
      "2026-02-11-aletheia-math-research-agent",
      "2026-02-12-gemini-3-deep-think-upgrade",
      "2026-05-20-openai-model-disproves-unit-distance-conjecture",
      "2026-06-30-fable-5-redeployed",
      "2026-08-01-openai-ten-advances-in-mathematics",
      "2026-08-10-claude-raises-riemann-zeta-zeros-bound",
      "2026-09-08-navier-stokes-solution",
      "2026-10-06-openai-publishes-ai-math-results",
      "2026-10-26-openai-three-discoveries"
    ],
    "stories": [
      "two-labs-refute-eth"
    ],
    "models": [
      "gpt-6-astra",
      "claude-fable-5"
    ]
  }
}