{
  "question_id": "W227",
  "slug": "ai-proves-century-old-conjecture",
  "title": "An AI proves a conjecture open for 100 years",
  "type": "binary",
  "resolution": {
    "levels": [],
    "values": [],
    "annotations": []
  },
  "forecasts": [
    {
      "question_id": "W227",
      "forecast_date": "2026-09-20",
      "evidence_cutoff": "2026-09-20",
      "method": "wide-v2",
      "opened": "2026-09-16",
      "linked_questions": [],
      "reading_adopted": null,
      "summary": null,
      "ambiguities": [],
      "key_drivers": [],
      "would_update_on": [],
      "forecasts": [
        {
          "period_end": "2026-09-30",
          "p_yes": 0.003
        },
        {
          "period_end": "2026-12-31",
          "p_yes": 0.0279
        },
        {
          "period_end": "2027-03-31",
          "p_yes": 0.0862
        },
        {
          "period_end": "2027-06-30",
          "p_yes": 0.1685
        },
        {
          "period_end": "2027-09-30",
          "p_yes": 0.2683
        },
        {
          "period_end": "2027-12-31",
          "p_yes": 0.378
        },
        {
          "period_end": "2028-03-31",
          "p_yes": 0.4838
        },
        {
          "period_end": "2028-06-30",
          "p_yes": 0.5767
        },
        {
          "period_end": "2028-09-30",
          "p_yes": 0.6529
        },
        {
          "period_end": "2028-12-31",
          "p_yes": 0.7154
        },
        {
          "period_end": "2029-03-31",
          "p_yes": 0.7638
        },
        {
          "period_end": "2029-06-30",
          "p_yes": 0.8016
        },
        {
          "period_end": "2029-09-30",
          "p_yes": 0.8313
        },
        {
          "period_end": "2029-12-31",
          "p_yes": 0.8549
        },
        {
          "period_end": "2030-03-31",
          "p_yes": 0.8738
        },
        {
          "period_end": "2030-06-30",
          "p_yes": 0.8889
        },
        {
          "period_end": "2030-09-30",
          "p_yes": 0.9012
        },
        {
          "period_end": "2030-12-31",
          "p_yes": 0.911
        },
        {
          "period_end": "2031-03-31",
          "p_yes": 0.919
        },
        {
          "period_end": "2031-06-30",
          "p_yes": 0.9255
        },
        {
          "period_end": "2031-09-30",
          "p_yes": 0.9315
        }
      ],
      "passes": []
    },
    {
      "question_id": "W227",
      "forecast_date": "2026-09-27",
      "evidence_cutoff": "2026-09-27",
      "method": "wide-v2",
      "opened": "2026-09-16",
      "linked_questions": [],
      "reading_adopted": "I treat a historically posed yes/no mathematical question as the corresponding conjectural assertion, while requiring the same statement—not merely its subject or a predecessor theorem—to meet the 100-year rule.",
      "summary": null,
      "ambiguities": [],
      "key_drivers": [],
      "would_update_on": [],
      "forecasts": [
        {
          "period_end": "2026-09-30",
          "p_yes": 0.002
        },
        {
          "period_end": "2026-12-31",
          "p_yes": 0.0719
        },
        {
          "period_end": "2027-03-31",
          "p_yes": 0.2204
        },
        {
          "period_end": "2027-06-30",
          "p_yes": 0.3919
        },
        {
          "period_end": "2027-09-30",
          "p_yes": 0.5378
        },
        {
          "period_end": "2027-12-31",
          "p_yes": 0.6395
        },
        {
          "period_end": "2028-03-31",
          "p_yes": 0.7116
        },
        {
          "period_end": "2028-06-30",
          "p_yes": 0.7635
        },
        {
          "period_end": "2028-09-30",
          "p_yes": 0.8014
        },
        {
          "period_end": "2028-12-31",
          "p_yes": 0.8292
        },
        {
          "period_end": "2029-03-31",
          "p_yes": 0.8497
        },
        {
          "period_end": "2029-06-30",
          "p_yes": 0.8662
        },
        {
          "period_end": "2029-09-30",
          "p_yes": 0.8796
        },
        {
          "period_end": "2029-12-31",
          "p_yes": 0.8904
        },
        {
          "period_end": "2030-03-31",
          "p_yes": 0.8992
        },
        {
          "period_end": "2030-06-30",
          "p_yes": 0.9067
        },
        {
          "period_end": "2030-09-30",
          "p_yes": 0.9133
        },
        {
          "period_end": "2030-12-31",
          "p_yes": 0.9189
        },
        {
          "period_end": "2031-03-31",
          "p_yes": 0.9238
        },
        {
          "period_end": "2031-06-30",
          "p_yes": 0.928
        },
        {
          "period_end": "2031-09-30",
          "p_yes": 0.9316
        }
      ],
      "passes": []
    },
    {
      "question_id": "W227",
      "forecast_date": "2026-09-30",
      "evidence_cutoff": "2026-09-30",
      "method": "wide-v2.1",
      "opened": "2026-09-16",
      "linked_questions": [],
      "reading_adopted": "A named century-old yes/no problem counts as a 'conjecture' only if the article or a cited scholarly source documents the same statement at least 100 years before the resolution was disclosed; borderline cases such as Nevanlinna's 1925 half-plane question get only partial weight (about 40%).",
      "summary": null,
      "ambiguities": [],
      "key_drivers": [],
      "would_update_on": [],
      "forecasts": [
        {
          "period_end": "2026-09-30",
          "p_yes": 0.002
        },
        {
          "period_end": "2026-12-31",
          "p_yes": 0.035
        },
        {
          "period_end": "2027-03-31",
          "p_yes": 0.12
        },
        {
          "period_end": "2027-06-30",
          "p_yes": 0.245
        },
        {
          "period_end": "2027-09-30",
          "p_yes": 0.355
        },
        {
          "period_end": "2027-12-31",
          "p_yes": 0.455
        },
        {
          "period_end": "2028-03-31",
          "p_yes": 0.535
        },
        {
          "period_end": "2028-06-30",
          "p_yes": 0.6
        },
        {
          "period_end": "2028-09-30",
          "p_yes": 0.655
        },
        {
          "period_end": "2028-12-31",
          "p_yes": 0.7
        },
        {
          "period_end": "2029-03-31",
          "p_yes": 0.735
        },
        {
          "period_end": "2029-06-30",
          "p_yes": 0.765
        },
        {
          "period_end": "2029-09-30",
          "p_yes": 0.79
        },
        {
          "period_end": "2029-12-31",
          "p_yes": 0.81
        },
        {
          "period_end": "2030-03-31",
          "p_yes": 0.83
        },
        {
          "period_end": "2030-06-30",
          "p_yes": 0.845
        },
        {
          "period_end": "2030-09-30",
          "p_yes": 0.855
        },
        {
          "period_end": "2030-12-31",
          "p_yes": 0.865
        },
        {
          "period_end": "2031-03-31",
          "p_yes": 0.873
        },
        {
          "period_end": "2031-06-30",
          "p_yes": 0.88
        },
        {
          "period_end": "2031-09-30",
          "p_yes": 0.885
        }
      ],
      "passes": []
    },
    {
      "question_id": "W227",
      "forecast_date": "2026-10-07",
      "evidence_cutoff": "2026-10-07",
      "method": "wide-v2.1",
      "opened": "2026-09-16",
      "linked_questions": [],
      "reading_adopted": null,
      "summary": "Machines have already proved problems over a century old, most clearly Koebe's 1908 circle-domain conjecture, released by OpenAI in October 2026. But no peer-reviewed journal has yet published such a proof with authors saying the machine did the main work, and current candidates are unsubmitted or vague about the machine's role. So this year looks unlikely, five years likely. A journal accepting such a paper, or journals broadly refusing them, would most change this.",
      "ambiguities": [],
      "key_drivers": [],
      "would_update_on": [],
      "forecasts": [
        {
          "period_end": "2026-12-31",
          "p_yes": 0.045
        },
        {
          "period_end": "2027-03-31",
          "p_yes": 0.088
        },
        {
          "period_end": "2027-06-30",
          "p_yes": 0.147
        },
        {
          "period_end": "2027-09-30",
          "p_yes": 0.215
        },
        {
          "period_end": "2027-12-31",
          "p_yes": 0.29
        },
        {
          "period_end": "2028-03-31",
          "p_yes": 0.372
        },
        {
          "period_end": "2028-06-30",
          "p_yes": 0.447
        },
        {
          "period_end": "2028-09-30",
          "p_yes": 0.513
        },
        {
          "period_end": "2028-12-31",
          "p_yes": 0.572
        },
        {
          "period_end": "2029-03-31",
          "p_yes": 0.619
        },
        {
          "period_end": "2029-06-30",
          "p_yes": 0.659
        },
        {
          "period_end": "2029-09-30",
          "p_yes": 0.693
        },
        {
          "period_end": "2029-12-31",
          "p_yes": 0.724
        },
        {
          "period_end": "2030-03-31",
          "p_yes": 0.749
        },
        {
          "period_end": "2030-06-30",
          "p_yes": 0.77
        },
        {
          "period_end": "2030-09-30",
          "p_yes": 0.79
        },
        {
          "period_end": "2030-12-31",
          "p_yes": 0.806
        },
        {
          "period_end": "2031-03-31",
          "p_yes": 0.821
        },
        {
          "period_end": "2031-06-30",
          "p_yes": 0.833
        },
        {
          "period_end": "2031-09-30",
          "p_yes": 0.845
        },
        {
          "period_end": "2031-12-31",
          "p_yes": 0.855
        }
      ],
      "passes": []
    },
    {
      "question_id": "W227",
      "forecast_date": "2026-10-14",
      "evidence_cutoff": "2026-10-14",
      "method": "wide-v2.1",
      "opened": "2026-09-16",
      "linked_questions": [],
      "reading_adopted": null,
      "summary": "AI has already resolved at least one clean century-old conjecture: OpenAI's model proved Koebe's 1908 circle-domain conjecture, with a machine-checked proof. But OpenAI posts its results on GitHub, not in journals, and peer review takes months to years. So I put the chance of a qualifying journal article low this year (3%), at about 37% by end-2027, and about 89% by 2031. The development most likely to change this is any journal accepting a write-up of such a result.",
      "ambiguities": [],
      "key_drivers": [],
      "would_update_on": [],
      "forecasts": [
        {
          "period_end": "2026-12-31",
          "p_yes": 0.03
        },
        {
          "period_end": "2027-03-31",
          "p_yes": 0.083
        },
        {
          "period_end": "2027-06-30",
          "p_yes": 0.166
        },
        {
          "period_end": "2027-09-30",
          "p_yes": 0.266
        },
        {
          "period_end": "2027-12-31",
          "p_yes": 0.365
        },
        {
          "period_end": "2028-03-31",
          "p_yes": 0.457
        },
        {
          "period_end": "2028-06-30",
          "p_yes": 0.539
        },
        {
          "period_end": "2028-09-30",
          "p_yes": 0.608
        },
        {
          "period_end": "2028-12-31",
          "p_yes": 0.665
        },
        {
          "period_end": "2029-03-31",
          "p_yes": 0.71
        },
        {
          "period_end": "2029-06-30",
          "p_yes": 0.746
        },
        {
          "period_end": "2029-09-30",
          "p_yes": 0.775
        },
        {
          "period_end": "2029-12-31",
          "p_yes": 0.799
        },
        {
          "period_end": "2030-03-31",
          "p_yes": 0.818
        },
        {
          "period_end": "2030-06-30",
          "p_yes": 0.834
        },
        {
          "period_end": "2030-09-30",
          "p_yes": 0.847
        },
        {
          "period_end": "2030-12-31",
          "p_yes": 0.858
        },
        {
          "period_end": "2031-03-31",
          "p_yes": 0.868
        },
        {
          "period_end": "2031-06-30",
          "p_yes": 0.877
        },
        {
          "period_end": "2031-09-30",
          "p_yes": 0.884
        },
        {
          "period_end": "2031-12-31",
          "p_yes": 0.891
        }
      ],
      "passes": []
    }
  ],
  "declined": []
}