{
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  "source": "vibemath",
  "problem_id": "vibemathed:matrix-multiplication-exponent-2371177",
  "title": "The Matrix Multiplication Exponent",
  "canonical_statement": "The matrix multiplication exponent $\\omega$ is the infimum of all $t$ for which two $n \\times n$ matrices can be multiplied in $O(n^t)$ arithmetic operations. Strassen showed in 1969 that $\\omega < 3$, and sixty years of work has driven the upper bound down without anyone knowing the true value. Whether $\\omega = 2$ is one of the central open questions of algebraic complexity.\n\nThe current bounds come from the laser method as refined by combination loss analysis. This paper attacks the optimization problem at the core of that refinement, reformulating it so it can be solved in a larger setting, designing a new optimization algorithm for it, and then refining that algorithm with AlphaEvolve.\n\nThe result is $\\omega < 2.371177$, improving the previous best of $2.371339$.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
  "solution_events": [
    {
      "id": "vibemathed:matrix-multiplication-exponent-2371177:event",
      "problem_id": "vibemathed:matrix-multiplication-exponent-2371177",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-08-17T00:00:00.000Z",
      "title": "Improving the matrix multiplication exponent with modern optimization and AlphaEvolve",
      "summary": "A record, not a resolution, and a small one by design. The bound moves from $2.371339$ to $2.371177$, about $1.6 \\times 10^{-4}$, and the authors describe it as a small step. Whether $\\omega = 2$ is untouched, and nothing here suggests the laser method can reach it.\n\nThe interesting claim is methodological rather than numerical. The bottleneck in this line of work is a hard optimization problem, and the paper reports progress by reformulating that problem and then improving the optimizer, with AlphaEvolve doing the final refinement. That is a different kind of contribution from a new mathematical identity, and it is why the entry is filed as computation.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:matrix-multiplication-exponent-2371177:attempt"
      ],
      "method_family_ids": [
        "vibemathed:matrix-multiplication-exponent-2371177:method"
      ],
      "source_assertion_ids": [
        "vibemathed:matrix-multiplication-exponent-2371177:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:matrix-multiplication-exponent-2371177:attempt",
      "problem_id": "vibemathed:matrix-multiplication-exponent-2371177",
      "model": "AlphaEvolve",
      "provider": "Google DeepMind",
      "attempted_at": "2026-08-17T00:00:00.000Z",
      "human_collaborators": [
        "Emilien Dupont",
        "Marvin Eisenberger",
        "Borislav Kozlovskii",
        "Abbas Mehrabian",
        "Francisco J. R. Ruiz",
        "Abigail See",
        "Renfei Zhou",
        "Josh Alman",
        "Virginia Vassilevska Williams",
        "Matej Balog"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The paper describes three improvements to the optimization problem at the heart of combination loss analysis, and AlphaEvolve is the third of them. In the authors' own order: they reformulate the problem so it can be solved in a larger setting than was previously possible, they leverage recent advances in machine learning to design a new optimization algorithm for it, and then they \"refine the resulting optimization algorithm with AlphaEvolve\".\n\nCo-developed rather than discovered. The model improves a component of a human-designed pipeline rather than being handed the problem, and the reformulation that made the larger setting tractable is the authors' own. It is more than tooling, though, because the refined optimizer is what produces the bound.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Balog's announcement thread",
          "url": "https://x.com/matejbalog/status/2089597390369984794",
          "kind": "announcement",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "Improving the matrix multiplication exponent with modern optimization and AlphaEvolve",
          "url": "https://arxiv.org/abs/2608.16884",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Matrix Multiplication Exponent",
          "url": "https://vibemathed.com/problem/matrix-multiplication-exponent-2371177",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:matrix-multiplication-exponent-2371177:verification",
      "problem_id": "vibemathed:matrix-multiplication-exponent-2371177",
      "solution_event_id": "vibemathed:matrix-multiplication-exponent-2371177:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A two-day-old arXiv preprint, unrefereed, and nothing was checked here. Bounds of this kind are not the sort of claim a reader can spot-check: the number falls out of a large optimization over laser-method parameters, so reproducing it means re-running the optimization rather than verifying a certificate.\n\nWhat the author list is worth saying: Josh Alman and Virginia Vassilevska Williams are authors of the prior bounds this improves on, which is unusual and cuts against the main risk with an automated search, namely that it optimizes something subtly different from the quantity everyone means by $\\omega$.",
      "sources": [
        {
          "label": "VibeMathed: The Matrix Multiplication Exponent",
          "url": "https://vibemathed.com/problem/matrix-multiplication-exponent-2371177",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Improving the matrix multiplication exponent with modern optimization and AlphaEvolve",
          "url": "https://arxiv.org/abs/2608.16884",
          "kind": "primary-mathematical-source",
          "license": null
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  "sources": [
    {
      "label": "Improving the matrix multiplication exponent with modern optimization and AlphaEvolve",
      "url": "https://arxiv.org/abs/2608.16884",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Matrix Multiplication Exponent",
      "url": "https://vibemathed.com/problem/matrix-multiplication-exponent-2371177",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:matrix-multiplication-exponent-2371177:signal:recent_partial_result",
      "problem_id": "vibemathed:matrix-multiplication-exponent-2371177",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}