2026-10-11 18:04 UTC

Expert review will determine whether Claude Fable produced a valid counterexample to the Jacobian Conjecture or a proof containing a substantive flaw.

state: expiredheat: lowuncertainty: mediumknownscott: mediumclaude-fable ai-mathematical-discovery jacobian-conjectureAnthropicLevent Alpoge

What is this?

Mathematician Levent Alpoge reportedly posted a concrete three-dimensional polynomial map, crediting “Claude Fable 5” with helping construct it, that would disprove the Jacobian Conjecture if its constant-Jacobian and non-invertibility claims hold. The object is described as mechanically checkable and as passing some exact independent checks, but it has not completed peer review and remains under expert scrutiny. The supplied snippets do not clearly establish what Claude Fable 5 is or its relationship to Anthropic, and some coverage ambiguously describes Fable as a mathematician rather than an AI system.

Why it matters to Scott

The radar already tracks the same unresolved AI-mathematics validation story in `radar:proofatlas-collatz-formalization`, `radar:gpt-5-6-cycle-double-cover-proof`, and `radar:gpt-5-6-convex-proof`. This instance still matters because a concrete, mechanically checkable counterexample to a major conjecture is a particularly sharp test of Scott’s formalisation-bottleneck and independent-closer claims, but until expert review resolves it, it does not yet materially extend them.
ip:concept.formalisation-bottleneckip:concept.adversarial-closerip:concept.mechanically-different-verifiersradar:proofatlas-collatz-formalizationradar:gpt-5-6-cycle-double-cover-proofradar:gpt-5-6-convex-proof
queries asked of Scott's wikis
  • AI agents as mathematical research collaborators
  • formal verification of AI-generated proofs and counterexamples
  • mechanically checkable outputs as AI trust boundary
  • expert review workflows for machine-generated discoveries
  • AI discovery claims versus peer-review standards
  • LLM tool use for symbolic mathematics

Measured heat

no measured readings yet — the hourly heat pass fills this in

How the heat travelled

no chain yet — the hourly chain pass fills this in

Evidence (22) — ⭐ canonical anchor

sourceobjectauthorscorecomments
🟧 hn ⭐Claude Fable produced a counterexample to the Jacobian Conjectureloubbrad742470
🟠 redditFable may have disproved a 100 year old conjecture.
ClaudeAI
momkeeeeeeee59492
🟠 redditApparently the Jacobian conjecture was just proven false by Fable
singularity
TFenrir2361592
🟧 hnTweet claiming Claude Fable 5 has helped disprove the Jacobian conjecturemeowface113
🟧 hnThe Jacobian Conjecture Is False per Anthropicgeorgeven30
🟠 redditQwen3.6-35B-A3B-UD-Q6_K_XL on homelab potato validates that Jacobian conjecture is false
LocalLLaMA
ElectronSpiderwort014
🟧 hnHuman mathematicians are being outcounterexampledartninja1988499253
🟧 hnAI just disproved a major math problem. A mathematician explains01-_-11
🟧 hnShow HN: How to Get a Fable CoT for the Jacobian Conjecture RefutationSonOfLilit10
🟧 hnShow HN: Maith – open math research with AIhemangkandwal50
🟠 redditFable 5 solved one of the most famous problems in Algebraic Geometry [R]
MachineLearning
we_are_mammals00
🟠 redditI had an AI agent (Fable 5) explore the Alpöge Jacobian counterexample in a sandbox for 24 hours
singularity
dasjomsyeet10
🟧 hnA digestion of the Jacobian conjecture counterexamplejeremyscanvic335103
🟧 hnTerrence Tao's ChatGPT Conversation about the Jacobian Conjecture Counterexamplegmays1127625
🟠 redditMathematicians grapple with a ‘very rapid and very unsettling change’ as AI cracks yet another century-old problem
OpenAI
KeanuRave10033590
🟧 hnMathematicians grapple with a 'rapid and unsettling change'ninjahawk120
🟧 hnLLMs break down in funny ways when told the Jacobian Conjecture counterargumentminimaxir10
🟧 hnJacobian Conjecture Refutation Reveals a Structural Limit of AI Interpretabilitypolynomial30
🟧 hnClaude used my pipeline to find a counterexample to the Jacobian conjectureJGPTechCo85
🟧 hnAI cracks yet another century-old problemyusufaytas10
🟧 hnClaude Fable 5 finds a tiny formula that topples an 87-year-old math conjecturetheanonymousone30
🟧 hnClaude Fable 5 AI finds a formula that topples an 87-year-old math conjecturethaherster10

Interpretation history

Decision trace