Consensus answer
Probably yes mathematically—but “Claude alone disproved it in a few hours” is misleading, and formal acceptance was still pending as of July 20, 2026.
The reported result came from Anthropic mathematician Levent Alpöge, working with Claude Fable 5. The model apparently helped find an explicit polynomial map \(F:\mathbb C^3\to\mathbb C^3\), rather than independently producing a complete, self-validating proof glitchwire.
The proposed map has two crucial properties:
- Its Jacobian determinant is identically \(-2\), a nonzero constant.
- It is not injective: three distinct points reportedly map to the same point.
Those facts directly contradict the general Jacobian Conjecture, which asserts that a polynomial map with constant nonzero Jacobian must have a polynomial inverse. The calculations are finite algebraic identities and can be checked by hand or with computer algebra. A Lean 4 formalization of the determinant and collision claims has also been made public, which substantially increases confidence—but still requires scrutiny of the formalization and its correspondence with the standard conjecture github.
So the fairest conclusion is:
- The general Jacobian Conjecture appears to be genuinely false.
- The counterexample is credited to a human–AI collaboration, not to Claude acting autonomously.
- “In a few hours” describes the discovery and initial verification, not the entire process of mathematical validation.
- The result was newly announced and not yet conventionally peer-reviewed or fully settled in the mathematical literature.
It also appears to refute the conjecture specifically in dimension \(3\) and therefore in higher dimensions by adding identity coordinates; it does not necessarily settle the separate two-variable version. wikipedia
Differences
1 notable difference (1 contradiction) across 5 models.
Whether the Jacobian conjecture is currently considered 'disproved' or merely 'a candidate counterexample'.
The conjecture is disproved.
Mistral, Gemini
“Claude Fable 5 appears to have genuinely contributed to disproving the Jacobian Conjecture”
The conjecture is not yet officially settled.
Grok, OpenAI, Anthropic
“a fully peer-reviewed theorem.”
How to verify: Check if the mathematical community has reached a formal consensus or if the result is still undergoing peer review.
Best answerOpenAI
Sources
- 1 An Anthropic Researcher Says Fable Just Helped Him Disprove The 85-year-old Jacobian Conjecture officechai.com
- 2 Fable 5 Jacobian Conjecture Claim — July 2026 explainx.ai
- 3 A Mathematician Used Claude Fable to Disprove the 87-Year-Old Jacobian Conjecture in a Few Hours — Glitchwire glitchwire.com
- 4 r/singularity on Reddit: Apparently the Jacobian conjecture was just proven false by Fable reddit.com
- 5 Jared Duker Lichtman on X: "This is quite a remarkable result: Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic geometry, but was just disproved by Alpoge, Matthew, and Claude Fable 5. The Jacobian conjecture roughly says that a multivariable polynomial F has a x.com
- 6 Verification Is the Real Capability - 2026-07-20 highlearningrate.substack.com
- 7 Chubby♨️ on X: "Claude Fable 5 has produced a hand-checkable counterexample to the Jacobian conjecture, an open problem dating to 1939. The conjecture says that a polynomial map with a constant non-zero Jacobian determinant must have a polynomial inverse. An 87-year-old problem was casually https:// x.com
- 8 Claude Fable produced a counterexample to the Jacobian Conjecture | Hacker News news.ycombinator.com
- 9 wikipedia.org vertexaisearch.cloud.google.com
- 10 glitchwire.com vertexaisearch.cloud.google.com
- 11 reddit.com vertexaisearch.cloud.google.com
- 12 aiweekly.co vertexaisearch.cloud.google.com
- 13 explainx.ai vertexaisearch.cloud.google.com
- 14 reddit.com vertexaisearch.cloud.google.com
- 15 ycombinator.com vertexaisearch.cloud.google.com
- 16 reddit.com vertexaisearch.cloud.google.com
- 17 Jacobian conjecture - Wikipedia en.wikipedia.org
- 18 x.com
- 19 zzhang-iu.github.io
- 20 mathoverflow.net
- 21 GitHub - deancureton/jacobian · GitHub github.com
- 22 artificialanalysis.ai
- 23 reddit.com
- 24 The Jacobian counterexample, explained jacobianfun.org
Cite this answer
consens.io. (2026-07-20). Consensus answer to "Did Claude Fable 5 Really Disprove the 87-Year-Old Jacobian Conjecture in Just a Few Hours?". Models consulted: OpenAI: GPT-5.6 Luna, Mistral: mistral-medium-latest, Anthropic Claude: Claude Opus 4.8, Google Gemini: Gemini 3.1, Grok: Grok 4.3. Consensus model: gpt-5.6-luna. Sources: https://officechai.com/ai/an-anthropic-researcher-says-fable-just-helped-him-disprove-the-85-year-old-jacobian-conjecture/, https://explainx.ai/blog/fable-5-jacobian-conjecture-counterexample-alpoge-july-2026, https://glitchwire.com/news/a-mathematician-used-claude-fable-to-disprove-the-87-year-old-jacobian-conjectur/, https://www.reddit.com/r/singularity/comments/1v1aie6/apparently_the_jacobian_conjecture_was_just/, https://x.com/jdlichtman/status/2079066717762863249, https://highlearningrate.substack.com/p/verification-is-the-real-capability, https://x.com/kimmonismus/status/2079115645409468491, https://news.ycombinator.com/item?id=48973869, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHJp2L37Lygm8Ye8JXXywzJIY8NtGDBhz_ar9JkLEyVGxJeru_RtvXoFaoPr5uWM5NbQDtNSlFqEwMG7oGAIXZyU-p6Y839JBxZw7WecVvECrIJXJRBYNJCdkzQEoZeM-PrinF4Lhs=, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGIA-kTrPw6qRJ0UsRpLNBXcSYfoVHkv8mAD4iqAoN74uEDI0gJcLNIH78j7-XyiQRMO10y9Crr7jdHHq6KKia-_aibWEp6gNb9xiMWpR1qprpLNYf0_3GuR36EMh_XeK5GpGu7_GhpElrd3xgTUW5iqOtLzMnddeigrr4YvuiuJe1v2xKBi-_DjhmjYwDzLHqL56IKYR4q4rRevPlVWjQc2WM=, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHcVV9KPfaxylX76dado3FTMaWZ6Wq3Xp_n6FKrn9UygBoRPZBQOjH34JUW9j90Gxb0_YsTwbUvpgl_57LULktPG7aF3cXPb8_y_QzfdkboS4g5orN5sKu78xZv5lfk2wjvSEDcoS7_0w1nlcCLfhvuVZ5sIdp-lFfnEHCHkFurDtf86TAR599FUkTdK7SZNoxQHTSPE-rb, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHdvFO0eHWvby77cF6ZNzOXO-kh6SUxleX9uPxbq5hbdXvl77rTLJQqhgO1VMCiQdNxBObIh2cv2YpPV8KtQr0tYaZKaMdFjAmPVkqQaO06hvBpKeLgYg==, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEbPjvN54nSjFvd-buqaiUPPayHrgRzKWf13wZZU6HUxcwNWnxcDO6COj6MlIXHCvGoMHrwj2Qi9KFCyxXHB6uIkvP2yx5nHHGz83GrCukXTU1mOovqUQ0eZoDCC4FgXBSmZaDXqLAY6s1FjjOvtuiXqzFSYbqQcXfiQoPl8Ao2-KWwxlJq8BhDtw==, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQH9mKPgSeSIU-NDstoMT2qzUqFcnEzdynWMcDzl0SSdCoD3sDcQYTEUCLvjFZYzlZCVNrrWQ9UaJHf7F0eiOpwepAiebgeAeFszZSSasjIB209REjYt8A9_W-oZ5UtvInQ0-P6ZR0gln-wFgOkl0dA1Gt9b9jZE8Ybs38_PV_TyeTlDvVJ6u2XQUyhmKUtOQydVhUFtFIBOEKZfUg==, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEoJ4DYu23ZQA67g6WrxOwcYFOKUC1znLe_-_O127DCWeG8xyeGvLeHWktHpIsrBL-Cz6hPm_hbuJByau2FP3mnqpUdCbvfwNOtaFSHxJCB6wnHcynCKxWtj33bkFaOj4s-bA==, https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGgtTc-okC4HvTo08FzmFtN7I4V7tr0H7I67nc3ZdQLajYTN-r2zf1zPFZkECa_kyli_I5fhzY4cQZNiF3DyM6n_c08FXj0oWfY06LO0aVtTHGRzR-mnVahwgijopktjuDHIn66z8Ui0TxhDnk71a2TmHOc666r-eO5MquLXJ9oJ2-pUuu4yAnTisgxAH09ir0JOcQZvUAFhdX2, https://en.wikipedia.org/wiki/Jacobian_conjecture, https://x.com/__alpoge__/status/2079028340955197566, https://zzhang-iu.github.io/papers/direct-consequences-jacobian/index.html, https://mathoverflow.net/questions/513387/galois-structure-of-the-new-counterexample-to-the-jacobian-conjecture-an-explic, https://github.com/deancureton/jacobian, https://artificialanalysis.ai/articles/claude-fable-5-mythos, https://www.reddit.com/r/BetterOffline/comments/1v1dbav/claude_fable_produced_a_counterexample_to_the/, https://jacobianfun.org/jacobian-explained Retrieved from https://www.consens.io/s/did-claude-fable-5-really-disprove-the-87-year-old-jacobian-sHy6psPsH1ja5Xfd
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