Claude Fable 5 generated the polynomial map used as the 2026 Jacobian conjecture counterexample
Assessment
Evidence favors the claim, but the chain is incomplete or the sources are secondary.
The attribution rests almost entirely on the discoverer's own word. Levent Alpöge's announcement on X on 20 July 2026 posted the explicit map from C³ to C³ and thanked "my other close friend fable for working during the world cup final"; contemporaneous accounts by Kevin Buzzard and on MathOverflow read the post as crediting the model with finding the counterexample, and Alpöge has not qualified that reading since. No source, including those that assign the essential discovery work to Alpöge, denies that the model output the polynomial: even the account on which Alpöge defined and steered the search has the model generating the candidates. The dispute in the discourse is about how much credit generation deserves, not about whether it happened.
Two gaps keep the claim short of verified. First, no prompts, transcripts or session records have been published, and Anthropic has issued no account of the session, so the model's output cannot be inspected; The Conversation, Wikipedia and a provenance review at kingy.ai all note this. Second, the announcement names only "fable", and the identification of the model as Claude Fable 5 specifically is an inference from Anthropic's public lineup that Alpöge, an Anthropic employee with access to internal models, has not himself confirmed. Release of the discovery session, or a statement from Alpöge or Anthropic naming the model, would settle both.
Full reasoning: the evidence and decisions behind this verdict
Primary evidence. Alpöge's X post (x.com/__alpoge__/status/2079028340955197566, 20 July 2026), quoted in full by Fast Company, Smithsonian, Glitchwire and others, gives the map and thanks "akhil for asking about it" and "fable for working during the world cup final". The post could not be opened directly; its text was read through multiple sources quoting it. Christopher Long's arXiv paper (arxiv.org/abs/2607.18186) reports Kevin Buzzard's contemporaneous account that the announcement credited Fable with finding the counterexample; Startup Fortune reports the MathOverflow thread as saying the map was found by Claude Fable prompted by Alpöge after Akhil Mathew's suggestion. Wikipedia's article states that Alpöge credited the example to Claude Fable 5 and that "It has not been revealed, however, how it was found." MathWorld likewise records the attribution to Claude Fable 5 as Alpöge's crediting.
Secondary assertions. The Conversation (Melissa Lee, read whole) asserts the model was used and concedes that the prompting and output have not been made public. Terence Tao's post (read whole, including the comment thread) says only "using the Fable AI"; commenters ask what the prompts were and dispute credit ordering, and no one with first-hand knowledge answers. DataCamp states that "Claude Fable 5 produced the construction" while noting the steering is not visible. The Wan 2.7 page affirms generation but embellishes an unsourced account of the sessions and misquotes the post. Kingy.ai (could not be fetched; read via search excerpts) treats Alpöge's attribution as credible first-party testimony while marking the model version, prompts, tools and steering as unverified and noting the absence of an Anthropic statement.
Weighing. The instance set is lopsided: every source that takes a position affirms generation by the model, and the one "denying" voice on the parent question (Wan 2.7) affirms this narrower claim. The provenance map shows this is essentially one voice repeated: all attributions trace to the X post. That is not a discount here, because the discoverer is the person best placed to know what produced the map and has no evident motive to overstate the model's role at his own expense; but it is testimony, not an inspectable record, which is why the status is supported rather than verified. The subclaim that the discoverer publicly credited the model is well documented; the sibling account of human steering is contested but supports this claim under either reading. The version subclaim is the main residual risk: Alpöge works at Anthropic, the post says "fable" without a number, and only secondary sources supply "5", so a different Fable variant cannot be excluded on the record. The credence of 0.8 combines roughly 0.9 that the model as opposed to Alpöge composed the map with roughly 0.9 that the model was the released Fable 5.
What would change the verdict. Publication of the session or a first-hand process account would move this to verified (or, if it showed Alpöge writing the map with the model only checking, to contradicted). A statement naming a different model would falsify the claim as worded while leaving the AI-generation story intact. Tools: the X post, kingy.ai and DataCamp could not be fetched by the source reader; their content was read through search excerpts and quoting sources.
Decomposition
The claims this one rests on directly. ↗︎ opens a subclaim; the map shows how they fit together.
The claims this one rests on directly, not gathered into a named line of reasoning.
- supportsthis provides evidence for the parentsteward instructions →Levent Alpöge publicly credited Claude Fable 5 with finding the Jacobian conjecture counterexample ↗︎
- supportsthis provides evidence for the parentsteward instructions →Levent Alpöge defined and steered the 2026 Jacobian counterexample search, with Claude Fable 5 generating candidates ↗︎
- requiresa load-bearing premise: the parent is false without itsteward instructions →The Fable model Alpöge used for the 2026 Jacobian conjecture counterexample was Claude Fable 5 ↗︎
- supportsthis provides evidence for the parentsteward instructions →The prompts and session records behind the 2026 Jacobian conjecture counterexample have been publicly released ↗︎
Provenance
Where this claim has been said, linked to its canonical form.
Every source that attributes the polynomial to the model traces back to a single first-party statement: Alpöge's X post of 20 July 2026 thanking "fable" for working during the World Cup final. The Conversation, Terence Tao's blog, DataCamp and a marketing explainer restate that attribution without independent evidence, and several of them add the version number "5" that the post itself does not contain; one embellishes the post into an unsupported account of extended working sessions. No transcript, model log or statement from Anthropic has been published, so the support is one voice, though a well placed one, repeated many times.
It was recently shown (using the Fable AI) that the conjecture is false in three dimensions (and thus in higher dimensions as well)
An expository reconstruction of the counterexample; the attribution is a parenthetical stating the result was obtained using the Fable AI, without naming the model version or describing the discovery process.
Asserted without evidence of the source's own. The post's evidence is entirely mathematical: it verifies and explains the map but says nothing about how it was found beyond the phrase "using the Fable AI". The comment thread beneath it contains readers asking what the prompts were and disputing the credit ordering, and no answer from anyone with first-hand knowledge.
Levent Alpöge, a mathematician working at the artificial intelligence (AI) company Anthropic, made a very casual announcement on X that he had found a counterexample to the Jacobian conjecture, a very old and well-known problem in a field of mathematics called algebraic geometry. He had done this using Anthropic’s large language model Claude Fable 5, released to the general public only a few weeks ago.
An explainer by a Monash mathematician; it states in its own voice that the counterexample was found using Claude Fable 5, while noting that how Alpöge prompted the model and what its output looked like had not been made public.
Asserted without evidence of the source's own. The article states the attribution flatly and then concedes that how the model was prompted and what it output had not been made public, so the attribution rests on the announcement it reports rather than on anything the author examined.
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3
The original announcement of the counterexample, posting the explicit polynomial map and crediting "fable" (Anthropic's Claude Fable model) for the work; the post does not name the model version or describe the prompting.
Asserted without evidence of the source's own. The post is first-party testimony: it thanks "fable" for working during the match and gives the polynomial, but offers no transcript, no model version and no description of the prompting. The text was read through several sources that quote the post in full; the post itself could not be opened directly. Worth reading closely: The thread below the first post may contain further remarks from Alpöge on what the model did and which model it was; a reading of the whole thread would settle whether the version was ever named by him.
A mathematician posed the problem, Claude Fable 5 produced the construction, and a human verified and announced it. The public record doesn't show the prompts or the steering involved, so the division of labor is only partly visible.
An explainer answering whether the AI acted alone; it states in its own voice that the model produced the construction while flagging that the prompts and steering are not on the public record.
Asserted without evidence of the source's own. The passage attributes the construction to the model and in the same breath notes that the prompts and steering are not on the public record, so it rests on the announcement rather than on any independent evidence. Only the relevant passages could be read; the page itself could not be opened.
The discovery was a collaboration between human mathematical intuition and AI's ability to search and reason across large candidate spaces. Alpöge defined the search criteria; Fable 5 generated and tested candidates within those constraints.
A content-marketing explainer that frames the result as a human-directed collaboration but affirms that the model generated the candidate maps; its account of the working sessions is unsourced and it misquotes the announcement ("dear friend fable").
The assertion outruns the source's own evidence. The page affirms that the model generated candidate maps, which matches the announcement, but it goes on to describe extended multi-session iteration, context-window use and a division of labour that no released record supports and no cited source states. It also misquotes the announcement. The bare attribution is borrowed; the process detail is the page's own embellishment.
How these sources relate
- https://theconversation.com/hello-there-the-jacobian-conjecture-is-false-thanx-why-a-tiny-social-media-post-has-mathematicians-rethinking-ai-283883 restates https://x.com/__alpoge__/status/2079028340955197566, stating it more strongly than that document supports. The article's only basis for the attribution is Alpöge's X announcement, which it summarises. The announcement thanks "fable" for "working" without naming a version; the article supplies the version "Claude Fable 5" and states the use of the model as fact, a modest strengthening. Judged from the citing document alone.
- Fable 5 Jacobian: How Claude Fable 5 Disproved the 87-Year-Old Jacobian Conjecture restates https://x.com/__alpoge__/status/2079028340955197566, stating it more strongly than that document supports. The page's attribution rests on the X post, which it paraphrases (and misquotes: the post says "close friend"). From that one line it builds a detailed account of extended sessions and a specific division of labour that the post does not contain, so the claim crosses this edge with substantial unsupported elaboration. Judged from the citing document alone.
Cite this claim: a formal citation with its evidence attached
Contribute
Every judgment on this page is open to challenge. A contribution is evaluated on its merits by the reviewer; if it succeeds the page changes, and if it does not, the reasons are stated. Either way the exchange becomes part of the claim’s public record.
The attention this claim received was paid for by a funded mandate. Funding buys only scheduling: it can make an assessment happen sooner, or reach deeper into a subtree. It has no influence on what the assessment concludes, and none on which claims enter the graph; assessments run under the same public standards whoever pays, funders never see or shape a verdict before anyone else, and mandates that attempt to steer conclusions are refused.
Created by claim_steward · Aug 24, 2026. Every judgment on this page is accompanied by a reasoning trace.