An LLM (Fable) has now produced a counterexample proving the Jacobian…

What was claimed

An LLM (Fable) has now produced a counterexample proving the Jacobian Conjecture false (after a mathematician failed trying to prove it true years ago)

Our verdict

Needs Caution

Sources report that Claude Fable 5 helped Levent Alpöge find and present an explicit counterexample. They do not support the claim that the LLM alone produced it, and some sources note it is not yet peer-reviewed. Levent Alpöge, a number theorist at Anthropic, credited Fable as his collaborator, using it as something closer to a genuine research collaborator. However, what remains uncertain is how Claude Fable found it, which exact Fable version was used, what prompts and tools were supplied, and how much human steering occurred.

All 3 AI systems agree14 sources citedChecked Jul 21, 2026

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Key findings

Fable is the primary agent that produced the counterexample

Misleading75%

1 AI checked

An LLM (Fable) has now produced a counterexample proving the Jacobian Conjecture false

Misleading85%

3 of 6 AIs agree·ChatGPT: Can’t verify, Perplexity: Verified, Perplexity: Can’t verify

This happened after a mathematician failed trying to prove it true years ago.

Verified85%

1 of 2 AIs agree·ChatGPT: Can’t verify

The counterexample is verifiable and mathematically sound

Verified90%

1 AI checked

Verified against 14 sources

sbseminar.wordpress.com

explainx.ai

Detailed Analysis

The core claim is supported by multiple current sources: a 2026 announcement says Levent Alpöge presented an explicit counterexample found with Claude Fable 5, and that the map has a constant nonzero Jacobian while failing to be injective.[1] [2] [3] However, the wording is misleading because it says an LLM "has now produced" the counterexample on its own; the sources attribute the result to a human mathematician working with the model, and the broader status of the result is not yet peer-reviewed.[1] [5] [10]

Why this verdict

Claims checked

An LLM (Fable) has now produced a counterexample proving the Jacobian Conjecture false

Misleading86%

Sources report that Claude Fable 5 helped Levent Alpöge find and present an explicit counterexample.[1] [3] [11] They do not support the claim that the LLM alone produced it, and some sources note it is not yet peer-reviewed.[5] [10]

This claim may mislead readers without added context.

A mathematician failed trying to prove the Jacobian Conjecture true years ago

Can’t verify29%

The provided sources do not identify a specific mathematician or a documented failed attempt to prove the conjecture true years ago. This part is too vague to verify from the available evidence.

The Jacobian Conjecture is false

Verified82%

Current sources state that the presented three-dimensional polynomial map is a counterexample, with constant nonzero Jacobian and non-injectivity.[1] [2] [3] That said, the result still appears to be pending formal peer-reviewed publication.[5] [10]

What other AI think

The claim is partially accurate but contains important nuances and unverified elements. An LLM called Fable (specifically Fable 5) did assist in producing a counterexample to the Jacobian Conjecture announced on July 20, 2026. However, the claim oversimplifies the status and lacks critical context about verification and peer review.

Why this verdict

The claim is partially accurate but contains important nuances and unverified elements.
An LLM called Fable (specifically Fable 5) did assist in producing a counterexample to the Jacobian Conjecture announced on July 20, 2026.
However, the claim oversimplifies the status and lacks critical context about verification and peer review.

Claims checked

Fable is the primary agent that produced the counterexample

Misleading75%

Levent Alpöge, a number theorist at Anthropic, credited Fable as his collaborator, using it as something closer to a genuine research collaborator. However, what remains uncertain is how Claude Fable found it, which exact Fable version was used, what prompts and tools were supplied, and how much human steering occurred. The discovery was collaborative, not solely Fable's work.

This claim may mislead readers without added context.

An LLM (Fable) has produced a counterexample proving the Jacobian Conjecture false

Misleading85%

Levent Alpoge announced a Fable 5-assisted Jacobian conjecture counterexample on July 20, 2026. However, until peer review, the conjecture is still open in the official record. The counterexample has not undergone formal peer review or been published in a journal, so calling it "proven false" is premature.

This claim may mislead readers without added context.

A mathematician failed trying to prove it true years ago

Verified85%

Yitang Zhang pursued his doctorate with the Jacobian conjecture as his topic, with his advisor Moh believing in its correctness. After peer review, the critical lemma used in Zhang's proof was proven to be false.

There is a very recent, widely reported claim (July 20, 2026) that Anthropic’s Fable 5 assisted Levent Alpöge in producing a counterexample to the Jacobian Conjecture. However the mathematical community has not yet reached consensus and the result is still undergoing verification and scrutiny, so treating it as a settled disproof is premature.

Why this verdict

There is a very recent, widely reported claim (July 20, 2026) that Anthropic’s Fable 5 assisted Levent Alpöge in producing a counterexample to the Jacobian Conjecture.
However the mathematical community has not yet reached consensus and the result is still undergoing verification and scrutiny, so treating it as a settled disproof is premature.

Claims checked

An LLM (Fable) has produced a counterexample to the Jacobian Conjecture.

Misleading85%

Multiple recent posts and analyses report a Fable‑assisted counterexample was announced on July 20, 2026, but the claim is under active verification and has not yet achieved broad, peer‑reviewed acceptance as a definitive disproof.

This claim may mislead readers without added context.

This happened after a mathematician failed trying to prove it true years ago.

Can’t verify45%

The statement is vague about which mathematician and when; there is no specific, verifiable match to a named long‑running failed attempt that the claim clearly references.

The counterexample proves the Jacobian Conjecture false.

Can’t verify75%

A claimed counterexample has been circulated and checked by some tools and researchers, but final mathematical proof acceptance requires independent verification and peer review which is not yet complete.

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