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Categories: TECHNOLOGY

Anthropic AI refutes Jacobian conjecture

Entities: Harvard University · Jacobian Conjecture · Anthropic · Levant AlpoGe · Claude Fable 5

Overview

On 19 July 2026 Anthropic announced that its Claude Fable 5 model had resolved the Jacobian conjecture, a 87‑year‑old problem in algebraic geometry. The claim, presented by researcher Levent Alpöge, sparked discussion about AI consciousness and the shift of some Bitcoin‑miner hardware to AI workloads.

The following day Alpöge, now identified as a Harvard‑affiliated mathematician, provided further details: the AI produced a concrete counterexample that disproves the conjecture. Columbia professor Andrew Blumberg emphasized that, while impressive, the AI‑generated result does not replace a full mathematical proof.

On 20 July 2026 Alpöge reiterated the finding in a public statement, underscoring the model’s ability to explore vast polynomial spaces. By 26 July he posted on X that the counterexample applies specifically to the three‑variable version of the Jacobian conjecture, noting that the simpler two‑variable case remains open. Experts again stressed the need for human oversight, pointing out that AI can locate counterexamples but the development of new theory still relies on mathematicians. The episode has revived debate over AI‑augmented pure‑mathematical research, echoing earlier AI‑driven advances such as OpenAI’s work on the Erdős unit‑distance problem.

Timeline

  1. about 20 hours ago

    [TECHNOLOGY] 2 sources
    Harvard's Levant AlpoGe Uses AI to Disprove 87-Year-Old Jacobian Conjecture

    Harvard mathematician Levant AlpoGe, aided by Anthropic’s Claude Fable 5 AI, presented a counterexample that disproves the three‑variable version of the 87‑year‑old Jacobian Conjecture.

  2. 6 days ago

    [TECHNOLOGY] 3 sources
    Mathematician Levent Alpöge uses Anthropic's Fable 5 AI to refute Jacobian conjecture

    Harvard mathematician Levent Alpöge used Anthropic’s Fable 5 model to find a counterexample that refutes the Jacobian conjecture, prompting debate on AI’s role in pure mathematics.

  3. 7 days ago

    [TECHNOLOGY] 2 sources
    Anthropic's Claude AI Solves 87-Year Math Conjecture and Sparks Consciousness Debate

    Anthropic's Claude model solved the 87‑year Jacobian conjecture, prompting Bitcoin market reactions, while the company admits a 5‑40% chance Claude could be conscious, raising ethical and economic questions.

Sources

assodigitale.it · brasilemfolhas.com.br · enavabharat.com · jubilo.dk · m.takvim.com.tr · nextbigfuture.com · tv9hindi.com