The latest AI model from Anthropic, Claude Fable 5, has successfully tackled a mathematical challenge that has puzzled scientists for 87 years. This breakthrough involves the Jacobian Conjecture, a mathematical hypothesis proposed in 1939, which has long been regarded as one of the most prominent unsolved problems in mathematics.
Understanding the Jacobian Conjecture
The Jacobian Conjecture raises the question of whether a certain type of mathematical function can always be inverted, enabling one to retrieve the original input values under specific conditions related to the Jacobian determinant. For nearly nine decades, mathematicians have struggled to either prove the conjecture or find a counterexample.
Claude Fable 5's Discovery
In a remarkable achievement, Claude Fable 5 identified a counterexample to the Jacobian Conjecture. The AI discovered a function that satisfies the conditions of the Jacobian yet cannot be inverted, as three different inputs yield the same output. This single counterexample is sufficient to demonstrate that the conjecture is indeed false.
Verification of the Result
The announcement of this significant finding was made by mathematician and Anthropic researcher Levent Alpoge on social media platform X (formerly known as Twitter). Alpoge noted that he and his colleagues manually verified the solution produced by Claude Fable 5 within approximately one day.
The Implications of AI in Mathematics
Despite the groundbreaking nature of this result, the findings from Claude Fable 5 were not accepted without scrutiny. Alpoge emphasized that the proof generated by the AI can be independently verified using traditional mathematical methods, allowing other mathematicians to confirm its validity.
This accomplishment illustrates a pivotal moment in the integration of artificial intelligence into high-level scientific research. AI's role is evolving beyond merely generating text or coding, as it begins to contribute to the discovery of new mathematical ideas that researchers can subsequently test and validate.
Source: https://tekno.kompas.com/read/2026/07/22/17030077/ai-anthropic-pecahkan-teka-teki-matematika-berusia-87-tahun
