Mathematician Levent Alpöge used Anthropic's Fable 5 model to disprove the Jacobian conjecture, which had remained unsolved in algebraic geometry for nearly 90 years.
What Happened
Using the computational power of Anthropic's Fable 5 model, the researcher found a specific counterexample within a massive array of polynomials. This allowed for the disproof of the Jacobian conjecture, which for decades was considered a fundamental problem in mathematics.
Context
The Jacobian conjecture was one of the key unsolved problems in algebraic geometry for nearly a century. Traditional methods for finding counterexamples in such complex mathematical structures often prove ineffective due to the colossal search space.
Why It Matters for the Industry
This case confirms the transition of frontier models from text generation to scientific discovery tasks. Models are becoming powerful computational engines for working in spaces with high combinatorial complexity, which opens new markets in automated R&D and scientific search.
Why It Matters for Users
AI is increasingly moving from content creation to solving fundamental scientific problems. For researchers, this means the emergence of new tools capable of finding flaws in long-standing theories through ultra-fast searching of possibilities that is inaccessible to humans.
What Is Not Yet Known / Limitations
The result is considered to have low scientific value for understanding the essence of the problem itself, as the model did not provide a logical derivation or structural explanation, but merely found a counterexample through brute-force searching, acting as a "black box."
Sources
Author
Look at AI, Editorial Team