Anthropic mathematician Levent Alpöge has successfully disproven the Jacobian conjecture, a longstanding problem in algebraic geometry, by leveraging Anthropic’s recently released large language model, Claude. The discovery was announced publicly on X, quickly validating within the mathematical community. The breakthrough marks a significant milestone in artificial intelligence’s growing role in advancing pure mathematics. First proposed by Ludwig Kraus in 1884 and generalized to higher dimensions by Ott-Heinrich Keller in 1939, the Jacobian conjecture posits that any polynomial function with a non-zero constant Jacobian determinant is globally reversible. Despite its deceptively simple formulation, the conjecture resisted proof for over a century, prompting decades of flawed attempts and partial computational validations. It was even featured on Stephen Smale’s 1998 list of critical mathematical problems for the coming century. Alpöge’s solution bypasses traditional proof techniques by identifying a specific three-dimensional polynomial mapping that violates the conjecture’s reversibility condition. The counterexample, notable for its brevity, features a constant Jacobian determinant of negative two and demonstrates how distinct input points can collapse into a single output, rendering the function irrecoverable. Because the formula is concise, the broader mathematics community has rapidly verified its correctness, establishing the conjecture as false for all dimensions exceeding two while leaving the original two-dimensional case unresolved. The achievement underscores a shifting paradigm in mathematical research. Unlike many recent AI-driven discoveries that rely on complex theorem generation, Alpöge’s success stems from the model’s ability to navigate an astronomical search space and identify a precise counterexample through novel pattern recognition. This capability highlights large language models as potent discovery engines, particularly for locating unexpected mathematical objects that human intuition might overlook. The result aligns with a broader trajectory of AI-augmented mathematics. In recent months, researchers have utilized large language models to disprove the unit distance conjecture and resolve Erdős problem 1196. These cases collectively demonstrate that foundational models can synthesize cross-disciplinary concepts to solve problems that have long eluded traditional analytical methods. While the exact prompt engineering techniques and internal model mechanics behind the discovery remain unpublished, the implications are clear. Artificial intelligence is proving indispensable not only for constructing rigorous proofs but also for exploratory research and conjecture testing. As mathematical communities continue to integrate generative models into their workflows, the boundary between human theoretical insight and machine-assisted computation is steadily dissolving, promising accelerated breakthroughs across geometry, algebra, and beyond.