The Jacobian Conjecture that plagued Yitang Zhang for 7 years was overturned and disproven by Fable 5 overnight
**Summary:**
The mathematical community was shocked when the longstanding **Jacobi Conjecture**—a core problem in polynomial mapping that had remained open for 87 years—was reportedly **disproven** by **Fable 5** (an AI model from Anthropic). The conjecture, first posed in 1939, asks whether a polynomial map with a constant, non-zero Jacobian determinant must have a polynomial inverse. Despite seeming intuitive, it had resisted numerous proof attempts by leading mathematicians.
The breakthrough came when a researcher, Levent Alpoge, shared a succinct counterexample generated by Fable 5: a specific polynomial map from ℂ³ to ℂ³ whose Jacobian is the constant -2, yet which is not injective (mapping three distinct points to the same image). This elegantly falsifies the conjecture in its general form for dimensions ≥3. The counterexample is simple enough to be verified by hand or with tools like Wolfram Alpha.
The event sparked intense discussion, with other AI models like GPT-5.6 quickly analyzing the result and even proposing a refined conjecture. It demonstrated AI's emerging capacity for genuine mathematical creativity, not just pattern matching.
The story carries a poignant human dimension: renowned mathematician **Yitang Zhang** had devoted seven years of his early career to this problem under his PhD advisor, using a flawed lemma provided by the advisor. This setback contributed to Zhang leaving academia for years, including a period working at Subway, before his later breakthrough on the Twin Prime Conjecture. The AI's swift resolution underscores the tragic waste of his early effort on a conjecture now shown to be false in higher dimensions.
It's important to note the disproof specifically targets the generalized (n-dimensional, n≥3) conjecture. The 2-dimensional case, which Zhang worked on, remains open and is considered mathematically distinct and even more challenging. Nonetheless, the event marks a significant moment, prompting reflections on AI's future role in mathematical discovery.
marsbit07/21 01:35
