Damn🤯A math conjecture unsolved for 87 years was independently falsified by AI-while humans were watching the World Cup. This wasn't just computational assistance. It marks the first time AI has taken on the role of discoverer in mathematics. Levent Alpöge， a mathematician at Anthropic， tasked Claude Fable 5 with investigating the Jacobian Conjecture-a problem dating back to 1939 and listed as Stephen Smale's 16th Millennium Problem. Then he went off to watch the World Cup final. Left to run， the AI produced an explicit counterexample for n=3： the Jacobian determinant is identically -2， yet the map isn't invertible-three distinct points all map to the same output. Even more striking？ The counterexample is low-degree and hand-verifiable. The math community confirmed it within hours. That might be the most underrated part of this story： Humans define the problem； AI explores intensively within those bounds-while humans are busy watching soccer. Not human-AI collaboration. Human-AI division of labor： humans provide the taste， AI brings the execution. We used to say AI was a calculator for mathematicians. Now it's a discoverer-capable of finding counterexamples that topple 87-year-old open problems. This isn't incremental progress. The role itself has changed. An 87-year-old problem， cracked in hours once the right tool appeared. It reminds us： many limits of human intellect are really limits of our current tools. Upgrade the tools， and the frontier shifts. That's the real weight behind that Fable 5 tweet， lol.
AYi@AYi_AInotes · XAnthropic 数学家 Levent Alpöge 让 Claude Fable 5 研究 1939 年提出的雅可比猜想，自己去看世界杯决赛。AI 独立给出了 n=3 的显式反例：雅可比行列式恒为 -2，但映射不可逆，且三个不同点映射到同一输出。该反例次数低、可手算验证，数学界数小时内确认——这是 AI 首次在数学中扮演发现者角色，而非计算辅助工具。
Damn🤯A math conjecture unsolved for 87 years was independently falsified by AI-while humans were watching the World Cup. This wasn't just computational assistance. It marks the first time AI has taken on the role of discoverer in mathematics. Levent Alpöge， a mathematician at Anthropic， tasked Claude Fable 5 with investigating the Jacobian Conjecture-a problem dating back to 1939 and listed as Stephen Smale's 16th Millennium Problem. Then he went off to watch the World Cup final. Left to run， the AI produced an explicit counterexample for n=3： the Jacobian determinant is identically -2， yet the map isn't invertible-three distinct points all map to the same output. Even more striking？ The counterexample is low-degree and hand-verifiable. The math community confirmed it within hours. That might be the most underrated part of this story： Humans define the problem； AI explores intensively within those bounds-while humans are busy watching soccer. Not human-AI collaboration. Human-AI division of labor： humans provide the taste， AI brings the execution. We used to say AI was a calculator for mathematicians. Now it's a discoverer-capable of finding counterexamples that topple 87-year-old open problems. This isn't incremental progress. The role itself has changed. An 87-year-old problem， cracked in hours once the right tool appeared. It reminds us： many limits of human intellect are really limits of our current tools. Upgrade the tools， and the frontier shifts. That's the real weight behind that Fable 5 tweet， lol.