An anthropic mathematician used the AI model Fable 5 to post a counterexample to the Jacobian conjecture on Twitter, a problem unsolved for 87 years. OpenAI's Codex model independently proved a similar counterexample. This event highlights AI's ability to solve hard math problems and also stirs discussion about toxic advisors in academia.
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An Anthropic mathematician, using the Fable 5 model, posted a counterexample to the Jacobian Conjecture on Twitter. An internal Codex version at OpenAI independently verified it. This event not only shook the math world but also reflects AI's evolving role in fundamental research.
On July 20, 2026, an Anthropic mathematician (Twitter handle @__alpoge__) posted a tweet claiming to have proven a counterexample to the Jacobian Conjecture using Anthropic's Fable 5 model. The tweet included a set of polynomial mappings from C³ to C³ and stated the conjecture is false. The tweet quickly garnered over 20 million views.
The Jacobian Conjecture is a classic problem in algebraic geometry, proposed 87 years ago and once listed among the 18 major mathematical challenges of the 21st century. No one had previously proven it true or false.
Subsequently, researchers at OpenAI independently proved a similar counterexample using an internal Codex version (offline), further validating the result's reliability.
Notably, the Jacobian Conjecture was the very problem that renowned mathematician Zhang Yitang attempted to solve in his doctoral thesis. Zhang's advisor gave him a lemma to pursue the conjecture, but the lemma turned out to be false, causing Zhang to struggle to complete his thesis. After graduation, he worked in fast food and even experienced homelessness.
Zhang later gained fame by proving the bounded gaps between primes, but the Jacobian Conjecture remained a regret in his academic career. Now, AI has casually solved it, a poignant turn of events.
This incident has also sparked discussions about the problem of toxic advisors in academia—where an advisor's misleading direction can have devastating effects on young scholars.
The proof's release was highly disruptive: no journal review, no formal paper, not even exceeding Twitter's character limit—just a formula that achieved tens of millions of views. This marks a paradigm shift in how research results are disseminated.
From a communication perspective, AI-assisted mathematical discovery reached an audience far beyond traditional academic channels at minimal cost (a single tweet), but it also raises questions about result verification and academic norms.
This report is primarily based on social media posts and lacks confirmation from official institutions or peer review. Neither Anthropic nor OpenAI has issued an official statement. Details about Zhang Yitang's doctoral thesis come from online discussions and have not been confirmed by him personally.
AI's breakthrough on a fundamental math problem not only demonstrates its reasoning capabilities but also exposes issues within the traditional academic system. In the future, AI-assisted discoveries may change how research is disseminated and validated.
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