When AI Started Solving Open Math Problems

The Big Picture

The video describes a sudden surge in AI-assisted mathematical discoveries. In just a few weeks, AI systems and researchers working with them reportedly disproved long-standing conjectures, improved mathematical bounds, and made progress on major open problems. The trend has prompted concern about how mathematics should verify and value AI-generated work.

Key Developments

• AI competition performance: About a year earlier, models solved five of six problems at the International Mathematical Olympiad, though this initially seemed limited to competition-style math.
• Erdős conjecture: In May, an OpenAI model reportedly disproved an 80-year-old conjecture about unit distances.
• Jacobson conjecture: Mathematician Levent Alpoge, with help from AI tool Fabel, posted a counterexample to the 87-year-old Jacobian conjecture, a renowned problem in algebraic geometry.
• Dense Garg–Gomory conjecture: GPT-5.6 reportedly found a seven-node, nine-edge counterexample to a 30-year-old graph theory conjecture. The problem can be understood as asking whether split shipments can always be consolidated into unsplit routes without increasing total cost.
• Other independent results: A Columbia PhD student reportedly solved six open problems in five days, while an amateur mathematician solved another.
• OpenAI’s reported results: The company said an unreleased model solved ten open problems in mathematics and theoretical computer science, publishing the results with Lean certificates—formal proofs that can be mechanically checked. Among them were an improved bound for packing identical balls and a disproof of Connes’ rigidity conjecture.
• Riemann hypothesis progress: Anthropic said an unreleased model made progress on the 167-year-old Riemann hypothesis. Bun JS creator Jared Sumner prompted Claude to investigate it; after an initial batch of failed ideas, the system coordinated 60 sub-agents, ran thousands of commands, and generated hundreds of scripts. It did not prove the hypothesis, but reportedly improved estimates for how often candidate solutions satisfy it. The work was checked by mathematicians and formalized in Lean.

Why It Matters

• The pace and depth of these results challenge the idea that AI is useful only for routine or competition math.
• Researchers have called for guardrails and raised concerns about mathematical standards, verification, and credit.
• Formal proof systems such as Lean can help check AI-generated claims, but major discoveries still require careful expert scrutiny.