Anthropic disclosed that its internal Claude research model took only about 30 minutes to solve a cryptography mystery that had puzzled researchers for roughly
OpenAI has released AI-generated solutions to 377 hard math and physics problems at once, all produced by a single agent from one prompt using a frontier model not yet public, according to Scientific American.
In math manuscripts OpenAI released on October 6, a 31-page paper claims a complete proof of the Cannon conjecture, accompanied by a formal Lean verification.
An unreleased research version of Claude has raised a zeta bound related to the Riemann hypothesis from 41.6% to 67.2%, according to a post on Anthropic's research site on October 5 that Ground News aggregated on October 7.
Six cognitive scientists have published a formal proof called the "Ingenia theorem": even under ideal conditions with perfect data, achieving human-level AI through learning remains an NP-hard problem, undermining the narrative that scaling inevitably leads to AGI.
Wharton associate professor Edgar Dobriban used GPT-5.6 Sol Pro to disprove a conjecture in multiple hypothesis testing that had stood for about 20 years, and posted the result as an arXiv preprint listing himself as sole author.
In 1946 Paul Erdős posed the unit distance problem: among n points in the plane, how many pairs can be at distance exactly 1? For nearly 80 years mathematicians widely believed the square grid was optimal. OpenAI says its internal reasoning model produced the first fully autonomous counterexample proof.
OpenAI has published a collection of mathematical results generated by an internal frontier model: 722 manuscripts and 372 "result families" covering number theory, algebra, topology, logic and theoretical computer science. The model reportedly faced about 4,000 open problems, and the results that survived were compiled and released.