Frontier AI models have begun solving open mathematical problems that resisted human experts for decades, according to an analysis by Latent Space author Ankit Maloo. The piece points to an internal OpenAI model that found a counterexample to Erdős's unit distance conjecture, a problem open since 1946. It then cites a run of later results, including a proof of the Cycle Double Cover problem, solutions to ten more open problems by July, and a claimed proof of the Navier-Stokes problem in September. Anthropic is credited with a formalisation of Fermat's Last Theorem and improved bounds on the Riemann hypothesis.
The author's central question is whether these successes follow a predictable pattern. Drawing on a framework from mathematician W.T. Gowers, he describes problem difficulty as the shortest sequence of insights an expert would need to reconstruct a proof, plus the work required to develop each one. Humans tend to search breadth-first, exploring many directions shallowly and abandoning most early. Language models work depth-first, committing to one trajectory at a time. The piece argues that automated verifiers change the economics: when a checker can quickly prune wrong attempts, it becomes rational to spend large amounts of compute on uncertain ideas, so the reach of the verifier shapes which problems models can solve.
For Australian businesses and professionals, this changes little immediately. The results are research-grade breakthroughs in pure mathematics and do not create new costs, risks or obligations under the Privacy Act. The practical takeaway is narrower: teams doing quantitative, engineering or modelling work could consider pairing frontier models with automated checks, such as test suites or formal verifiers, where an answer can be tested cheaply. Those whose work is not mathematically intensive can reasonably ignore it for now.
Key Points
An OpenAI internal model reportedly found a counterexample to Erdős's unit distance conjecture, open since 1946.
The article cites further claimed AI results, including Cycle Double Cover, ten additional open problems, and Navier-Stokes.
Gowers' framework treats difficulty as the shortest sequence of insights needed to reconstruct a proof, plus the work to develop them.
Humans search breadth-first and abandon most directions early, while LLMs search depth-first along single trajectories.
Automated verifiers make it rational to spend heavy compute on uncertain ideas, because wrong attempts can be pruned quickly.