OpenAI is reportedly nearing a solution to the Hodge conjecture, one of the seven Millennium Prize Problems. According to sources cited by The Information, the company is currently evaluating how to present its findings to the mathematical community to avoid potential public relations issues.
This development follows the company's recent success with the Navier-Stokes existence and smoothness problem. On September 8, OpenAI announced that an internal, unreleased model outperformed the GPT-6 Astra in solving this specific challenge. The project involved a variant of a pre-training model codenamed Doug and incurred costs in the millions of dollars.
Researchers at OpenAI view mathematics as a logical next step for large models, noting that mathematical results are easily verifiable. The company anticipates that the automation trends seen in software engineering could extend to mathematics within the next 6 to 9 months.
The effort to solve these complex problems serves as a benchmark for evaluating the reasoning capabilities of AI models. Furthermore, success in this area supports the broader goal of recursive self-improvement, where AI systems contribute to their own development and research processes.
