OpenAI is reportedly close to solving the Hodge conjecture, one of the seven Millennium Prize Problems. Sources indicate that internal staff expect a proof to be completed soon, though the company is currently evaluating how to announce the results to avoid public backlash from the mathematical community.
The company previously worked on the Navier–Stokes existence and smoothness problem. That research involved a variant of a next-generation pre-trained model codenamed 'Doug' and incurred costs estimated at several million USD.
OpenAI researchers view mathematics as the next logical frontier for large models, following software engineering. Both fields require step-by-step logical reasoning and offer results that can be automatically verified. Experts anticipate that the automation trends seen in software engineering over the past year could emerge in mathematics within 6 to 9 months.
The pursuit of these complex problems serves several strategic goals. It advances machine learning automation, which is critical for the company's long-term objective of recursive self-improvement. Furthermore, solving such challenges allows researchers to benchmark the complex reasoning capabilities of frontier models, potentially signaling an ability to tackle similarly difficult tasks in biology and chemistry.
