OpenAI Reportedly Trying to Solve Hodge Conjecture Amid Feud With Math Community

Not long after OpenAI swept in to announce it had solved the famous Navier-Stokes math problem, angering the math community and spurring speculation that the AI lifted its findings from other mathematicians, the company is allegedly homing in on another Millennium Prize Problem.

The Information reported Thursday, citing a single source at OpenAI, that employees at the AI firm expect to soon crack the Hodge Conjecture. That’s a famous unresolved question in math concerning whether certain topological features of geometric figures defined by polynomial equations can always be constructed by smaller geometric slices of the same figure. Scientific American noted it is “arguably the most abstract of the seven Millennium Prize puzzles,” of which just five remain to be solved. (Each puzzle carries a $1 million reward.)

Critics have argued AI firms are appropriating the work of mathematicians to pump out quick solutions to unsolved problems without contributing to overall understanding of mathematics. They’ve also noted that AI firms don’t seem nearly as interested in less glamorous academic tasks like verifying their solutions—which can take third-party experts and the Clay Institute, the Millennium Prize’s sponsor, years—as they are a quick PR hit. Numerous mathematicians have signed onto open letters excoriating OpenAI, and it has withdrawn its sponsorship of next month’s AI-themed Caltech Mathathon.

The Information noted that OpenAI engineers not only seem to see a business opportunity in doing for math what large language models did for coding, but also believe dominating math is an important pathway to recursive self-improvement (RSI). That’s the idea that a sufficiently smart computer will enter a phase of exponential, autonomous self-improvement. Depending on who one asks, RSI is a marketing buzzword, tech-bro philosophical babble, or the gateway to the apocalypse.

OpenAI does at least seem aware, in the wake of the Navier-Stokes, fiasco that mathematicians now view it like a Dust Bowl farmer eyeing an approaching cloud of locusts.

“It could take the company longer to announce the solution, though, because it’s trying to figure out how to collaborate with the math community to make the announcement without triggering another PR nightmare,” The Information paraphrased its source as saying.