OpenAI recently published solutions to three complex mathematical problems, including a refutation of the Exponential Time Hypothesis (ETH). This hypothesis has long served as a fundamental assumption in computer science regarding computational difficulty. Anthropic subsequently released its own independent refutation of the same hypothesis.
The release process differed by discipline: mathematicians received the work via GitHub, while computer scientists and physicists formed working groups to evaluate the findings. MIT professor Ryan Williams is coordinating the computer science community's response and collaborating with OpenAI to interpret the results alongside ETH authors Russell Impagliazzo and Ramamohan Paturi.
The ETH suggests that solving certain logic puzzles requires exponentially more time as variables increase. OpenAI and Anthropic claim their models developed algorithms capable of solving these puzzles in sub-exponential time. If validated, these findings could challenge existing intuitions about computational complexity and P vs NP problems.
While the findings could impact scientific literature relying on ETH, initial assessments suggest current cryptographic systems remain secure. Researchers are now calling for a conference to discuss the implications of these AI-generated algorithms and to establish new norms for how AI contributions are integrated into scientific research.
