Understanding the Exponential Time Hypothesis, and OpenAI's claim it is false (gravitypersists.github.io)

On October 26, 2026, OpenAI released a paper titled *The Exponential Time Hypothesis is False*, proposing a challenge to a long-held belief in theoretical computer science. The Exponential Time Hypothesis (ETH) posits that no algorithm can solve NP-complete problems like 3-SAT in significantly less than exponential time as the problem size increases. OpenAI's manuscript, produced by an internal model and verified using Lean, claims that this hypothesis can be refuted, but the implications for the renowned P vs NP problem remain unaddressed. A working group, including the authors of the original ETH, is set to review OpenAI’s claim, emphasizing that participation in this process does not equate to endorsement. This announcement is significant for the AI/ML community as it touches upon the foundational aspects of algorithm efficiency, which directly affect the feasibility of solving complex computational problems in practice. If OpenAI’s assertion holds true, it could reshape our understanding of algorithmic limits and lead to breakthroughs in developing faster algorithms for NP-complete problems. However, the paper's authors acknowledge that the result does not imply subexponential algorithms for all NP problems, a reminder of the complexity surrounding this topic. The challenge to ETH could alter not only theoretical computer science but also practical applications of AI and machine learning, depending on the outcomes of the ongoing review.