Theoretical computer science is currently experiencing a historic moment as longstanding assumptions about computational limits face unprecedented challenges. On October 26 and 27, 2026, leading artificial intelligence laboratories OpenAI and Anthropic announced that internal models had discovered a deterministic subexponential algorithm for the classical 3-SAT satisfiability problem. If validated, this development would refute the Exponential Time Hypothesis, commonly known as ETH, after more than a quarter of a century. Formulated in 1999 by computer scientists Russell Impagliazzo and Ramamohan Paturi, the hypothesis has served as a foundational benchmark for computational complexity.
Boolean satisfiability represents one of the oldest and most thoroughly analyzed challenges in algorithm design. In essence, the Exponential Time Hypothesis states that NP-complete problems such as 3-SAT cannot be solved exactly in subexponential time in the worst case. The algorithm proposed by the frontier models claims to count satisfying assignments for Boolean formulas substantially faster than theoretical limits previously permitted. To eliminate human error and ensure mathematical rigor, OpenAI translated the entire proof into the interactive proof assistant Lean, enabling automated step-by-step verification of every logical deduction.
Just hours after OpenAI shared its initial announcement, Anthropic followed with comparable research conclusions derived from its own models. The nearly simultaneous discovery of matching mathematical formulations by two direct competitors has heightened scrutiny across the international academic community. Despite the palpable excitement, senior complexity theorists urge patience before declaring the problem solved. The original architects of the hypothesis, Russell Impagliazzo and Ramamohan Paturi from the University of California San Diego, responded immediately by forming an independent working group alongside Ryan Williams from the Massachusetts Institute of Technology to examine the proofs.
The implications of a verified refutation would extend across numerous scientific disciplines. For 25 years, the ETH served as the mathematical anchor for establishing hundreds of conditional lower bounds in graph algorithms, computational biology and structural cryptography. While finding a subexponential algorithm does not prove that P equals NP, it fundamentally disrupts theoretical assumptions regarding runtime barriers. Countless established complexity proofs would need revisions, potentially altering how researchers approach combinatorial hardness in both theory and practical software engineering.
Beyond its direct impact on computational mathematics, this announcement signals a qualitative leap in how advanced artificial intelligence contributes to fundamental science. Until now, the practical utility of generative models in computer science was largely confined to code autocompletion, refactoring and heuristic testing. If the formalized Lean proof withstands the rigorous peer review led by Impagliazzo, Paturi and Williams, it would mark the first time autonomous models have resolved an open question that eluded human theoreticians for decades. The transition toward autonomous scientific discovery has thus reached a decisive turning point.