OpenAI and Anthropic Publish Refutations of the Exponential Time Hypothesis
OpenAI and Anthropic Publish Refutations of the Exponential Time Hypothesis
OpenAI and Anthropic say internal models independently disproved the Exponential Time Hypothesis, publishing papers and formal proofs in Lean.
OpenAI and Anthropic have published refutations of the Exponential Time Hypothesis (ETH).
Both results were reportedly achieved by the companies' internal models on October 16, almost simultaneously. The companies have already published papers and proofs formalized in Lean.
The Exponential Time Hypothesis is a stronger version of the P ≠ NP statement. It posits that some problems can be solved only by brute force; proving ETH would also imply P ≠ NP. It is difficult to say what practical consequences this refutation will have now.
In addition to this refutation, OpenAI also published significant breakthroughs in mathematics and physics.
Why it matters
AnalysisIf ETH is truly refuted, core assumptions in computational complexity and cryptography may need to be revisited, while Lean proofs show AI moving toward machine-checkable mathematics.
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