OpenAI has released solutions to three major math problems, and one of them is a claimed rejection of the Exponential Time Hypothesis (ETH), a long-standing assumption in computer science about what makes certain problems hard to compute, according to TechCrunch. Anthropic's own team of mathematicians subsequently published a refutation of ETH as well, after Anthropic mathematician Levent Alpöge suggested OpenAI's solutions were based on pre-existing work.
The claim lands in the middle of a sensitive debate about how frontier AI labs should contribute to pure research. MIT professor Ryan Williams, who is organizing the computer science community's response to the finding, told TechCrunch that OpenAI asked him to help interpret the result alongside UC San Diego researchers Russell Impagliazzo and Ramamohan Paturi, the pair who first published ETH in 1999.
The story matters beyond academic circles. If the AI labs' claims hold up, an improved algorithm could affect the cryptographic systems that protect everyday communications, and it could force researchers to revisit a decade of scientific papers built on the ETH assumption. Williams said one of the first questions he asked OpenAI science lead Dan Roberts was whether they had checked if any crypto systems were affected.
What is the Exponential Time Hypothesis?
ETH belongs to a broader family of problems known as P versus NP, a question that has animated computer science for decades. In simple terms, researchers want to know whether every problem whose solution can be quickly verified can also be quickly solved.
The Sudoku puzzle is a common example. Once a solution is filled in, checking it is fast, but finding that solution from scratch can take an enormous amount of time. That same dynamic underlies modern cryptography: with the right key, an encoded message opens easily, but cracking an effective code without the key takes too long to be practical.
ETH took that intuition further. It says that even the fastest known algorithms need exponentially more time to solve a specific class of logic puzzles as the number of variables grows. OpenAI and Anthropic now claim their models have produced algorithms that solve those puzzles in "sub-exponential" time, faster than previously thought possible. If true, ETH would be refuted in scientific terms, and a path toward algorithms that generally perform P = NP could open up.
