OpenAI has released claimed solutions to three major mathematics problems that have long challenged researchers. One of them is a surprise rejection of the Exponential Time Hypothesis (ETH)—a long-standing assumption in computer science about how hard certain problems are to solve. Anthropic later issued its own claimed refutation of ETH.
The Exponential Time Hypothesis sits inside the wider P versus NP question: whether every problem whose answer can be checked quickly can also be solved quickly. Most researchers assume the answer is no. ETH, first published in 1999 by UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, strengthened that view by saying that for a class of hard logic puzzles, even the best algorithms need time that grows exponentially as the number of variables rises.
What the AI labs claim
OpenAI and Anthropic say their models produced algorithms that solve those puzzles in “sub-exponential” time—faster than ETH said should be possible. If the claims hold, ETH would be refuted in the scientific sense: shown to be false. That would force many papers written over the past decade that relied on ETH to be revisited, and it would nudge researchers to put a little more weight on the idea that P might equal NP—though MIT Professor Ryan Williams stressed that this is probably not the final word, and that OpenAI’s algorithm is unlikely to be the best possible.
Anthropic mathematician Levent Alpöge suggested OpenAI may have built on pre-existing work. Hours afterward, Anthropic released its own ETH refutation.
How scientists are responding
OpenAI handled the three fields differently: mathematicians received work on GitHub; computer scientists formed a working group seeking public proofs and an OpenAI-funded conference; physicists formed a group to decide how their result will be shared.
Williams, who studies computational complexity at MIT, is organising the computer-science response. He has criticised OpenAI’s earlier October proof dump as a “DDOS attack on mathematicians,” but agreed to help interpret the new ETH solution alongside Impagliazzo and Paturi. Their first step was an open letter seeking feedback on the science and on norms for AI contributions.
“Some parts [of OpenAI’s proof] are, maybe you could say routine, but then yes, there are two or three alien-looking parts,” Williams said, arguing the community must examine those pieces together.
Security checks and what comes next
Before pure theory, Williams raised cybersecurity. Stronger algorithms could, in principle, weaken cryptography that depends on certain key sizes. He asked OpenAI science lead Dan Roberts whether any systems were newly insecure; Roberts indicated the lab had checked and was reasonably confident the result did not imply breaks.
Williams still wants a conference: researchers need to understand the algorithms and rethink foundations that assumed ETH. He is optimistic about AI-aided discovery but worried about how the next generation of scientists will be trained, saying AI is pushing people to ask harder questions once routine work becomes “low hanging fruit.”
Timeline: what has happened so far
- 1999: Russell Impagliazzo and Ramamohan Paturi publish the Exponential Time Hypothesis.
- Earlier October: OpenAI drops earlier proofs; Williams calls the approach a “DDOS attack on mathematicians.”
- OpenAI’s latest release: Claimed solutions to three major problems, including a rejection of ETH.
- Hours later: Anthropic releases its own claimed refutation of ETH.
- Since then: Williams, Impagliazzo and Paturi open a call for scientific feedback and discussion of norms; computer scientists push for public proofs and a funded conference.
Aasan alfaaz mein
OpenAI aur Anthropic ke AI models ne kaha hai ke Exponential Time Hypothesis galt hai—yeh ek purana computer-science ka andaaza tha ke kuch mushkil masle bohot slow solve hote hain. Agar yeh sahi nikla to kai research papers dubara dekhne padenge, lekin abhi proof check ho rahe hain. Crypto systems ke bare mein OpenAI ne kaha ke unhone check kiya aur abhi koi clear break nahi dikha. Aam logon ke liye seedha faida ya nuqsan abhi clear nahi; pehle scientists ko algorithms samajhne hain.
