OpenAI has released solutions to three blockbuster math problems that have long vexed researchers, including a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that shapes how we understand what is difficult to compute. The claim has thrilled and unsettled the scientific community in equal measure.
Exponential Time Hypothesis (Credits: TechCrunch)
As with previous proof drops from frontier labs, the response has been a mixture of thrill and dismay. Anthropic mathematician Levent Alpoge suggested OpenAI was building on pre-existing work, and hours later Anthropic released its own refutation of ETH. The race to claim, check, and interpret the result is now unfolding in public.
What Is the Exponential Time Hypothesis?
The ETH sits inside the broader class of problems known as P vs NP, which has animated computer science for decades. In simple terms, researchers are trying to understand whether any problem whose solution can be easily verified can also be easily solved.
A familiar example is Sudoku: once a solution is in place, it can be checked quickly, but finding it takes much longer. That same dynamic underpins cryptographic systems. With the key to an encoded message, you can reveal it, but cracking an effective code without the key takes too long to be useful. Scientists have yet to prove whether that gap is always real, and the ETH is a key assumption about how hard certain problems truly are.
How Scientists Are Responding to the AI Proof
This time, OpenAI structured its releases differently for each of the three disciplines involved. Mathematicians received the work on GitHub, computer scientists formed a working group and asked for the proofs to be shared publicly along with funding for a conference to discuss them, and physicists formed a working group to decide how their result will be released.
MIT Professor Ryan Williams, a computer scientist whose work focuses on computational complexity, is organizing his field’s response. Williams has criticized OpenAI’s approach in the past, calling an earlier proof dump a DDoS attack on mathematicians. Even so, he agreed to collaborate, helping to shepherd ideas he considers vital to the field, alongside UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who first published the ETH in 1999.
Their first step was an open letter calling for feedback from scientists interested in these problems and a discussion of the norms around AI contributions to their work. Williams told TechCrunch that while some parts of OpenAI’s proof look routine, there are two or three alien-looking parts, and it is exactly those parts that he believes the whole community needs to work on together.
Why the ETH Refutation Matters Beyond Math
If the refutation holds up under scrutiny, it would reshape assumptions that ripple far beyond pure mathematics, touching cryptography, algorithm design, and our understanding of what computers can ever do efficiently. If it does not, the episode still marks a turning point in how AI-generated proofs are released, checked, and debated.
Either way, the days of a single lab quietly dropping a proof and moving on appear to be over. The scientific community is now building the process to meet the machines halfway.
Source: TechCrunch — read the full story there.
