For some computer scientists, years of mathematical research may have just become irrelevant. And unlike the usual academic drama of someone publishing a competing paper or proving another researcher wrong, this time, AI is behind the disruption.
OpenAI and Anthropic have both claimed to have disproved the Exponential Time Hypothesis (ETH), a long-standing assumption in theoretical computer science. The hypothesis, which has been around for 27 years, suggests that solving certain computational problems becomes exponentially harder as those problems grow in size.
That assumption has influenced decades of research into algorithms, computational complexity and what computers can realistically solve. If the new AI-generated proofs hold up, a significant amount of that work will need to be reconsidered. That could mean the rewrite of textbooks. Let’s explore just how much researchers have at stake.
Watching years of work unravel
Peter Jonsson, a professor at Linköping University, is among those directly affected. His research is scheduled to be presented at the prestigious IEEE Symposium on Foundations of Computer Science in two weeks. But following the new AI findings, he believes much of it may no longer hold up. He expects other researchers attending the conference to face similar problems.
“People will start the talks: ‘ETH is false, half of my paper does not work,’” he stated.
UC Santa Barbara professor Daniel Lokshtanov is facing an even bigger reckoning. He estimates that if the findings are confirmed, around 50 of his published papers could become pointless or require substantial revisions.
He describes the development as being “galactically wrong” about something he has spent much of his career studying. “It’s just a giant bomb dropped into the middle of the field. It’s really cool and terrible at the same time,” he said.
For Thore Husfeldt, head of the algorithms research group at the IT University of Copenhagen, the disruption is particularly personal. He had spent most of the year working on a problem that now appears to depend on an assumption that may not be true. “As far as I can tell, it’s now all irrelevant,” he told WIRED.
The AI proofs still need human verification
Researchers have not independently verified the proofs. Both companies have published their findings on GitHub in natural language and Lean, a format that allows mathematical proofs to be checked by computers. But producing a proof and establishing that the wider research community can understand, verify and build on it are two different things.
OpenAI is already trying to get more mathematicians involved. The company has asked the UC Santa Barbara researchers who originally proposed the hypothesis, alongside an MIT academic who previously challenged a version of it, to help organize an independent examination of the findings.
So far, that effort includes a Google form for researchers willing to contribute and a commitment from OpenAI to fund a conference dedicated to the subject.
There’s also a practical problem, as the sheer volume of AI-generated research is becoming difficult for academics to process. Earlier this month, OpenAI uploaded 722 manuscripts covering 400 mathematical problems to GitHub. The release frustrated researchers, some of whom complained about errors and the difficulty of reviewing so many papers at once.
Husfeldt has experienced that problem firsthand. During his interview with WIRED, he received a suspected AI-generated 17-page paper discussing the consequences of the ETH result, sent from an unfamiliar Gmail account. He wasn’t interested in reading it. “Reading math is a very big investment of cognitive time,” he said.
Some mathematicians are excited about what comes next
Despite the professional and psychological strain, not everyone sees the development as a disaster. Husfeldt, for instance, considers the discovery a breakthrough worth celebrating. He compares the experience of working in mathematics to stumbling around in a dark room, trying to understand what is in front of you.
The new findings, he says, are like suddenly switching on the floodlights. In his words: “It’s like somebody just illuminated an entire subfield in floodlights of knowledge, and now we just run around like overexcited bunnies and look at all the nooks and crannies that we can suddenly explore. So it’s a super exciting time.”
There are already researchers thinking about problems they previously abandoned because they assumed ETH was correct. Victor Lagerkvist, an associate professor at Linköping University, has stated that he plans to revisit some of those problems if the hypothesis is indeed disproved.
Perhaps one of the more fascinating consequences of the discovery is that AI could open up avenues of investigation that scientists previously considered too difficult or impractical. Still, the emotional impact should not be overlooked. Husfeldt says the repeated announcements of AI breakthroughs have created an atmosphere of uncertainty across the research community.
“The last few months have been really tough. It’s a lot of doom and gloom, because every week, or every second week, the results announced by AI just annihilate the ongoing research projects of many people,” he stated. He added that the situation has become psychologically taxing, with some researchers feeling deeply discouraged.
The security of the internet
The implications may also extend beyond academic research. Modern digital security relies partly on mathematical problems that are believed to be too difficult for computers to solve within a practical timeframe. Cryptographic systems use these assumptions to protect everything from online transactions to private communications.
If researchers discover that certain supposedly difficult problems can be solved much more efficiently than expected, that could raise questions about the foundations of some security technologies.
The current ETH findings don’t directly break existing cryptography. However, Lokshtanov believes the development should get the attention of people designing cryptographic systems. “It should definitely scare some cryptosystem designers,” he said.
That is one reason researchers insist that the findings need careful examination rather than immediate acceptance or dismissal. Husfeldt argues that understanding the limits of computation is particularly important because so much of today’s digital infrastructure depends on those assumptions. “We want the open scientific process to identify our misunderstandings about computation,” he revealed, “in particular because lots of modern digital infrastructure is built on assumptions about computation.”
Rewriting the rules in mathematics isn’t so simple
For Jonsson, the disruption has not taken away his enthusiasm for the field. He intends to revisit his own research and see whether some of it can be salvaged using different approaches. He is also interested in understanding the AI-generated proof and applying what it reveals to other problems.
And he is not particularly concerned about whether the breakthrough came from a human or a machine. “I don’t care if it’s a human-written proof, or it’s written by AI, or if an alien transmitted this proof to us. If it’s true, then we must simply use it in the future,” he said.
Don’t throw out your text books yet. AI does not get to rewrite mathematics simply because it produces a convincing paper. Its findings still have to survive scrutiny, verification and independent scientific review. But if these proofs hold up, computer scientists could be looking at a rare opportunity to take another look at decades of established knowledge.
Sources: WIRED, New Scientist