It’s rare in science to witness a single moment when an entire field suddenly feels the ground shift beneath its feet, but that is exactly what happened this week for theoretical computer science. Professor Peter Jonsson of Linköping University in Sweden was preparing to present a paper at one of the most prestigious conferences in the field, the IEEE Symposium on Foundations of Computer Science, in just two weeks. His work, built carefully over years, was based on a widely accepted mathematical assumption called the exponential time hypothesis, or ETH. That hypothesis, first formulated 27 years ago, essentially holds that certain computational problems grow exponentially harder as the size of the input grows, and that no clever shortcut can ever escape that fundamental limit. It has been the bedrock for thousands of papers, Jonsson’s included. But as of Monday, much of his work had been rendered obsolete. Both OpenAI and Anthropic, the two leading AI research companies, announced that they had produced proofs showing ETH is false, using sophisticated AI reasoning systems. Jonsson described the situation bluntly: his paper is now, in large part, “dead.” It is a devastating and disorienting experience, but he also recognizes that this is how science is supposed to work. The assumptions we build on are meant to be tested, and sometimes they collapse. “People will start the talks: ‘ETH is false, half of my paper does not work,’” he predicted. It’s vexing, he admitted, “but at the same time, we learn a lot from it. And this is what science is about.”
The scale of the disruption is hard to overstate. The exponential time hypothesis is not just a niche idea; it is a cornerstone of computational complexity theory and algorithm design. Researchers have used it as a starting point for decades, assuming that certain problems—like finding the fastest possible algorithm for a given hard problem—can’t be solved in polynomial time, only in exponential time. This assumption has guided countless papers on everything from graph theory to satisfiability problems, from artificial intelligence to cryptography. If ETH is false, then the entire edifice begins to wobble. The AI-generated proofs are not yet independently verified by human researchers, which is a serious caveat. Neither OpenAI nor Anthropic has had their work peer-reviewed in the traditional sense, though both have published their proofs on GitHub in two forms: a natural-language explanation that human mathematicians can read, and a machine-checkable format called Lean, which is essentially a formal system that verifies every logical step. That Lean component means the proof is, in a sense, already checked by a computer—but human mathematicians still need to interpret the high-level ideas, understand why the proof works, and confirm that it actually disproves the hypothesis as it has always been understood. It’s a new and strange situation: the proof may be logically bulletproof, but no human has yet fully grasped it. To help untangle this, OpenAI has reached out to the University of California, Santa Barbara computer scientists who originally proposed the hypothesis, as well as an MIT academic who had previously refuted a version of it. Together they are rallying researchers to unpack the proofs, with a Google form asking for volunteers and feedback, and a commitment from OpenAI to fund a conference dedicated to understanding the result. It’s a remarkable and somewhat surreal way for a field-altering discovery to enter the world.
For the researchers whose careers have been built on ETH, the news is both thrilling and terrifying. Daniel Lokshtanov, a professor at UC Santa Barbara and one of the original proposers of the hypothesis, has been processing the shock with unusual candor. He estimated that if the AI proofs are confirmed, he will be “galactically wrong,” and that around fifty of his published papers will become either “pointless” or in need of significant revision. That’s not a small thing to absorb. It means years of work, collaborations, grants, and intellectual energy have been aimed at a foundation that has suddenly crumbled. Yet Lokshtanov didn’t sound defeated. He called the result “a giant bomb dropped into the middle of the field,” and then immediately added, “It’s really cool and terrible at the same time.” That ambiguity is present throughout the community. There is the sharp, personal sting of seeing one’s life’s work rendered irrelevant, but there is also the electric thrill of a frontier opening up, a chance to ask questions that were previously considered impossible to answer. This is the nature of scientific progress: the old map gets torn up, but a new, more interesting map is waiting to be drawn. The emotional whiplash of that experience is hard to articulate, but Lokshtanov’s words capture it perfectly—the catastrophe and the wonder intertwined.
Another researcher, Thore Husfeldt, who heads the algorithms research group at the IT University of Copenhagen, has had an even more personal connection to the hypothesis. He had spent most of the past year working on a single problem in his subfield, and he now believes that all of it is “irrelevant.” He was also one of the early formulators of a version of ETH, so the disproval feels especially intimate. As the news spread, he found himself standing at his blackboard, scribbling calculations to figure out what else in his body of work might have just become obsolete. It’s a scene that will likely repeat itself in offices and seminars around the world over the coming months. But interestingly, Husfeldt did not express the kind of archness or resignation that has gripped some mathematicians who have faced similarly field-upending proofs generated by AI models. Instead, he radiated enthusiasm. He called the finding “fantastic,” and explained why with a beautiful metaphor. “Being a mathematician is a lot like stumbling about in a completely dark room,” he said. “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.” That image—of delighted scientists scurrying through a newly lit space—is the opposite of despair. It reminds us that the point of research is not to protect our old theories but to discover what is true. Even when the truth means our own work has been upended, the knowledge itself is a gift.
There is something broader happening here that goes beyond the specific crisis of ETH. For years, AI has been used as a tool, a kind of super-powered assistant that can search through huge spaces of possibilities and generate creative guesses. But now, with OpenAI and Anthropic producing proofs that humans didn’t anticipate, AI is beginning to act less like an assistant and more like an autonomous scientist. It doesn’t just contribute a step here or there; it reshapes the intellectual landscape. This is unsettling to some, exhilarating to others, and deeply confusing to everyone. The researchers in this story are not reacting with fear or resistance. They are rolling up their sleeves and trying to learn. The fact that OpenAI is funding a conference specifically for unpacking its proof shows that the companies themselves recognize how important it is for the human community to catch up. It also raises the question of how to handle such discoveries in the future. Should there be a protocol, a kind of scientific ethics that governs how to release proof bombshells? How do you ensure that a result is trusted before the entire field abandons its assumptions? The process is still being invented in real time. The Lean format, which allows a computer to verify every logical step, provides one kind of trust, but human understanding remains crucial. A proof can be technically correct and still hide a subtle conceptual shift that needs to be absorbed. This is the new frontier of mathematics and computer science: not just solving problems, but learning to live with a machine that can solve them for us, and then getting to the hard work of understanding why.
In the end, the story of ETH’s potential collapse is a story about the resilience and beauty of science. It would be easy to write this as a tragic tale of wasted careers, of fifty papers suddenly pointlessly gathering dust, of a year of work evaporated overnight. But the researchers themselves are not letting it be that. Jonsson, Lokshtanov, and Husfeldt all share a deeper perspective. They know that science is not a collection of eternal truths, but a dynamic, messy process of correction and discovery. The exponential time hypothesis was always a conjecture, an educated guess about the way the universe of computation works. It was extraordinarily useful, so useful that we came to treat it as nearly sacred. But the moment it is disproven, a huge new area opens up. If certain hard problems are not as difficult as we thought, then perhaps there are new and faster algorithms waiting to be found. Perhaps problems we thought would take centuries to solve can now be solved in hours. Perhaps the security of cryptographic systems, which often rely on exponential hardness, needs to be rethought. These are deep and consequential questions, and they are now live because someone—actually, some machine—had the audacity to challenge a sacred assumption. That is not a tragedy; that is the most exciting thing that can happen in science. For the human researchers involved, it may feel like losing a beloved but faulty compass. But it is also an invitation to explore a world that was previously hidden in the dark. The overexcited bunnies are already running. And the field of theoretical computer science, shaken and stunned, is beginning to realize that it has just been given one of the greatest gifts a scientist can receive: the sudden, humbling, and exhilarating realization that there is still so much more to learn.
