The ETH, a 27-year-old tenet of the field, posits that the effort required to solve certain computational problems increases exponentially with the size of the problem. This assumption has served as the bedrock for vast swaths of research into complexity and algorithm design. If the AI-generated proofs are confirmed, the premise underlying these studies collapses. Jonsson expects his predicament to be “very common” at the upcoming symposium, predicting that presenters will begin their talks by acknowledging, “ETH is false, half of my paper does not work.”
The disruption extends well beyond Jonsson’s immediate circle. Daniel Lokshtanov, a professor at UC Santa Barbara who originally proposed the hypothesis, estimates that the result, if confirmed, will render him “galactically wrong.” He calculates that approximately 50 of his published papers will either become “pointless” or require a complete revisit. “It’s just a giant bomb dropped into the middle of the field,” Lokshtanov says. “It’s really cool and terrible at the same time.”
The speed of this paradigm shift has caught the academic community off guard. Thore Husfeldt, head of the algorithms research group at the IT University of Copenhagen, had spent the majority of the year focused on a single problem within his subfield. Upon learning of the disproof, he stated, “As far as I can tell, it’s now all irrelevant.” Husfeldt, who had previously formulated a version of the now-refuted hypothesis, has been writing calculations on his blackboard to determine which other parts of his work have become obsolete due to what he describes as a “once-in-a-generation result.”
Unlike previous instances where AI models produced proofs that caused quiet frustration among mathematicians, the scale of this event has triggered a distinct psychological response among researchers. Husfeldt notes that the last few months have been “really tough,” characterized by “doom and gloom” as AI announcements have repeatedly “annihilated” ongoing research projects. The psychological toll has been severe enough that his department considered hiring an occupational psychologist, as some faculty members are “really depressed and really sad.” The volume of AI-generated content, including what Husfeldt terms “slop-level” results, has further complicated the landscape. During an interview, he received a 17-page paper via a random Gmail account, which he suspected was AI-generated; he declined to read it, noting that “Reading math is a very big investment of cognitive time.”
OpenAI has contributed significantly to this influx of information, having dumped 722 manuscripts on 400 problems on GitHub earlier in the month. Academics have expressed annoyance at the difficulty of digesting this volume, particularly because several documents contained errors. Some mathematicians viewed the hasty rollout as an attempt to bolster OpenAI’s planned initial public offering rather than to advance the field. However, regarding the specific 60-odd-page paper on ETH, academics note that the quality appears higher than the company’s previous publications. The proofs have been published on GitHub in both natural language and the machine-checkable Lean format.
The immediate task for the global research community is verification. Neither OpenAI nor Anthropic’s results have been independently verified, and researchers have not yet had time to fully understand the proofs. To address this, OpenAI has asked the UC Santa Barbara computer scientists who proposed the hypothesis, along with an MIT academic who previously refuted a version of ETH, to rally the community. This effort includes a Google form for volunteers and feedback, as well as a commitment from OpenAI to fund a conference on the topic. Lokshtanov plans to join this effort to unpack the proofs.
The implications of a false ETH extend beyond theoretical interest into practical infrastructure. Victor Lagerkvist, an associate professor at Linköping, views the disproof as “exciting,” planning to return to problems he had previously abandoned under the assumption that ETH was accurate. More critically, the result may impact cryptography, which underpins web security and relies on the assumption that certain mathematical problems take an impractically long time to solve. While this specific result does not directly break current cryptosystems, Lokshtanov warns that “it should definitely scare some cryptosystem designers.” Husfeldt emphasizes the importance of continued human and AI-assisted work in theoretical computer science to identify misunderstandings about computation, given that modern digital infrastructure is built on these assumptions.
Despite the invalidation of their life’s work, many researchers express a sense of liberation rather than despair. Husfeldt compares the experience to a mathematician stumbling about in a dark room, noting that the new result is like “floodlights of knowledge” illuminating the field. “So it’s a super exciting time,” he says, describing researchers as “overexcited bunnies” exploring nooks and crannies previously inaccessible. Jonsson, while facing the salvageability of his conference paper, believes a definitive verdict on ETH is something he could only “dream of” before. “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,” Jonsson says. “If it’s true, then we must simply use it in the future.”
As the academic community scrambles to verify the AI-generated proofs, the focus shifts from the validity of the disproof to the next phase of research. The upcoming IEEE Symposium on Foundations of Computer Science will serve as the first major public test of how the field adapts to a world where its foundational complexity assumptions no longer hold. Researchers like Jonsson and Lagerkvist are already revisiting abandoned problems, eager to apply the new computational realities to issues that were previously deemed intractable.
