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Both OpenAI and Anthropic announced this week that they have disproved the exponential time hypothesis (ETH). This premise has underpinned vast amounts of theoretical computer science research on complexity and algorithm design, assuming that solving specific problems requires effort that increases exponentially with problem size.
Researchers React to Obsolete Papers
Pontus Jonsson, a researcher, anticipates that this predicament will prove very common at the upcoming IEEE Symposium on Foundations of Computer Science, where one of his coauthors will present his work. As WIRED reported, Jonsson notes that researchers will likely open their talks by acknowledging that ETH is false and that half their papers no longer work. Although this presents a vexing problem, Jonsson emphasizes that researchers learn a great deal from it, viewing it as the essence of science.
Independent verification of the AI-produced proofs has not yet occurred, and researchers have not had sufficient time to fully understand them. Both firms published the proofs on GitHub in natural language and its machine-checkable Lean format. OpenAI has enlisted the UC Santa Barbara computer scientists who originally proposed the hypothesis, alongside an MIT academic who previously refuted a version of ETH, to help coordinate researchers in unpacking the proofs. This initiative currently involves a Google form for volunteers and feedback, as well as an OpenAI commitment to fund a conference on the subject.
Daniel Lokshtanov, a professor at UC Santa Barbara, intends to join the effort. He estimates that the confirmed result will render him galactically wrong, making approximately 50 of his published papers either pointless or in need of revision. He describes the development as a giant bomb dropped into the middle of the field, noting that it is simultaneously really cool and terrible.
Floodlights of Knowledge and Psychological Toll
Thore Husfeldt, head of the algorithms research group at the IT University of Copenhagen, spent most of the year focusing on a single problem in his subfield, which he now considers entirely irrelevant, as he told WIRED. Having formulated an early version of the hypothesis now disproved by OpenAI, he has utilized his blackboard to calculate which other parts of his work might be obsolete due to this once-in-a-generation result. Unlike math researchers experiencing ennui from similar AI-generated proofs, Husfeldt expressed enthusiasm for the new findings.
Describing the finding as fantastic, Husfeldt explains that being a mathematician resembles stumbling about in a completely dark room. He compares the breakthrough to someone illuminating an entire subfield with floodlights of knowledge, allowing researchers to run around like overexcited bunnies to explore new nooks and crannies.
Science has historically advanced by formulating hypotheses and proving them wrong, and academics being scooped or undercut by other groups is not unusual. However, artificial intelligence has accelerated this process, obliterating entire research programs and causing anxiety among specialists in math and science fields who question their standing against machines.
Husfeldt notes that the past few months have been difficult, filled with doom and gloom as AI-announced results frequently annihilate ongoing research projects. He states that this situation proves psychologically taxing, mentioning that his department has considered hiring an occupational psychologist because some individuals feel genuinely depressed and sad.
Concerns Over AI Volume and Future Implications
Researchers have also faced overwhelming volumes of AI-generated content, including low-quality results. During his interview with WIRED, Husfeldt received a suspected AI-generated 17-page paper concerning the consequences of the ETH result from a random Gmail account, which he declines to read due to the significant cognitive investment required for mathematical reading.
OpenAI has contributed to this volume by previously releasing 722 manuscripts on 400 problems on GitHub, drawing annoyance from academics who found the results difficult to digest. Frustration grew further when several documents contained errors, which some mathematicians viewed as a hasty rollout intended to support the company’s planned initial public offering rather than advance the field. In contrast, academics told WIRED that OpenAI’s current 60-odd-page paper on ETH appears better written than previous publications.
Academics are currently scrambling to unpack the paper and identify other results they can deduce from it. Victor Lagerkvist, an associate professor at Linköping, notes that if ETH is false and problems do not require exponentially more time as complexity increases, the situation is exciting. He plans to revisit problems he previously abandoned under the assumption that ETH was accurate.
Lokshtanov suggests that OpenAI’s finding could also impact the cryptography underpinning web security, which relies on the assumption that certain mathematical problems require impractically long times to solve. Although this specific result does not directly affect cryptography, Lokshtanov states that it should definitely scare some cryptosystem designers.
Husfeldt adds that continued human and AI-assisted work in theoretical computer science remains important to ensure the open scientific process identifies misunderstandings about computation, particularly because modern digital infrastructure relies on computational assumptions.
Jonsson plans to revisit papers by himself and others that depend on the truth of ETH, believing his conference paper might eventually be salvaged using another method. He expresses excitement about examining the details of OpenAI’s proof to learn from it and apply the insights to new problems, noting that having a definitive verdict on ETH was something he could previously only dream of. He concludes that these are exciting times that most people will never experience in their careers, adding that whether a proof is written by humans, AI, or transmitted by aliens, if it is true, researchers must simply use it in the future.
