Two leading AI labs say they have finally knocked down the exponential time hypothesis—a 27‑year‑old conjecture that underpins much of modern algorithm research—leaving scholars to reassess a swath of their work.
Key points
- AI models have produced a proof that, if validated, would overturn the exponential time hypothesis, a foundational assumption in theoretical computer science.
- The proofs are currently unverified; leading researchers are organizing a collaborative effort to review the Lean‑encoded arguments.
- A confirmed refutation could reshape algorithm design, invalidate numerous published results, and prompt a reassessment of cryptographic security assumptions.
- The episode highlights both the disruptive potential of AI in mathematics and the psychological strain on researchers facing rapid, large‑scale paradigm shifts.
OpenAI and Anthropic announced this week that AI‑generated proofs, posted on GitHub in both natural language and the machine‑checkable Lean format, appear to refute the exponential time hypothesis (ETH), a conjecture that has guided theoretical computer science for nearly three decades. The claim, reported by Wired, has sent shockwaves through the community that builds its complexity and algorithm‑design results on the assumption that certain problems require exponentially more time as they scale.
Peter Jonsson, a professor at Linköping University, said his own paper—scheduled for presentation at the IEEE Symposium on Foundations of Computer Science—has become “dead” because it relies on ETH. He expects many presenters to open with, “ETH is false, half of my paper does not work,” and notes that the situation, while unsettling, is part of the scientific process.
AI‑generated proof challenges a cornerstone of complexity theory
The AI‑produced proofs have not yet been independently verified. OpenAI has reached out to the original proposers of ETH at UC Santa Barbara and to an MIT scholar who previously challenged a version of the hypothesis, asking them to lead a community effort to unpack the results. A Google form has been shared to recruit volunteers, and OpenAI has pledged funding for a dedicated conference, according to the source.
Reactions among researchers range from anxiety to excitement. Daniel Lokshtanov of UC Santa Barbara warned that, if confirmed, the result could render about 50 of his papers “pointless” or in need of revision, calling it “a giant bomb dropped into the middle of the field.” Conversely, Thore Husfeldt of the IT University of Copenhagen described the development as “fantastic,” likening it to turning on floodlights in a dark room and opening new avenues for exploration.
Researchers scramble to verify and reinterpret decades of work
While the immediate proof does not directly threaten current cryptographic schemes, Lokshtanov cautioned that designers of cryptosystems should take note, as many security assumptions rest on the belief that certain problems are computationally infeasible. Victor Lagerkvist, an associate professor at Linköping, said the potential falsity of ETH could revive problems he had abandoned under the hypothesis’s constraints.
The broader community is now wrestling with a flood of AI‑generated manuscripts—OpenAI released 722 papers on 400 problems earlier this month, some of which contained errors. Scholars report feeling “doom and gloom” as AI outputs repeatedly overturn ongoing projects, prompting discussions about mental‑health support within departments.
Reader questions
What is the exponential time hypothesis (ETH)?
ETH is a conjecture in computational complexity that posits certain problems require time that grows exponentially with input size; many algorithmic lower‑bound results are built on this assumption.
How are scientists verifying the AI‑generated proofs?
OpenAI has invited the original ETH proposers and other experts to lead a review, using a public Google form to recruit volunteers and planning a funded conference to examine the Lean‑formatted proofs.
Could disproving ETH affect internet security?
The current proof does not directly break cryptographic schemes, but because some security protocols rely on the hardness of problems assumed to follow ETH, cryptographers are being urged to reassess their designs.
Source: wired.com
