OpenAI released solutions to three longstanding math problems yesterday, including a surprising rejection of the Exponential Time Hypothesis (ETH). ETH is a fundamental assumption in computer science regarding the difficulty of computation.
The scientific community responded with a mix of excitement and skepticism. Anthropic mathematician Levent Alpöges suggested OpenAI's solutions relied on pre-existing work, and hours later, Anthropic released their own refutation of ETH.
OpenAI is evolving its release strategy. This time, the lab structured dissemination differently for each discipline: mathematicians received the work on GitHub, computer scientists formed a working group requesting public sharing and funding for a conference, and physicists formed a group to determine release methods.
MIT Professor Ryan Williams, organizing the computer science response, has criticized OpenAI's past proof dumps as a "DDOS attack on mathematicians." However, he agreed to collaborate to shepherd vital ideas, teaming up with UC San Diego's Russell Impagliazzo and Ramamohan Paturi to interpret the solution.
They initiated an open letter seeking feedback on AI contributions and norms. Williams noted the proofs contained routine sections and "alien-looking" parts that require community effort. "It's exactly these parts that made me think, wow, this is something the whole community needs to work on together," he told TechCrunch.
ETH belongs to the broader P vs NP problem class. Reductively, P vs NP investigates if problems easily verifiable (NP) are also easily solvable (P). A Sudoku example illustrates this: verification is quick, but finding the solution is time-consuming; cryptography similarly relies on this asymmetry.
Scientists have yet to prove P = NP, so ETH provided evidence for P ≠ NP. ETH posits that finding solutions requires exponentially more time as variables increase. OpenAI and Anthropic claim their models solve these puzzles in sub-exponential time, potentially falsifying ETH.
Williams stated this increases the plausibility of P = NP and challenges intuitions about problem tractability. However, he views this as an intermediate step, likely not the final optimal algorithm. The durability of ETH in past research necessitates a review of many scientific papers.
Williams advocated for a conference to discuss the implications beyond just the algorithms, focusing on scientific foundations. Regarding cybersecurity, Williams asked OpenAI science lead Dan Roberts if this affects encryption. Roberts confirmed they checked and found no immediate insecure systems.
Despite concerns about training future scientists, Williams remains optimistic. He believes AI forces researchers to be more ambitious, prompting them to rethink the kinds of high-level questions they pursue if AI takes over "low-hanging fruit."
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