OpenAI announced that its AI models have reportedly made scientific discoveries in mathematics, computer science, and physics. The company stated that its models proved the local smoothing conjecture, a central proposition in harmonic analysis, across every spatial dimension, a feat previously limited to three dimensions. Alex Iosevich, a professor of mathematics at the University of Rochester, called the achievement a "historic development." OpenAI also claimed to have disproved the Exponential Time Hypothesis (ETH), a concept related to the time required to solve complex computational problems, and provided a proof of the existence of quantum chromodynamics. The company structured the release of these findings differently across disciplines: mathematicians received the work on GitHub, computer scientists formed a working group, and physicists established a separate working group to interpret the results.
Regarding the ETH, which is part of the broader P vs NP problem, the hypothesis suggests that solving certain problems requires exponentially more time as the number of variables increases. The claims from OpenAI and Anthropic suggest algorithms that solve these puzzles in "sub-exponential" time, potentially refuting the ETH and suggesting a path toward P = NP. MIT Professor Ryan Williams, a computer scientist organizing the field's response, noted that while some parts of the proofs might be routine, "there are two or three alien-looking parts, and it’s exactly these parts that that I saw that made me think, wow, this is something that the whole community needs to work on together." Williams stated that "P = NP is asserting that this is true for every single problem you can verify quickly — if you can verify it quickly, you can solve it quickly. So this just seems too good to be true."
The release process involved consultations with three expert groups, which OpenAI described as "shepherds." While the groups working on mathematics and computer science problems opted for immediate public release of the AI-produced data, the physics group decided to defer its release to allow time for internal interpretation. OpenAI stated that these approaches involve tradeoffs, noting that "choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information."
This announcement follows other reported breakthroughs; last month, Anthropic announced the discovery of a new enzyme resembling CRISPR. Anthropic mathematician Levent Alpöge suggested that OpenAI was basing its solutions on pre-existing work, and Anthropic subsequently released its own refutation of the ETH.
