OpenAI and Anthropic models beat a 27-year-old complexity conjecture

OpenAI seems to be experimenting with a new policy of releasing scientific findings. for physics and cs, they form external research groups. but for MATH, they just release the raw AI output for anyone to study, no external group of collaborators.

INCREDIBLE detail from OpenAI’s latest discoveries: the two researchers who originally proposed the Exponential Time Hypothesis 25 years ago, are now leading a group to verify OpenAI’s proof that could DISPROVE their own conjecture.

This is an incredible moment in this history of mathematics, computer science, physics & science with some of the hardest problems in human history being solved by AI over a period of weeks. Depending on your perspective, it's either a crisis, a triumph, or both. I don't think anyone knows for sure. We're all trying to make sense of it. I oscillate between fear/dread and optimism/excitement on a daily basis. The rate of progress is insane, including today's announcement from OpenAI of more problems solved. To help make sense of all of it, here's my conversation with three mathematicians about this moment. Each of them is an expert in the field of each of the biggest problems solved: Navier-Stokes, quasi-Riemann hypothesis, the unique games conjecture and complexity theory more generally.…

This is extremely confusing, but an internal Claude research model also independently refuted the Exponential Time Hypothesis on October 16, with 14M output tokens and no human input. 'Anthropic researchers worked with Claude to improve the presentation, resulting in this paper.'

SITUATION DETECTED: An Anthropic internal model also produced an independent refutation of the Exponential Time Hypothesis, it was discovered on October 16.

Two professors spent 27 years as the guys whose guess an entire corner of computer science was built on. This month a machine proved the guess wrong, and the two of them got asked to grade its homework. Back in 1999, Russell Impagliazzo and Ramamohan Paturi at UC San Diego made a bet about a logic puzzle called 3-SAT. You've got a bunch of switches you can flip on or off, plus a long list of rules they all have to satisfy at once. Trying every combination means 2^n tries for n switches, so every switch you add doubles the work. People found ways to make that less brutal over the years, but their bet, the Exponential Time Hypothesis, said it would always stay exponential. Computer scientists treated it like a law of physics. Hundreds of papers proving that problems like map coloring and…

OpenAI just claimed to disprove one of computer science's most fundamental assumptions. But why is this such a big deal? Here's our quick breakdown. Imagine you have a bunch of switches, each either ON or OFF, and rules like: Switch A must be ON, OR switch B must be OFF Switch B must be ON, OR switch C must be ON At least one of switches A, D, or F must be OFF With 6 switches, there are only 64 possible combinations. But with 100 switches, there are approximately 1.27 trillion trillion trillion combinations (2¹⁰⁰), and the rules can connect switches in complicated ways, making it extremely difficult verify which combinations work. So the mathematical challenge is finding even ONE combination that satisfies every rule, or proving that none exists. The assumption right now is that even…