OpenAI and Anthropic both say their AI models broke the Exponential Time Hypothesis (ETH), a 27 year old foundation of computer science. On the same day: October 16, 2026. So does this mean P = NP? Here’s what was actually claimed, and what it really means.
In this video: what ETH actually says (explained with a simple map coloring puzzle), what OpenAI and Anthropic claim, why hundreds of papers depend on ETH, why a Lean proof is not an absolute guarantee, and how the people who invented ETH are now leading an open review. The verdict is not in yet.
CHAPTERS
0:00 Two labs, one day
0:41 The problem made simple
2:47 OpenAI’s math blitz
3:50 The October 26 announcement
5:12 The Anthropic twist
6:38 The creators step in
7:51 Why so many papers depend on ETH
9:02 Real proof or compilation trap?
SOURCES
OpenAI math repository and ETH paper:
Anthropic paper, “A 2^o(n) Time Algorithm for 3SAT”:
Anthropic Lean formalization and README:
Community examination (Impagliazzo, Paturi, Williams):
Ryan Williams on Bluesky:
TechCrunch coverage:
Clay Institute, Yang Mills problem:
Impagliazzo & Paturi, “On the Complexity of k-SAT” (2001):
Impagliazzo, Paturi & Zane, “Which Problems Have Strongly Exponential Complexity?” (2001):
PHOTO CREDITS
Russell Impagliazzo: Martin Böhm, CC BY-SA 4.0, via Wikimedia Commons
Ryan Williams: Alexander S. Kulikov, CC BY-SA 3.0, via Wikimedia Commons
Paper excerpts shown for commentary, from the public preprints linked above.
Both claims are unreviewed preprints. Nothing in this video is a verdict on whether they are correct.
#ExponentialTimeHypothesis #PvsNP #AI
source
6:50 via bluesky then you show X?
FACT – We have a machine capable of solving complex mathematical problems through brute force. A machine that searches within a space of possibilities, making millions of attempts until it finds the correct path. Big deal, we need much more than that. That is not how mathematicians work. We will still need mathematicians to expand the boundaries of the search space, otherwise, mathematics will eventually die. The semantic dimension of mathematics still belongs to us. We are the bearers of understanding.
Looks like AI could be building the blocks so prove P=NP
It broke nothing… because that is only true for n>10^10,000 LOL Ten to the ten thousand is absurd, if every neutron, proton and electron in the universe held a different bit for every second in the 15 billion years of the universe, we are not even at one millionth of one billionth of one trillionth of that number…
This is intriguing. Although, while P = NP might be true, it's entirely possible the you have to discover NP before you can find the trick tp it. A lot of math goes that way. A formula holds something for a century or two, and later it gets shortened.
Good presentation though.
I gave them the hints about recurrence 😏
This is a really good, concise and straight-to-the-point video! One point regarding your "researchers will race to find faster algorithms" notion – somehow I've got the feeling that it's not going to be human researchers (unfortunately).
We are witnessing the "Great Convergence." Two different paths, two different labs, one same day. The machine is no longer just mimicking human thought; it is navigating the geography of truth in ways we are only beginning to map.
Two rival AI labs, the same breakthrough, both dated October 16. Coincidence? 🤔
Will the proofs survive the expert review? Tell me your prediction!