This is crazy.↵
↵
People used to think that 3SUM couldn't be solved in O(n^1.99999), but couple of weeks ago that conjecture was [disproven by Anthropic's AI](https://arxiv.org/abs/2610.06783). They also disproved some related conjectures to other similar problems, but importantly they didn't disprove the Exponential Time Hypothesis (ETH). The conjecture states that no subexponential algorithm for 3SAT exists. ↵
↵
Today, ETH was [disproven by openAI](https://github.com/openai/math/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf). See also [this](https://openai.com/index/building-scientific-understanding-with-academic-communities/).↵
↵
There is an entire field of research, called fine grained complexity, that fundamentally is built on these two conjectures. This means that in half a month, an entire field of theoretical computer science has completely collapsed.AThis has been a funeral for an entire field of science.↵
↵
The entire reason 3SUM was interesting was because people thought this conjecture to be true.↵
With the conjeture being false, any research that assumed it is basically worthless.↵
People were never interested in finding an algorithm for 3SUM. They just hoped there wasn't one.↵
↵
A new algorithm for 3SAT is definitely interesting in its own. But this is not the outcome that anyone had wished for.↵
↵
Who knows, maybe $P = NP$.
↵
People used to think that 3SUM couldn't be solved in O(n^1.99999), but couple of weeks ago that conjecture was [disproven by Anthropic's AI](https://arxiv.org/abs/2610.06783). They also disproved some related conjectures to other similar problems, but importantly they didn't disprove the Exponential Time Hypothesis (ETH). The conjecture states that no subexponential algorithm for 3SAT exists. ↵
↵
Today, ETH was [disproven by openAI](https://github.com/openai/math/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf). See also [this](https://openai.com/index/building-scientific-understanding-with-academic-communities/).↵
↵
There is an entire field of research, called fine grained complexity, that fundamentally is built on these two conjectures. This means that in half a month, an entire field of theoretical computer science has completely collapsed.
↵
The entire reason 3SUM was interesting was because people thought this conjecture to be true.↵
With the conjeture being false, any research that assumed it is basically worthless.↵
People were never interested in finding an algorithm for 3SUM. They just hoped there wasn't one.↵
↵
A new algorithm for 3SAT is definitely interesting in its own. But this is not the outcome that anyone had wished for.↵
↵
Who knows, maybe $P = NP$.
