Repost @ProofOfKeags:
Alright I’ll bite here.
I don’t think it follows from AI solving old problems (read: proving conjectures) that computational problems of decidability and computational complexity suddenly go from hard to trivial.
Many problems that are assumed to be hard are backed by the assumption that P ≠ NP, which is a sensible intuition that we haven’t been able to prove.
I’m not deeply familiar with attempts to prove P =? NP but I suspect everyone’s trying to prove inequality not equality.
The hardness of cryptographic problems does not depend on the provability of inequality, merely the truth of it. And nothing about the latest generation of models getting cracked at frontier math suggests to me that there is something fundamentally easy about NP hard problems in general.
Proving theorems is a mostly mechanical process with some creative insight. Algorithmic design wherein you compute a value is a categorically different problem space that bears no resemblance to proving stuff.
We should expect these models to be good at and get better at proving stuff. That doesn’t mean hard problems become easy.
Stephan Livera
npub159…7mhqj
2026-10-09 01:23:00 UTC
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npub159p7amvdh2eefqj2wrad3xv59m2c2tlwx5u4ykg6rt3lvxsg7ussu7mhqjSeen on
wss://nos.lolPublished at
2026-10-09 01:23:00 UTCEvent JSON
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"content": "Repost @ProofOfKeags:\nAlright I’ll bite here.\n\nI don’t think it follows from AI solving old problems (read: proving conjectures) that computational problems of decidability and computational complexity suddenly go from hard to trivial.\n\nMany problems that are assumed to be hard are backed by the assumption that P ≠ NP, which is a sensible intuition that we haven’t been able to prove.\n\nI’m not deeply familiar with attempts to prove P =? NP but I suspect everyone’s trying to prove inequality not equality.\n\nThe hardness of cryptographic problems does not depend on the provability of inequality, merely the truth of it. And nothing about the latest generation of models getting cracked at frontier math suggests to me that there is something fundamentally easy about NP hard problems in general.\n\nProving theorems is a mostly mechanical process with some creative insight. Algorithmic design wherein you compute a value is a categorically different problem space that bears no resemblance to proving stuff.\n\nWe should expect these models to be good at and get better at proving stuff. That doesn’t mean hard problems become easy.",
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