Why the question remains open
The argument
Because relativizing, natural, and algebrizing proof techniques cannot resolve whether P equals NP, any resolution must use methods outside the families that have driven most of complexity theory, and given that no claimed proof that P equals NP or that P differs from NP has withstood expert scrutiny, the question has no answer on the record in either direction; the claim's status therefore rests on heuristic evidence rather than proof.
Does it work?
Not yet evaluated.
Premises
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →Relativizing, natural, and algebrizing proof techniques cannot resolve whether P equals NP.
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →No claimed proof that P equals NP or that P differs from NP has withstood expert scrutiny.
Where it is made
Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.
No source is recorded as making it.
Earlier ratings
- Sep 16, 2026
The inference holds: given that relativizing, natural, and algebrizing techniques cannot resolve the question, which is a set of proved theorems (Baker, Gill and Solovay; Razborov and Rudich; Aaronson and Wigderson), and that no claimed proof in either direction has survived scrutiny, the question is open and any assessment must rest on heuristic evidence. Both premises are settled in the discourse. The argument is neutral on the answer; it fixes the kind of evidence that can bear on the claim and explains why the missing proof of inequality is not itself evidence for equality.