# Any reason to believe that $NP \neq P$ is unprovable in ZFC

We know $NP \neq P$ from a lot of point of view like empirical reason,or theoretical reasons such as finite model theory or descriptive complexity.Although we find so many reasons to believe $NP \neq P$,we have not found any proof for it now.

So any reason to believe that $NP \neq P$ is unprovable in ZFC?Any result about unprovability of $NP \neq P$ in ZFC or weaker system than ZFC.

• Decade out of date: Aaronson, Scott. "Is P versus NP formally independent?." Bulletin of the EATCS 81 (2003): 109-136. (PDF download link). Or better: Quantum Computing Since Democritus. – Joseph O'Rourke Sep 11 '14 at 0:48
• @JosephO'Rourke,thank you for the reference.It seems that the critical hard part for a proof is relating bound,usually,problems about bound in math is hard. – XL _At_Here_There Sep 11 '14 at 1:00
• Your spacing is off. You want not $NP! = P$ but rather $NP\;{!\!=}\;P$ ... or (for mathematicians) even better $NP \ne P$. – Gerald Edgar Sep 11 '14 at 1:03
• @GeraldEdgar,thank you very much ,I will edit it. – XL _At_Here_There Sep 11 '14 at 1:06