Well, if someone found a quasipolynomial time algorithm – O(n^log(n)) – for an NP-complete problem, that would technically be compatible with P!=NP, but might have quite significant practical implications.
To have a really big impact you'd have to have that be the dominating factor at lower n and keep that "log(n)" part of the equation below 10 or so for all practical n. The latter one in particular seems unlikely to me.
[–] Dylan16807 2 days ago