The informal consensus that P≠NP is 'probably' unprovable by current methods is epistemically compatible with, and may even suggest, genuine independence rather than mere technical difficulty.

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Epistemically compatible(describing logical relationships between ideas): Able to exist together without contradicting each other from the perspective of what we can know or believe.
Independence (in logic/mathematics)(describing the property of Euclid's postulate within geometric systems): A statement is independent if it cannot be proven true or false using other basic rules in the system—meaning you can't derive it from the other assumptions.
P≠NP(as used in computer science and mathematics): A famous unsolved question asking whether problems that are quick to check are also quick to solve. Most computer scientists believe they're different, but no one has proven it yet.
Technical difficulty(contrasted with independence): A problem that is hard to solve with current methods but could theoretically be solved if we were smarter or had better tools.

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