Is the Riemann hypothesis true, false or unprovable in ZFC?
MathPhilosophyMathematicsPrime Numbers
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Ṁ501
2026
61%
It is provably true in ZFC.
34%
It is provably false in ZFC.
4%
It is unprovably true in ZFC.
1.2%
It is unprovably false in ZFC.

To be safe I put in all possible pairs {unprovably, provably} x {true, false} even though I know some are not conceivable from the start, but I wasn't sure which ones.

Will resolve to the answer if found one day.

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If I'm not mistaken, one of the things Godel showed with his incompleteness theorems is that things are true in models, not theories. Since ZFC is a theory, not a model, asking whether the Riemann hypothesis is unprovably true or false is meaningless, just like asking "is the continuum hypothesis true or false in ZFC" is meaningless. It's true in some models of ZFC and false in others, which is why it's called "independent" of ZFC.

As soon as ZFC is shown to be inconsistent, both provably true and provably false would need to be resolved as YES, right?

How could it be unprovably false in ZFC? If it's false, there should be a counter-example.

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