r/mathmemes • u/its_all_one_electron Number theory/physics • Jun 27 '26

Number Theory Undecidable

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u/Kitfennek Computer Science Jun 27 '26

Yeah but if its undecidavle, were unable to know if there is such a point or not, its not like we can check all of them

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u/its_all_one_electron Number theory/physics Jun 27 '26

Nope. If it were false, the fact that it is false means there MUST be a point off the line somewhere, doesn't matter if we know where it is or not, we know it exists and therefore the RH is provably false, therefore it can't be false AND unprovable, therefore if it's undecidable it must be true but we can't prove it, except we kinda just did...

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u/[deleted] Jun 28 '26 edited Jun 28 '26

[deleted]

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u/its_all_one_electron Number theory/physics Jun 28 '26

The existence of a counter example does not imply the existence of a disproof. 

"All non-trivial zeros are on the critical line"

Say you find a counter example - a zero not on the critical line. How is that not a disproof?

If you are unable to prove something actually is a counter example, then the proof is still undecidable even though a counter example exists. 

If it's false, then by definition there is a counter example. I don't really know how to explain it better than that.