[Satam]

To verify the answer you'll always need to trust the technical implementation that's doing the computation. Doesn't matter if it's our brains or a calculator.

Somewhere between "it's always wrong" and "it's always right unless the bits got flipped by cosmic rays" we deem the accuracy to be good enough.

[RandomLensman]

Disagree, the theory exists outside of any specific technical implementation (every single one of those could be wrong, for example). You might not be able to verify something without being subject to random errors, but that doesn't mean the theory itself is subject to random errors.

Any implementation (or write down etc.) of something can have errors, but the errors are in the implementation and do not give rise to uncertainty outside of the implementation. There is no uncertainty as to what the sum of two integers should be (within the usual mathematics).