To the other comments here I have to add - proofs (in math, science, computer science, any subject area..) never reflect absolute reality, but rather just your view of reality or the parts of reality that you have chosen to model.
So the reality of your "proven" program will never 100% match the reality of it running on hardware or some other software context than you anticipated. Let's call this the Hacker's Postulate...
As for math specifically I think this is a very deep and interesting philosophical tangent to go down.
So the reality of your "proven" program will never 100% match the reality of it running on hardware or some other software context than you anticipated. Let's call this the Hacker's Postulate...
As for math specifically I think this is a very deep and interesting philosophical tangent to go down.