I beg to differ. Case in point: type classes, the Monoid type class, and Monoids as the mathematical concept; all well understood, proofs of their existence and properties are stated exactly, and when implemented by a compiler behaves exactly as expected when the program is executed. This is precisely what people mean when they say "abstraction is the essence of progamming"...
... when they understand what abstractions are and use a precise definition.
Unfortunately there exist many programmers in the world who do not use precise definitions and don't know how to state mathematical laws or invariant properties of relations. They too use the word "abstraction" and they often mean... whatever it is they mean. It differs from person to person and is often used when they're waving their hands and trying to make a point.
Update: The overwhelmingly vast majority of programmers don't think about integer representations and how arithmetic is implemented these days; some do and that's fine, but the software world continues to ship vastly complex programs and systems without having to care about it and everything still works. That's abstraction at work.