I've seen an number of papers focusing on the mathematical side of things. While I'm not a PL researcher, it does seem to me that math is the universal language and it seems reasonable to focus on that rather than non-sense concepts like objects.

How would we mathematically represent usability?

By capturing relations. If we define an algebra it will have certain properties (eg commutative, associative). You don't think twice when writing a physics equation on how to factor, compose, or compute a value. It comes naturally from the rules of algebra.

In category theory we might have different categories. Some might instruct the compiler and programmers that the function obeys certain rules when applying. It could be trivial to parallel or perhaps it specifies a strict sequencing for computation. Following Haskell research, you can really see the evolution as people find more useful generalizations (which in the end, has made things simpler!)

can you provide empirical evidence to support your theory?