I've heard many times that all programming is really a subset of math. Some suggest that OO, at its roots, is mathematically based. I don't get the connection. Aside from some obvious examples:

• using induction to prove a recursive algorithm
• formal correctness proofs
• functional languages
• lambda calculus
• asymptotic complexity
• DFAs, NFAs, Turing Machines, and theoretical computation in general
• the fact that everything on the box is binary

In what ways is programming really a subset of math?

I'm looking for an explanation that might have relevance to enterprise/OO development (if there is a strong enough connection, that is). Thanks in advance.

Edit: as I stated in a comment to an answer, math is uber important to programming, but what I struggle with is the "subset" argument.