The fact that chess programs play at such a high level by definition means that chess can be expressed in logic and mathematics. Therefore, solely from that perspective, chess equals mathematics.
Huh? Please explain further, as I don't understand how mathematics correlates to the power computers have running through various lines and the speed with which they do it.
Nevermind the fact that ducks can be expressed as birds, but that doesn't mean that ducks=birds.

I don't think this is true. If you train a child in chess for 10 years but don't teach him to count or do simple mathematics he could be a good chess player but a lousy mathematician.
The theory is that if you can be good at one without the other than the reverse must be true.
However, I would agree that if you are good at one you can be good at the other but they aren't codependent.