I'd guess (*guess*, not *know*, since I'm not a brain scientist) that the brain processes involved for calculating several moves ahead in chess and for mentally calculating with numbers are the same or at least similar. (I'm not very good in both :) Otherwise I don't see much that chess and math have in common ...
Chess=Math?
I'd say it has more in common with computer programming.
I'm a sloppy programer, my methods can be inefficient, but I'm very good at thinking logically, and how each stage will come together before I've even declared a variable. Just like my chess, its not accurate, glaring errors, but seems to get the job done.
I suppose knowing more than one programming language is a bit like knowing more than one opening. The mid game is like programming the guts, and the end game is like debugging, do one bit poorly and you're stuffed.

Being an mathematics student still in college, majoring in math education, I would say its more like chess teaches analytical skills that are used in not only math, but in other subjects as well, like the analysis of a story and its comcpts. In math, I would liken solving a proof in number theory to finding the right chess move, or sequence of moves, to play, because math like chess, one move implies another. All this being said, I'm not a chess student, but I will say, I have learned something from the game that i use in places other than the chess board. Bronstein said that chess is art, but to me math is my art, I can see its beauty, even if others can't, which is why i'm also an education major, I would love to be able to enlighten others to see what i see.
geometry,calculation,logic,intuition,surface area(owning more space), intelligence, nerdiness, memorization, pattern recognition, subtraction(how much more time does he have?), telling time(at 2:00 game and have that philly cheese steak in my fridge.), numbers, force, computers, arithmetic(4 minor pieces for a queen? not too bad!), creative thinking, algebra (how do I isolate the variable?), etc...