Chess and math. What relations are there?

Chess has been around me lately. So is math. They are somehow close friends, but I can't seem to see why. So here's my research so far.

The chessboard is symmetric in main diagonals in terms of its colour. The
chessboard is made of four identical small boards if it is divided by one horizontal
line and one vertical line going through the centre. The set-up position of chess
pieces is symmetric between Black and White. The chess pieces set-up position
on either side is palindrome excluding the king and queen.
The ranks and files are related to coordinates. When a piece is being attacked or
defended, it requires some arithmetic calculations in terms of the number of
attacking and defending pieces and this is the first lesson a child would learn in
counting numbers.

Example:

This is the movement of a horse. A horse can go in "L" shape and can go all the blocks in a chess set.

More to come.