For the Greeks it was about philosophy (and religion.)

They believed in a concept of perfection, and mathematics was thought to be the key to learning and understanding perfection. So we have "perfect shapes" and so on and so forth (basically, Pythagoras started math as a religion.)

Their drive to uncover more and more abstract principles is what led to geometry and algebra (eventually) and a lot of other things. The Egyptians were only interested in it for legal things (measurements and weights.)

-- Byrd
Moderator, Hall of Ma'at