One comes to see beauty in the field and develops an intuition for the kinds of structures that exit in abstract mathematics. You have to have good computational skills to get to this point, but for those who do, it is a rewarding field of study. Mathematics is developed and precedes applications, sometimes by many years. Rules and procedures are not all there is to mathematics. Like any other art, math has its own sense of aesthetics.
Mathematical proofs require ingenuity and creativity and are lasting works of art.
When one reads a classic mathematical proof for the first time, such as Cantor's argument that the rational numbers are countable, you will be struck by the simplicity, ingenuity, and beauty of the mind that crafted the proof.