Order and Unity
A central aspect of Islam is the Unity that binds the Islamic community together. Unlike the structural separation that characterizes Christianity, the Muslim world is remarkably cohesive. This of course, can be seen in the utter similarity
between Arabesque artwork from very different geographic regions. In fact, the similarities are so pronounced, that it is sometimes difficult for experts to tell where a given style of Arabesque comes from. The reason for this is that the science & mathematics that are used to construct Arabesque artwork are universal. So this, along with Islamic Divine Law or Sharia, come together to form the glue that binds the Umma or Islamic Community together into a coherent whole.
Therefore, for most Muslims, the best artwork that can be created by man for use in the Mosque, is artwork that displays the underlying order and unity of nature. The order and unity of the material world, they believe, is a mere ghostly approximation of the Spiritual World (which for many Muslims is the place where the only True reality exists). Discovered geometric forms, therefore, exemplify this perfect reality because God's creation has been obscured by the sins of man.
In fact, Sufi Muslims believe that there is no distinction between the spiritual and material worlds. And that the reason we cannot experience the Spiritual world, is that there are 'veils of concealment' that shield us from the perfection of the Spiritual world. They therefore work to lift these veils, in order to become one with God while they are still on Earth. One of the ways that Sufi Muslims try to do this, is to use the Arabesque in depictions of the world.