Off course they can mix together. For example, the art of physic or mathematics is to create as simplest equation as possible. One professor once said that the nature like simple and beautiful equations. I would like to agree with him.
Art is full of science. Music is applied physics. Color is applied physics. Many knitters use mathematical formulae to create knitted art. All creation works together, so there is no hard line between art and science or philosophy or any other human pursuit.
Art requires intuitive, creative interpretation. So does science. They are also both proven in the application. Art by producing itself and science by producing proof of the new interpretation through experimentation. They are not diametrically opposed. They are so much alike that they overlap.
Science and art were mixed during the Classical Age and during the Renaissance and the Enlightenment. The compartmentalization of every little discipline, each to be hoarded by "professionals", is a relatively new concept. Scientists need to possess abstract thought from which to generate ideas. They aren't mathematical robots, but are people who sometimes have to create, invent, and imagine concepts that others may not grasp. Science and religion are two opposing forces. Science requires generating an idea and constantly testing that idea to prove or disprove it. Religion is based on believing one person without ever questioning what that person says in the name of faith. Often, religious beliefs do not accept proven laws of science.