This is a good question. Marketing is surely an art and a science. Let's go with science first. Marketing is an science, because good marketing requires the work of analyzing people's tastes, spending habits, and essentially what they want. This is not easy to do. This work has to be systematic and analytical. You may even have to crunch some numbers. For this reason, marketing can be very scientific.
Marketing is also an art, because you are dealing with people's tastes. In other words, what you want to do is to reach their imaginations, thoughts and feelings. Good arts moves people, it lingers in the hearts of people, and can even change them. There is almost a spiritual quality. Art can do this. In light of these two points, the best marketing is both scientific and artistic.