Imagine that I am a master woodworker, and that I spend years studying ergonomics and techniques of woodcraft and also of painting in order to produce the world's best paintbrush. This is art; the craft of working wood and hair into the form of the world's best paintbrush clearly requires skill and talent and perhaps a bit of luck. Now imagine that you are a skilled painter and use this feat of a paintbrush to create the world's best painting. Everyone who sees it agrees that it is elegant and obvious, that every part of it had to be exactly as it is for it to be this beautiful, for it to instill such feeling of inherent worth in them. This, also, is art; it requires the bringing together of the knowledge of applied painting technique, the use of paintbrushes (the world's best!), knowledge of the effect of canvas texture, and the mixing of paint, possibly right down to its molecular makeup.
As a result of my skill, I am given the title of Master Woodworker. As a result of your skill, you are given Master Painter. But no one is going to call me a Master of Making World's Best Paintbrush, and no one will ever call you Master of Using World's Best Paintbrush. The paintbrush, regardless of all the skill that went into its production, and all the skill that went into its use, is still just a piece of wood with hair attached to it. It is merely a tool for the use of Master Painters. There are many fields of art: Painting, Sculpting, Photography, Woodworking, Performance, etc. but you will never list Paintbrush among them.

Likewise, you will never find a mathematician who specializes in studying Calculus. You can find calculus instructors, and you can find experts in Analysis, but Calculus is not a field of Mathematics. It is merely a tool, and a very specialized tool at that. Being a mathematician doesn't mean being able to solve differential equations. Euclid didn't. The Han dynasty mathematicians who discovered Cavalieri's Principle didn't. Pascal and Fermat didn't. And all of them discovered things we still use today.