Tradition recognizes 4 professions: Medicine, Engineering, Accounting, & Law.

People who master these professions possess special abilities. They are able to quickly identify patterns, see the big picture, and understand the details in many areas under the big picture. This combination of big picture thinking and detailed thinking enables them to be problem-solving specialists. Not only are they able to solve problems when they arrive they are also often able to anticipate problems and create solutions before the problems actually arrive.

Mastering a profession: Is that an art or a science or some combination of two?

Before answering that question it's necessary to understand the role discipline plays in the professions.

Consider the medical profession.  When you visit a doctor do you want the doctor's advice to be backed by disciplined thinking? Do you want the doctor to analyze your symptoms, identify a pattern, understand the root cause of the problem, and present a remedy/solution? Those are the things most people want when they visit the doctor. Very few want their doctor to be speculative, offering inventive solutions and illustrating innovation or creativity. Most people want medical solutions that are tried-and-true. That's their expectation. People expect their doctor to have a disciplined education, a disciplined process for diagnosing symptoms, and a disciplined process for prescribing remedies. These are the expectations of the vast majority of clients of the medical profession.

Consider the engineering profession. When an engineer designs a road you will drive on what is your expectation? When an engineer designs a bridge you will cross what is your expectation? When an engineer designs the building you will work in what is your expectation? Typically people just want a road to function properly so they can use it to get from point A to point B as quickly and safely as possible. People expect those things from bridges too. However, often they expect more from bridges. They want bridges to have aesthetic appeal. Similarly, people set a higher standard when it comes to buildings. Often people want buildings to have not just functional value, they also want aesthetic value. These are the expectations held by people who seek engineering work.

While some professions can be said to be mostly science, engineering is a blend of art and science.