Considering the nature of programming, it is difficult to say if it is really science-oriented,an art or an engineering discipline.Broadly speaking,it is easy to view programming as a science subject since it is the heart of computer science which involves the scientific and practical approach of designing computational system using established theories.However, it is interesting to know that it can be seen as an engineering discipline where one is expected to create a new system. you will have to create the design(using UML-class diagram etc),define components(classes, interfaces etc),make prototype(GUI building) and specify and execute tests(using various testing methods e.g white and black box testing).Also just like building a car, a program sub-systems/subcomponents must work perfectly together to achieve the aim of which it was created.More importantly is the fact that it can be an art just like painting where a programmer starts on blank canvas and uses his/her skill to paint a picture.In this case, it involves the mastery of the necessary programming skills, using the appropraite programming tools(IDEs,design patterns,frameworks etc) and unleashing your creativity. Due to the ambiguous characteristics exhibited by "programming", it becomes challenging to categorize it. I would really appreciate valuable insights/contributions to demystify how programming should be conceived as. Thanks....

programming has these strict requirements,
logical reasoning, problem solving, creativity, mathematics and the ability to see ahead and know the result of your decisions before you make them

so you can group it now.

In my opinion programming is a craft that can be learned and mastered like any other vocation. For me a programmer is a software craftsman.