Part of the reason why management can be considered both is that it possess critical principles from both domains. On one hand, there are strict rules and measures that guide management. Failure to abide by these rules results in consequences, as in Science. There are tested patterns of behaviors which can lead to the correlation of responses, similar to Science. At the same time, management can be considered an art because while there are principles that guide it, there are also realms where individual creativity and expression will be able to yield conceptions not yet seen or envisioned. The ability to be able to create and interject concepts that lie in what could be in the hopes of making them part of what is can represent where the art of management is present.
Management includes fields such as computer science, political science, operations research, statistics, economics, mathematics, and many more. All of these fields are highly scientific.
Management is the art and science of making people more effective. Doing so takes a certain amount of skill on many levels. The art aspect of it is getting people to be more effective than they were without you, and the science aspect of it is how you actually got them to achieve the goals you wanted them to achieve, or how you were able to get them to reach that level of effectiveness.
Management takes a lot of planning and organization. Goals must be set and there needs to be a systematic plan set in place to get these goals turned into realities. This is very scientific. People need to be pointed in the right direction and monitored for progress.
There are fundamental principles of management that involve labor costs, profit margins, quarterly reports, etc. These elements of management have formulas and procedures that are consistent and reliable and must be applied with a scientific precision.
On the other hand, management involves, most times, the coordination of a team of human beings and their efforts. The human factor is not scientific. Managers deal with personalities, personal strengths and weaknesses, illnesses, family stresses and demands for their workers, and all sorts of other things that can't be predicted or measured with a scientific formula or procedure.
The most effective managers, therefore, are able to find a balance between applying the science while never forgetting that you are managing humans and not machines.
Management is both an art and a science because it is possible to manage in both styles: a number and statistic-oriented that awards the greatest benefits to the percentages, and also relies on personal skills of good-will, feelings, and emotional involvement on the part of the manager.
It is easy to manage on raw numbers alone with marketing, finance, production, and other sectors of the business that just come down to costs versus revenue. On the other hand, the role of the manager is also to make employees feel needed, wanted, and important, otherwise there might not be any employees left in the business to manage. Also, the same thing can be said of other segments such as customers, stockholders, the general public, etc.