This question was posed to me on a networking forum for graduates from the university that awarded my Master's degree. The full question was: "Is managing people and projects an art or a science?"
There are really two questions here, since managing a project and managing people actually are two different things, though they share some skills. Starting with the people managing side though I would say this is in part a science and in part 'intuitive.' I have worked for many 'managers' who work 'by the book,' following all the correct 'rules' and procedures, but are lousy 'managers' because they fail to understand the needs of the people they are managing.
I am often apalled by how many claim to 'know Maslow's Heirarchy' and yet manage i ways that demonstrate that they have failed to understand it at all. I think that, in part, this is because their own personality traits and insecurities actually make them unfit to manage, though they may be highly competent within their own specialist field. This also feeds into one of the reasons I do not, under any circumstances, subscribe to the concept that anyone with a 'management' qualification can go off and manage any discilpine or activity. At some point they will find themselves undermining someone with a vast field of experience and knowledge and attempting to direct that person in the function of their job. This is a major reason for the failure of "Change Management" and many commercial enterrises. It is also one of the underlying problems in Whitehall and the communication failures between Government and People.
The best 'managers' I have encountered are often also the 'leaders' and the difference between a leader and a manager is probably more about style and method than anything else. A good 'leader' knows his people well. He/she recognises they have individual needs and works out how to make those needs part of the corporate fulfilment strategy. Ergo, they establish a system whereby X has a need for recognition or reward, but is unsuitable for promotion for a variety of reasons (Not being able to relate to others needs may be one!) and then finds a way to reward X for doing what they do best in the role they have. An example of this kind of leadership stays in my mind from the occasion I met one of the countries oldest established hereditary peers. Within minutes of meeting, he made me feel completely at ease, had me taking about my work, my position, my family and managed to make me feel I was the most imprtant person he would meet that day. All of it without my ever feeling I was being patronised or that in another situation we could change places. This is all too often absent in todays 'managers' who want to run with the hares today, but be the hound tomorrow and can't understand why this builds resentment.
The second part of your question, Project Management, again requires some 'science' of management since it requires an abilitity to organise, to evaluate and to assess, then to build the Critical Path Process by which the project can be completed on time, on budget and as planned. It requires a lot of people skills in dealing with different discipilnes and it requires clarity of thinking - and it is NOT a team effort. As the old joke says, a camel is a horse designed and built by a committee. Once again some of the worst projects I have worked on were 'managed' by people with no technical background, yet they presumed to 'manage' the project by insisting that each of the technical people involved submit detailed 'reports' at every meeting, yet never read anything more than the 'Executive Summary' and even then patently didn't grasp the importance of some of the details they were inclined to dismiss as 'details we can work out later...' Frequently 'later' is far too late.
By contrast the best projects I have been involved in were led by people with a technical background who were good at assigning a task, allowing the person assigned to get on with it and bring back to the table a detailed proposal for achieving that part of the proposal. They micro-managed where it required it and stood back where it didn't.
This contrasts sharply with the Prince 2 process which, to the best of my knowledge has never delivered a project on time or on budget, though every government 'project' is now required to follow this process. The problem with it is that it requires reports and a range of other 'paper trail' form filling activities which are supposed to ensure adherence to the project outcomes, but this simply adds a layer of bureaucracy and cost without any direct benefit to the project.
I think one of the things we have forgotten or lost in the last forty or so years is that management is a function of a wide range of technical and non-technical activities and it is folly to think that someone trained in office management can transfer to managing the production line of a factory. Likewise in Whitehall, someone who has spent years developing their management skills in - say - immigration - can transfer to a department and 'manage' - say - the fire policy unit with no knowledge or understanding of how or why the professionals in that department wish to develop something in a certain way. It leads immediately to a clash and usually ends in building frustration and confrontation between manager and expert. Maslow Rules!
In conclusion I think 'management' is a much abused term and concept. There is a lot of 'science' to it, but the 'art' lies in the 'manager' being able to 'sell' his/her perception of the corporate 'need' for progress, for teamwork and for the achievement of the common goal to those they manage. As I said earlier, it requires a high degree of intuition and it certainly requires a degree of confidence and security in oneself that many of the 'managers' I have suffered under over the last twenty or so years lacked.
I once encountered a definition of the difference between a Manager and a Leader which said -
"Managers always do things right; Leaders always do the right thing."
I would suggest that if you are managing people or projects you have to know the difference and when to do things right and when to throw away the 'rules' and do the right thing.
I have made it a rule never to blame someone on my staff when things went wrong. Responsibilty always rests with the person in charge, even when it is delegated with a task to someone lower down the food chain of management. If there was a problem in my department or section, I took responsibility and then sat down with the person concerned to find a solution, something my Chief always found difficult because, at the end of the day, the ultimate responsibility was his - and by being completely open with him he found it difficult to do more than acknowledge that I had identified the problem, and found a solution.
Sadly, he was an exception as I discovered working under the 'new regime' in the UK - but that is another story.