Onto a more personal note. I have always loved mathematical puzzles and problem solving. Computer science involves hands-on problem solving with quick feed back. Problem solving techniques, abstractions and the varied ways which people approach problems are fascinating. I enjoy exploring new abstractions, testing their power in enabling people to understand, communicate about, analyze and solve problems.
Problem solving involves understanding and creativity.
One must be open to entirely grasp a problem with all its subtleties. One must also creatively come up with approaches and solutions to problems. These are important activities for a leader. A good leader does not simply convince people to follow. A good leader is also a good listener.