Everything we do, in the large (or at a macro level), involves problem solving and, and in the small (or at a micro level), involves the scientific method. Whatever we do, it involves problem solving and the scientific method around a problem and solution!
Problem solving entails progressive analysis of the problem and synthesis of a solution. The scientific method involves analysis, which entails forming and testing hypotheses, and the scientific method involves synthesis, which entails refining hypotheses based on the results of the tests, thus, ultimately moving toward a solution to the problem.
This is what iterative and incremental development is all about! This is what Scrum’s “inspect and adapt” is all about!