Physicist Michael Nielsen has some good advice on problem solving in research. The following is his insight on the skills of a problem solving approach to research:
- Clarity, goals, and forward momentum: Nielsen mentions that being clear about one’s goal and continuing to work towards it is critical.
- Have multiple formulations: Having alternative formations of a problem provides multiple ways to attack the problem. Sometimes, a different way to describe the problem gives new insight.
- Spontaneous discovery as the outcome of self-development: Nielson writes that discovering something new while understanding and exploring some problem is a classic way to solve problems.
- Working on important problems: Nielsen writes that successful problem solvers work on important problems. He identifies various reasons why some one may be hesitant to tackle important problems. The first reason could be lack of self development and tools. The second reason could be that short term goals make him work only on doable small problems. The third reason is simply intimidation. This is especially relevant to PhD students who are reluctant to tackle problems that the best minds of the last century have not solved!
- Committing to work on an important problem: Nielson writes that commitment to work on an important problem is a long term process and requires patience.
- People who only attack difficult problems: In the end, Nielson also warns against just attacking difficult problems. He gives the analogy of pole-vaulting where one should raise the bar gradually.