During my earlier years as a postdoc at MIT, and as a junior faculty member at Stanford, I had developed a heuristic in carrying out research. I would look at how everyone else was tackling a certain problem and find the core central thing that they all agreed on so much that they never talked about it. Then I would negate the central implicit belief and see where it led. This often turned out to be quite useful. For a year or so I worked with Tomas Lozano-Perez on algorithms to find collision-free paths of industrial robot arms as they moved through a cluttered work space to minipulate parts, or weld, or spray-paint. I realized that everyone who was working on these algorithms was concentrating on how the obstacles in real space appeared as obstacles in a higher-dimensional mathematical space of motor control -- everyone concentrated on how to represent these higher-dimensional obstacles. I decided that instead of representing where the stuff was, I would try representing where the stuff wasn't. In my algorithms there was to be a representation of where it was safe to move the robot arm, and within those constraints they would try to plan a path to get the desired job done. This turned out to provide an immediate payoff and led to some practical algorithms where none had existed before.
(via Tom Carden, thanks!). Which sounds like Richard Feynman's approach too.
More How we work.