Gallager gave a nice concise summary of what he learned from Shannon about how to do good theory work:
- Simplify the problem
- Relate it to other problems
- Restate the problem in as many ways as possible
- Break the problem into pieces
- Avoid getting locked into thinking ruts
As he said, “it’s a process of doing research… each one [step] gives you a little insight.” It’s tempting, as a theorist, to claim that at the end of this process you’ve solved the “fundamental” problem, but Gallager admonished us to remember that the first step is to simplify, often dramatically. As Alfred North Whitehead said, we should “seek simplicity and distrust it.”
I know I’ve read this before, but it deserves a re-read/review every now and then.