3/8 Turning Specific Problems to General Problems 

3/8/2021 lu

You should do your job in such a fashion that others can build on top of it, so they will indeed say, ``Yes, I've stood on so and so's shoulders and I saw further.'' The essence of science is cumulative. By changing a problem slightly you can often do great work rather than merely good work. Instead of attacking isolated problems, I made the resolution that I would never again solve an isolated problem except as characteristic of a class.

Now if you are much of a mathematician you know that the effort to generalize often means that the solution is simple. Often by stopping and saying, ``This is the problem he wants but this is characteristic of so and so. Yes, I can attack the whole class with a far superior method than the particular one because I was earlier embedded in needless detail.'' The business of abstraction frequently makes things simple. Furthermore, I filed away the methods and prepared for the future problems.

-Richard Hamming, You and Your Research (1986)

In principle, this seems good but it is difficult to figure out how to actually do it. 

Actual application of the principle finally clicked today: a friend asked me if I have any productivity hints and instead of writing an email I decided to write a post; with a simple modification it becomes possible for my answer to help hundreds of people instead of one.