This is one more post on the Hamming series about how to select your research career topics.
It takes courage to think about important unsolved problems. (Excepting of course the officially canonized problems, such as Hilbert’s, Fermat’s Last Theorem, P = NP, …). But the solutions that made a difference were to problems that were not even recognized as such!
Today my post will be a bit more high-level than usual. Most of us select scientific topics without paying much attention to overall strategy (i.e., which ones may produce the most benefit).
On this, the best piece of writing I have found is Richard Hamming‘s famous essay “You and Your Research” (which is a transcription of a talk he gave at bell labs, e.g., here, and here), Richard Hamming suggests that you ask yourself three questions:
“If you do not work on an important problem, it’s unlikely you’ll do important work. It’s perfectly obvious. Great scientists have thought through, in a careful way, a number of important problems in their field, and they keep an eye on wondering how to attack them.”