It's interesting to complement the last point, "Only geniuses (or cranks) head straight for the grandest and most fundamental problems", with two of Hamming's [0] points:

> When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go.

but also

> If you do not work on an important problem, it's unlikely you'll do important work.

[0] https://www.cs.virginia.edu/~robins/YouAndYourResearch.pdf