Donald Knuth on pursuing a PhD:
A PhD is awarded for research, meaning that the student has contributed to the state of the world’s knowledge. That’s quite different from a bachelor’s degree or a master’s degree; those degrees are awarded for a mastery of existing knowledge. (In some non-science fields, like Art, a master’s degree is more akin to a PhD; but I’m speaking now about the situation in mathematics and in the sciences.) My point is that it’s a mistake to think of a PhD as a sort of next step after a BS or MS degree, like advancing further in some academic straight line. A PhD diploma is another animal entirely; it stands for a quite different kind of talent, which is orthogonal to one’s ability to ace an examination. A lot of people who are extremely bright, with straight A+ grades as undergraduates, never get a PhD. They’re smart in a way that’s different from “research smart.” I think of my parents, for example: I don’t believe either one of them would have been a good PhD candidate, although both were extremely intelligent.
It’s extremely misleading to rank people on an IQ scale with the idea that the smarter they are, the more suitable they are for a PhD degree; that’s not it at all. People have talents in different dimensions, and a talent for research might even have a negative correlation with the ability to tie your own shoes."
Donald Knuth is considered the father of the analysis of algorithms, better known as the author of the multi-volume The Art of Computer Programming, and recipient of the ACM Turing Award (informally considered the Nobel Prize of Computer Science.)
H/t to this great recompilation of Knuth on work habits, problem solving, and happines.