These iterative failures are, at a very deep level, the essence of creating new knowledge, and are therefore inseparable from the job. If you can’t imagine going to bed at the end of nearly every day with a nagging feeling that you could have done better, academe is not for you.
The academic workplace is a really unusual one. For instance, it’s one of the few places to work where you’re nobody’s boss and nobody’s your boss. It really suits some people — I’m one. But lots of other people feel otherwise: it’s too slow, too lacking in immediate feedback, too content with the way “it’s always been done.” And a lot of those people have great things to contribute to mathematics and don’t fit in the system we’ve set up to pay people to do math.
So while the ideal career path leads from graduate school to a tenure-track position, the one you will more likely find yourself on leads from graduate school to a series of short-term positions that will require you to move — often.
is less true in math than in many other areas, but still kind of true. And it works badly not just for people who temperamentally hate moving, but for people who want to have kids and have a limited childbearing window.
McCormack is right: without catastrophizing, we should always be trying to give our Ph.D. students as real a picture as possible of what academic life is like, and not just the advisor’s life with tenure at an R1 university. Lots of people will still happily sign up. But other people will think more seriously about other great ways to do mathematics.