Comment by hiAndrewQuinn
20 hours ago
This is what I've observed as well. By my own metrics and grades, I was a somewhat bright math minor (near-perfect score in abstract algebra, etc), would have been middle of the pack as a PhD student, may have been below par if I managed to complete the PhD, and almost certainly would have been deadweight as a pure mathematician myself. That's just how the scaling and competitive dynamics have worked out; it's not really something to feel personally bad about, any more than you might feel personally bad about not having the potential to be a competitive figure skater.
EDIT: Uh, actually, it looks like I may have underestimated myself at basically every point here and would have become a basically okay mathematician based on updated priors.
The silly thing about this is that context is everything. I bet it's extremely easy to be a top-tier figure-skater in, say, a small tropical island nation? In a similar way, I very much doubt that you'd really need to be in the top 0.2% of the population to complete a phd. Do you need to be in the top 0.2% of people to compete as a contributor with absolutely everyone else in the whole world at the same time? Well yeah, but at that point the statement is so obviously true that it doesn't mean much.
You're right in a sense, but I took the context we're working in as somewhat of a given based on the title of the post. Our goal is to work, full time, as a professional pure mathematician; that naturally puts us in the labor market for pure mathematicians. We can't know that market exactly, of course, but it's far from arbitrary. We are in competition with other market participants, and we can study their properties and use that knowledge to guide our actions productively - including making the decision to exit the market if that's what makes sense to us.
> Our goal is to work, full time, as a professional pure mathematician; that naturally puts us in the labor market for pure mathematicians. We can't know that market exactly, of course[...]
For what it's worth, my classmates from college who have completed PhDs, based their postgrad career decisions on completely different factors – mostly their families and partners, and whether they're willing to move around (especially to rural areas) to target an extremely shrinking academic job pool.
EDIT: example that came to mind – I had a classmate who postdoc'd at Chicago, who decided to stay in town and work in finance rather than pursue some tenure-track offers at R1s, because his young one went to a prestigious UChicago Lab School and didn't want to uproot her.