Like many others here, I hope to someday become a professor. I've heard that it's very, very difficult and competitive in pure math, and I thought I would come here to ask your opinions.
For those of you that have finished your PhDs, where have your classmates ended up, and how many have left academia? My fear is that if I stay in academics, I will be stuck in temporary postdocs and lecturing positions for the rest of my life.
How much does the prestige of the graduate school matter in job hiring? Is there any hope for the hard-working-but-not-outstanding types of students from mid-tier schools, or will I have to rely on luck and hope that my research area becomes a hot topic when I start looking for jobs?