What is the difficulty of landing a tenure track professorship at a top 25 program nowadays? I am considering pursuing a PhD in mathematics (thinking applied or computational) and curious on what the market is like. For example, If I attended a top math program (just say Columbia), what are the chances of landing a professorship at a program like UCLA or UT Austin?
It is very hard.
A few years ago, a professor I had had told me that he advises students to aim to get a job at a school a tier or two below where they went to grad school, as a general rule. The reasoning is simply that there are far too few jobs. How many graduate students are in a cohort at Columbia? Now compare that to the number of new faculty they hire each year.
The math is straight forward: If every university hires one new faculty a year, that means that you need to be (on average) the best at your university to get a job at an equivalent institution. Most universities have more than 10 incoming graduate students. I don’t know how many new faculty top math universities hire on average, but I would be shocked if the answer was greater than 2.