As a quant with a PhD. in math this answer is 100% correct. Every sentence really. I read it twice just to make sure I agreed.

The depth of mathematics in quantitative finance **PALES** in comparison to true research level math (including in fields such as stochastic processes and PDEs, which were my fields of study), and even more so today that structured finance is, essentially, no longer a thing and all the pricing models that are needed have been written.

Now it's even more diluted. The jobs that make serious use of Stochastic calc are sparse, and buy side firms just want people who can do linear regression between time series of things they've been researching.

But the academic job market is cartoonish. The US produces something like 1100 to 1400 math PhDs a year, yet there are only <200 tenure track job openings a year. Which people usually get after forgoing even more years of their lives jumping from place to place as Post Docs. The ones that finally land a tenure track gig only do so because of connections, and then have to kiss ass and publish "discoveries" that no one needs to read for 10 years straight, making not much more than the median household, to actually get tenure. There're even more reasons to leave. For one, the pretentiousness of academia as a whole is astronomical.

The best places for actual research and discovery are the national labs. But 1) they're in the middle of fucking nowhere, 2) your adviser needs to have connections with them to give you a good chance to get in, 3) they don't pay that great, 4) because of the rush to build everything in "C++" in the last 20 years development times have skyrocketed and you essentially need to be a software engineer. I say "C++" because truly scalable high performance C++ isn't idiomatic. It's mostly well vectorized C with classes and inline assembly. Give me good ole' Fortran any day of the week