[kxyvr]

This is an important point, but I don't think it's insurmountable for a broader group of people.

Though technically not required, I think it helps to know a good deal of mathematical theory as well in order to check properties that should hold, which helps in tracking down subtle bugs. In my experience, tracking these bugs is a royal pain in the ass and writing good tests for these properties is tedious. Even then, there's a lot of funny stuff that goes on. One of my favorites is that it's possible to take the Choleski factorization of an indefinite matrix in some situations. That means it's not safe to use a Choleski to check for whether or a not a matrix is positive definite for mission critical functions:

https://scicomp.stackexchange.com/a/26223

But, anyway, mostly I contend that writing these algorithms is extremely tedious, so there's not that many people with the patience. I also still maintain that there's room for contribution here. Although most often these routines are written in C and Fortran, the parallel tooling for these languages is less sophisticated than that of modern languages. I've been wondering whether a language like Rust would make it easier to code and parallelize some of these algorithms.