You often need to be pretty good at math. But not because you’re “doing math” to write the code.
In real world software systems, you need to handle monitoring and alerting. To properly do this, you need to understand stats, rolling averages, percentiles, probability distributions, and significance testing. At least at a basic level. Enough to know how to recognize these problems and where to look when you run into them.
For being a better coder, you need to understand mathematical logic, proofs, algebra/symbolic logic, etc in order to reason your way through tricky edge cases.
To do AI/ML, you need to know a shitton of calculus and diff eqs, plus numerical algorithms concepts like numerical stability. This is kinda a niche (but rapidly growing) engineering field.
The same thing about AI also applies to any other domain where the thing being computed is fundamentally a math or logic solution. This is somewhat common in backend engineering.
I’m not “doing math” with pen and paper at work, but I do use all of these mathematical skills all. the. time.
I am an SRE on a ML serving platform.
So, I’d argue that “frontend” and “backend” are the default modes of software engineering these days, and that embedded is a more niche field.
That said, if you’re doing encryption code, you’re doing far more advanced math than backend monitoring and alerting.