Donald Knuth is an elitist. It is not necessary to have a background in mathematics to write software. I taught myself PHP and I certainly don't have any kind of mathematics background whatsoever. It isn't dumbing down as he claims. It's about creating opportunities. If you can code and you can do it well without mathematics, so be it. The math side is for those that want to do research. I work in the real world
There's a lot of jobs for coders who don't know math, but there's a ceiling on how good a programmer you can become.
Fundamentally all programming is research, you have a problem and you need to develop a robust solution on how to solve it.
Sometimes those problems don't involve math, but sometimes they do. You might need to implement a specific calculation (and understand how to verify and debug it), if you have a large data base you need some math for your queries to return quickly. And for any non-trivial problem where you need to design your own algorithm you need to have enough of a mathematical mindset to write it efficiently.
Think of it like race car driving. Driving a race car has a lot of special skills useless for 99% of of driving in a city. But someone who trains with race cars is probably going to be better at that 99% because they push past their limits. And the 1% where those special skills do come in handy they'll see a drastic difference.