You can definitely learn basic levels of programming without getting too deep into the math, enough to put together simple programs that can automate small tasks.

The issue is that math is incredibly important for enterprise level programming, particularly for optimization. Programs you write for yourself can be slow, inefficient beasts that hog way more resources than they need. If you wanted to write code as a job though, you'd need to be able to find the line between speed and accuracy, and that can require some complex math.