I.e. Learning math is not a pre-requisite, it's a byproduct.

You don't need to know math to program, but as you become a better programmer, you _want_ to tackle more challenging problems - some of which inevitably involve math (and knowledge in general) that you aren't familiar with. To solve these problems, you have to learn as you go and that, as others have noted, is the real hallmark of a good programmer.