Simple answer; Math makes you fast. Sure, you can google/se/wikipedia your coding problems away, but get enough math done and you won't need to. Believe it or not, the properly trained human brain is faster than google. Moreover the more math you know the faster you will be able to understand the results google/se/wiki gives you, and the less you'll need to drill down to understand what people tell you. In the process of solving your programming problems you'll end up learning math anyway but if you focus on math it will be a far more efficient process.

Your question is kind of like a rock musician asking why they would need formal musical training. Is it possible to be successful without it? Sure. Does it make you much more of a badass if you do go with it? Absolutely.

Slightly more complicated answer - When mathematicians and programmers use the word "solution" (for problems, that is, not equations - ie not "roots") - they mean pretty much the same thing. Learning to solve math problems helps you to learn to solve programming problems.

BTW - and no offense intended to anybody whatsoever - anybody who says s/he is a good programmer but s/he hates math is a Big Fat Liar. What happened was, they got turned off of formal math by a bad hs or college instructor and ever since then they feel like they "aren't good at math". Anybody without a learning disability (ie anybody capable of learning an OO language) is capable of everything up to and including Sophomore Calculus.