As aforementioned, math is thought to be important to be a good programmer. Does that mean, just learning formulas make you a good programmer?
Per my experience it is the ability to observe situations, and decide based on the observation that is needed: you see a case and pose a question about it. And look for answers to solve it. If you can break it into parts as means of solution it is the better. But it is still in the realm of logic.
The ability to think logically, and looking at problem with the attitude of solving it is very rare in society... in terms of percentage. Even between smart and intelligent people there are ones that perceive faster or slower.
Math happens to be a field that people don't understand and hold confusing. While the logic people using their reasoning "work with it" until they understand it. Therefore often the ones not having understood math, tend to associate the two fields with each other. While they are not.
Being able to observe and decide can make you also a good leader, a good cook, and so on. But it is eventually your decision and motivation that makes you a programmer.