Quote: "I'm trying to find out if you can be a programmer scientist. My maths is terrible, but I can achieve a lot with a computer program"
If you can create software, I would argue that your maths isn't terrible. You might be too hard on yourself.
Your calculus or algebra might be terrible, but I would argue your discrete math ability would be much better than average.
I would also argue that programmers are engineers. And by definition, are people who are adept at applying scientific and mathematical knowledge to solve a problem.