I think standardized exams like the GRE (Graduate Records Examination) are onto something when they test the verbal, mathematical, and analytical capabilities of potential graduate students. I think most good programmers are people who would have high analytical scores in such exams, with mathematics being much less relevant. Analytical people are often those who understand the intuitive and qualitative aspects of mathematics, but who have trouble with quantitative methods, which require much more work before they become intuitive.
It is, however, useful for programmers to have a good feeling for arithmetic.
The limits on how far you can go in programming depend a lot on the direction you are going in. As a linguist, I see this problem a lot in the way mathematicians and computer scientists are taught to think; they tend to look for statistical solutions to problems better-solved by someone with a more thorough understanding of the cognitive processes underlying human language. This is just one example from my area, but I'm sure there are many others that require much more knowledge about the system you are trying to implement rather than about abstractions taught to most mathematics and computer science students (probably many engineering fields, biology, etc.) Luckily for these students, there is still a lot that can be represented in terms more familiar to them.
So, if you're bad at mathematics, be good at something else. It will pay off in the end.
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