I always thought of myself as good at math, but I had an unexpectedly hard time in required freshman calculus courses en route to a CS degree. I think the sourc

I always thought of myself as good at math, but I had an unexpectedly hard time in required freshman calculus courses en route to a CS degree. I think the source of all of these paradoxes is that math is too broad a thing to be simply good or bad at. The objective in first year calculus seemed to be to practice basic techniques until they became rote. If you were an engineer, you'd have much more calculus to do and the early stuff was like learning to tie your shoes. I didn't encounter any really mind-bending concepts (I actually had to retake some calculus I originally took in high school and placed out of); the problem was that I couldn't do the problems fast enough on the tests, and I had to devote way more energy than expected to practicing doing them fast, which felt sort of like learning to play a musical instrument -- training muscle memory so the mind didn't have to be involved. I figured that calculus wasn't for me and I stopped after I met the degree requirements. My point is that different scenarios involve different "math." For engineering, math is a hill to climb on the way to the interesting part. For CS, math is not about learning math per se, it's about learning to prove things and think rigorously. For math majors, it's about deep concepts in math itself. You could be good at proofs and bad at adding numbers in your head, and be good and bad at "math" at the same time. Dividing people into good at math and bad at math is pretty meaningless. If you were truly bad at all math, you could probably not function in any job, because everyone needs to do something that could be called math. On the other hand, hardly anyone is just plain good at math, because you would have to be good at pretty much every hard subject that exists (statistics, economics, physics, and so on). If anyone is that smart, there can't be more than a couple of them.