Of course not. Certainly, you won't be bad at physics or engineering BECAUSE OF your math skills. You NEED math for physics, and both math and physics for engineering, so somebody who is not good at math is more likely to have trouble with physics or engineering.
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No. A lot of physic has to do with equations and math. Physics will be easier if you are good at math. I was for me :)
Because math, physics, chemistry and computer science are not the same things. Just because you're good at using maths doesn't necessarily mean you're not good at applying them. Theoretical and applied mathematics are widely considered very different fields.
Not necessarily.
I don't think so! Long before there were computers (and computer science), there were brilliant physics and engineering students and they obviously were good at math.