>> Although it did leave me wondering for a moment: Am I actually "good at
>> math"? Or am I just good at following directions?
>
>    Perhaps it could be compared to computer algorithms: If you are given
> a computational problem for which you need to create an efficient algorithm,
> how good are you at coming up with such an algorithm?

To be honest, I've yet to discover a computational problem which hasn't 
already been solved 25 different ways (usually before I was even born). 
The art of writing efficient computer programs appears to be the art of 
figuring out where the **** all these algorithms are written down. 
Because, let's face it, any algorithm that I can invent will be several 
complexity classes worse than what the greatest minds of the 20th 
century could think up.

>    If you routinely can devise efficient algorithms for given computational
> problems, then one could say that you are good at algorithmic programming.
> Likewise I'd say that if you routinely can solve mathematical problems,
> devise mathematical formulas to describe things and so on, you are good
> at math.

Well, when I was a teenager I wrote my first ray tracer. Which doesn't 
sound that impressive, until you realise that I have to figure out how a 
ray tracer actually *works* in the first place, using nothing other than 
the documentation for POV-Ray. (This is *before* Warp added the SDL ray 
tracer, I should point out... That would have made it significantly 
easier, obviously.)

In short, I had to deduce that you perform ray intersection tests by 
solving simultaneous equations. (Usually if you want to draw a shape, 
you want a parametric representation of it. But POV-Ray seems to talk a 
lot about equations rather than formulas, which was a big tip-off.) And 
then I had to work out how you actually solve simeltaneous (non-linear) 
equations. (No, I didn't know how to do that.) And then I had to shift a 
bunch of algebra around to make it happen. (That, arguably, is just 
blindly applying rules. Mathematica(tm) could have done it just as 
capably as me.)

FWIW, I was utterly astonished when I ran the program and it actually 
freaking *worked*!

>    Anybody can calculate 2+2 or even solve an equation, in the same way
> as anybody can write a "hello world" program or a program which calculates
> the sum of a list of numbers, but that doesn't make that someone *good* at
> math/programming.

Actually, I suck at arithmetic. (Fortunately, I have a computer to do 
that for me...) What I consider myself to be modestly good at is 
mathematical reasoning.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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