>> ...and then I spend 2 hours drawing squares and cubes, and shifting 
>> algebra around to painstakingly derive [a special case of] the 
>> binomial theorum from first principles. The euphoria of finally 
>> figuring out the hidden pattern is topped only by the frustration at 
>> discovering that somebody else already figured this out - several 
>> thousand years ago.
> 
> Actually, I kinda like the idea of *knowing* that a certain formula, 
> derived by someone else, is correct, and that I am not simply taking it 
> on faith.

Well, it's not so much that. Obviously I suck at math and there are 
several centuries (if not millennia) of mathematicians far more clever 
than me to check it. It's more that I'm curios to know *why* it works.

(For example, if you have a group of size X, it has subgroups of every 
size that is a factor of X - including 1 and X itself. I still don't 
completely understand why, but it's still cool.)

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