good memory == smart?

EDIT (AS OF TUESDAY @ 9 PM): apparently i don't know euler's formula, either. i suppose it's all the more reason why i should be impressed by those who do.

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today's calc ii class was a review/refresher on how to manipulate taylor series, and i informed my students that certain series are good to remember.

then one student asks about the homework. to start that particular problem, i begin writing down the Taylor series for sin x about x = 0 .. or maybe it was e^x; i forget.

what i do remember is turning around, ready to start an explanation, and there is already a hand up. preparing for the worst, i call on the owner of the raised hand.

"you knew the taylor series of that function, off the top of your head?"

"er, yeah."

"wow."

"well, write it down enough times, and it tends to stick."

then someone else asked if we need to know that series for the exam. i think i caused a minor tumult by saying "yes, and these three others."

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what surprised me was .. well, the surprise. i mean, it's just a formula, and it's a well-known series. it's like knowing that the harmonic series diverges.

i dare say that any mathematics major or grad student worth his or her salt would know the taylor series for e^x off the top of their head.

would you be impressed if you met someone who remembers:

the quadratic formula?
or the pythagorean theorem?
or that sin(π/6) = 1/2?

i might be a little delighted if someone did know euler's formula:

e^iπ - 1 = 0.
e^iπ + 1 = 0.

for instance, the guy from xkcd knows it. great comic, that one.