Seeing as I view "nerdy" subjects is obscure technical knowledge, while "geeky" subjects are those more closely related to entertainment; the former can be useful, the latter is almost entirely just for fun. As such, that narrows down the qualifiers to mathematics and computer sciences.
And to answer that little predicament, the answer is surprisingly simple -- mathematics.
Pure mathematics is also referred to as "formal logic", and beyond the lowest levels doesn't involve any numbers at all. Mathematical proofs can be astoundingly complex, and can involve a large amount of lateral thinking; Fermat's Last Theorem [http://en.wikipedia.org/wiki/Fermat%27s_last_theorem] more or less speaks for itself. It also has a very close relationship to physics, and at the highest levels the difference between the two is all but non-existent.
Computer sciences on the other hand? While it certainly can be quite complex, it's also very limiting; it's mostly about problem-solving (I think), getting the computer to do what you want it to than figuring out how to do something new. Very useful for doing repetitive computations quickly, but for the most part it's just doing the pure mathematics faster (and usually with less accuracy; definitely "good enough" for the vast majority of people, but pure math only accepts exact accuracy).
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And for one of the greatest expressions of nerdiness ever conceived.... The Prisoner of Benda Theorem [http://en.wikipedia.org/wiki/The_Prisoner_of_Benda]
