I'm having a little difficulty wrapping my head around Lie theory (I'm a computer scientist, so perhaps that's to be expected).
Specifically, considering the following definition from Wikipedia for the exponential map. What is the significance of the identity element? I think that this could be to do with the derivative of exp being equal to the function itself, but I'm not quite sure if I'm on the right track here. Any nudges in the right direction would be highly appreciated.
"Let G be a Lie group and $\mathfrak{g}$ be its Lie algebra (thought of as the tangent space to the identity element of G). The exponential map is a map $\exp\colon \mathfrak g \to G$ which can be defined in several different ways."