The surprising bit is not that it explains the observations that it was modelled on, but that it explains further, unexpected observations that were unknown at that time.
It's not that maths is so great, or even that models are great, but that we were able to model some essence of a phenomenon, beyond what we witnessed.
This happens not because it's a model (you can have as many models/theories as you like), but because we selected that model, usually due to beauty/parsimony/elegance - which amounts to some version of Occam's Razor: to not make a model more complex than needed to explain the observations. (do not multiply elements unnecessarily; given different models that explain the observations, the simplest one is most likely the truest of them). http://en.wikipedia.org/wiki/Occam%27s_razor
The real puzzle (if it's a puzzle) is why Occam's Razor works so well...
It's not that maths is so great, or even that models are great, but that we were able to model some essence of a phenomenon, beyond what we witnessed.
This happens not because it's a model (you can have as many models/theories as you like), but because we selected that model, usually due to beauty/parsimony/elegance - which amounts to some version of Occam's Razor: to not make a model more complex than needed to explain the observations. (do not multiply elements unnecessarily; given different models that explain the observations, the simplest one is most likely the truest of them). http://en.wikipedia.org/wiki/Occam%27s_razor
The real puzzle (if it's a puzzle) is why Occam's Razor works so well...