economics is applied mathematics...
economic models are usually mathematical in principle... but
rarely if ever accurate
The sad fact is that those who get loads of high praises in
public are those who derive "practical maths" and claim
it to be applicable in everyday life.
Once you delve into the subject proper, you'll see beyond the
maths and see instead the foundations upon which the maths were
built on.
It is not entirely correct to say that the basic principles are
mathematical. Stuff like Arkelof's lemon markets, which is an
impressive paper on asymmetrical information, uses some maths to
prove that signalling (eg. phdguy getting phd to prove himself)
improves the economy and individuals and helps explain why we are
obsessed with certs and all. But the basic intuition is practically
common sensical and the maths is a justifying component, not the
main building block.
THIS is also economics, but sad to say, hardly one that the
public sees. Freakonomics is another load of bull-crap.
Part of the reason why people have come to associate economics,
which really is a study of HUMAN BEHAVIOUR, with maths, is also due
to the society's unhealthy obsession with the financial market, and
its constant drive to find EQUATIONs that would derive the "best
result".
Understandably, many of them failed simply because the
assumptions (much maligned stuff also) obviously do not hold in the
real world. A good example is the famous now discredited
Black-Scholes formula.
Does that mean Economics is useless? It doesn't. Anything you
learn should be done so with a pinch of salt. That's all.
Assumptions do not make it entirely unrealistic. It allows us to
home in on intriguing factors. Most papers (that publics do not
see) make their points, but cover their backsides because the
writers know when the papers fail. The public sees the point, but
not the cautions the writers usually include.