I am no expert but I would think economics is very much a social science based on statistical mathematics. It relies very much on human habits viewed as a whole.
As such it is not an exact science where mathematics can give a precise answer to economical problems.
Physics on the other hand is an exact science though this old idea has been somewhat shaken with the advent of quantum mechanics.
But of course non exact sciences like economics and medecine affect people's life just as much as exact science. So it is unfair to glamorise one against the other.
Interesting post. Thanks!