[dmm]

Psychology isn't mathematically formulated either. Is it science? Perhaps an Austrian economist would argue that economics is more closely related to psychology than physics.

I have seen several mathematical "proofs" that not only god exists but that he is catholic. Is that science?

What does the artifact of being mathematically formulated have to do with something being science?

[philwelch]

Psychology (at least contemporary research psychology) is based on empirical research and judicious use of statistical techniques; Austrian economics is based on philosophical handwaving. Psychology involves observation and allows for an element of surprise; Austrian economics, at least since the days of Rothbard, involves coming up with moralistic arguments for libertarianism. (The early Austrians were important in the history of economics, but being an Austrian economist today is like being a Freudian psychologist today; people do it, but one has to look askance at such a person.)

[borism]

of course math is not the only ingredient needed to do science, but it's something you can't do without. If your theory is based on "self-evident axioms" that nobody is allowed to challenge, what you've created is a cult or religion, not scientific branch.

behavioral economics uses quite a lot of math alongside psychology.