If you are one of these people, let me try to disabuse you of these notions. Your mathematical abilities are actually not that much better than most economists (if they are better at all). You will have to spend a lot of time acclimating to the subject and the path to actually making contributions will be long and difficult. In all likelihood, there are very few (perhaps zero) off-the-shelf models or techniques in physics (or engineering, or chemistry, …) that will produce meaningful economic results. High-tech methods and approaches will be valued only if they can be described in simple, direct ways.
Chris House ignores the post-1970′s explosion of research on asset price modeling, which employs mathematical and physics methods such as heat diffusion.
The theory of random walks, stochastic calculus, risk neutral pricing, and the Black Scholes option pricing formula are possibly among the most significant findings of the past 100 years in the field of economics, because:
-practical applications (the option and futures market is huge, and they all involve these formulas).
-inspiring subsequent research (if you go on arXiv, the original work done in the late 60′s and 70′s is still spawning tons of research to this day on asset pricing and asset price dynamics, whereas other economic fields seem to have stagnated).
-being mathematically empirically sound (meaning it’s a complete theory that does an adequate job describing reality), and is was groundbreaking in that the result was unexpected and answered a nagging question about how to price option contracts without having to define a drift variable.
-introducing mathematical and statistical rigor into the field economics, a trend that continues to this day. Many economics papers since the 60′s employ complicated statistical methods. Stochastic models have now become indispensable to all modern finance and economics research.
Research in neoclassical economics, although active up until the 70′, has stagnated. The problem is not that the math is too complicated, but that there are simply too many variables for such models to be of any practical use, and making small adjustments to any one of these variables can dramatically change the outcome. You can’t have a ‘theory’ if there are, say, only two equations and dozens of ill-defined variables. This is problem because gathering data, in and of itself, is an imprecise science, so dubious data inputted into a dubious model compounds the mistakes. The Black Scholes model, however, only has a single ill-defined variable, the volatility. Behavior finance and prospect theory also has the same issue, where there are simply too many parameters for the models to be useful. Prospect theory says people are disproportionately averse to losses, but so what. The research stops there and doesn’t lend itself to further inquiry.
The most active areas of research in economics right now is applying physics and high-end mathematical methods to model asset prices. I predict advanced math and physic methods will play an increasingly important role in economics research. Just like how physics in the 20th century was subsumed by the most advanced of math, so too will economics.