Even before the financial crisis, there has always been a surprising number of ex-physicists who find their way to graduate study in economics. It could be that many of these math-physics people have simply concluded that they no longer like physics and are interested in economics instead. (Moreover, the job market for economics Ph.D’s is much better than the job market for physics Ph.D’s.) I suspect however that some of them are here because they have some incorrect perceptions about the field. A student with a mathematical-physics background could easily convince himself that he has superior mathematics abilities than typical economists and superior statistical and computational skills than most economists. He might go on to conclude that, as a consequence of his superior mathematical and computational abilities, he should be able to enter economics and start contributing quickly and easily. He might also anticipate that he could easily adapt established models or techniques in physics to study economic phenomena and impress the profession.
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.
Economists are not held back because of a deficiency of mathematical tools and techniques. As soon as I hear a physicist (or a mathematician or whoever) start talking about the need for economists to use “the right mathematical techniques” I immediately think that the person has absolutely no idea what the main problems and questions in economics actually are.
Eric Weinstein for instance has somehow managed to convince himself that the instability of preferences is a huge problem for economics (it’s not) and that the application of Gauge Theory to economics will improve things. Now, I don’t know anything about Gauge Theory but I would be willing to bet that it has virtually nothing to add to economics. If Eric Weinstein has some insight that he wants to share then fine – send it my way and I’ll listen but I’m not going to listen just because the math is difficult. The fact that it’s difficult to understand something does not mean that it is important to pay attention to it. Eric Weinstein might be perfectly well-intentioned but if he thinks that because he knows some fancy mathematics, economists are obligated to grant credence to his work, he is sorely mistaken.
As another example, take Mark Buchanan, an ex-physicist who writes the blog The Physics of Finance. Mark seems genuinely interested in economics, particularly macro, but it doesn’t sound like he has a good grasp of the field or of the problems in the field. In a recent column in Bloomberg, he calls for a new age of pluralism in economics:
[M]acroeconomists should learn to speak the languages of other fields, including sociology and psychology, as well as neuroscience and engineering.
An appeal to pluralism like this is usually a sign that the appellant’s ideas are probably not particularly helpful. If you have a good idea, it won’t need affirmative action to get a hearing. True, new ideas and techniques are often met with hostility from the establishment but the reason to listen isn’t that the ideas come from outside the field. The reason to listen (if there is one) is that the ideas are good.
Lee Smolin is yet another physicist who has (at least in the past) waded in to economic waters. Smolin, like all physicists, is clearly very smart and he is asking good questions, but they are the questions of a smart undergraduate. According to Smolin, the “well known fault” of neoclassical economics is the possibility of multiple equilibria and the possibility that equilibria may be “path dependent.” Like Mark Buchanan, Professor Smolin thinks that researchers from other fields (he mentions complex systems as one) are needed to help push economics forward. Also, despite apparently having no direct familiarity with finance, Smolin is prepared to offer his diagnosis of the current state of economics as it relates to the financial crisis:
[T]he whole thing is a disaster if I can say that as an outsider. And it [was one of the reasons] why regulations were lifted on markets and trading through the decades, but when people were making arguments to Congress, to the President’s office that the economy would be better off without regulation, this was the “scientific rationale for it” and led to the very unstable situation of the last economic crisis.
Mathematical fads often pop up in economics but they won’t last unless they have concrete value. Chaos theory was tried briefly but it produced essentially nothing of any value in economics. Neural-networks, agent based modeling, path-dependent equilibria, knot theory … the list of techniques that sound impressive is long but the list of accomplishments associated with these techniques is decidedly quite short.
Naturally, there are counter-examples. The introduction of calculus in economics represented a huge leap forward. Dynamic Programming, originally developed by the mathematician Richard Bellman in the 40s and 50s, is one of the most widely used mathematical tools in economics today. The famous mathematician John Von Neumann  was instrumental in the early development of Game Theory, and so on. However, guys like Alfred Marshal, Richard Bellman and John Von Neumann and don’t come along all that often.
If you are a physicist and you want to work in economics, you had better strap yourself in and prepare for a long challenging path – one that is only worth following if you are really interested in the subject itself. There isn’t very much low-hanging fruit left (as Lones Smith once said, ‘there certainly isn’t any low-hanging fruit left in the middle of the yard!’). Don’t think that after watching Inside Job you can jump in to economics and save the day just because you understand the Navier–Stokes equations.
 For brevity I will use ‘he’ for this post when the gender is unknown.
 I’m not sure I should necessarily classify Von Neumann as a mathematician. It’s a testament to his genius that he is routinely “claimed” by so many fields. He’s a physicist! No, wait, he’s a mathematician! No, wait, he’s a computer scientist! No, wait, he’s an economist! No wait …