Purpose Of Mathematical Formalism: Incomprehensibility
But not so in academic neoclassical economics, particularly not at the "advanced" level. There the idea seems to be to make it as incomprehensible as possible. Everyone who has taken such courses knows what I'm talking about. The advanced mathematical formalism used there make the theories much more incomprehensible, yet at best they do nothing to advance the real world analysis and often it is worse than that, as theories are adjusted to enable them to be mathematically formalized. For more on this subject see my post "The Real Problem With Non-Austrian Economics".
So why do they do it? In part it is because of the delusion that the use of advance math somehow makes it more "scientific", even though no one has ever been able to point to anyway in which it has enabled us to learn more about anything else except...well, advanced math.
The Free Exchange blog at The Economist today reveal another function:
"The maths may even serve a filtering function, by making those with a tenuous grasp of the subject matter less likely to directly cite the research (out of fear of saying something stupid). Instead, they may consult acadmemic experts for comments"
In other words, the purpose with making it incomprehensible is to ensure that people will think that they're stupid because they can't understand papers that were made deliberately incomprehensible. This in turn will make people think that the people who expressed themselves in an incomprehensible way are really smart, and that only they can have an opinion on economic issues.
It's a fraud, of course, which is used to conceal the deficiency in grasping the actual subject matters of economics by many of these academic neoclassical economists.