"In Modeling Risk, The Human Factor was Left Out." (New York Times, November 4, 2008) This article argues that, while the financial crisis has been blamed on the mathematical models of financial engineering, "the larger failure, [experts] say, was human - in how the risk models were applied, understood and managed." There is a good analysis of the role credit-default swaps played in the current situation, and a brief mention of the computer credit-scoring models that replaced human judgment in approving mortgages.
One of the people quoted also touches upon the difficulty in quantifying factors like "complexity, transparency, liquidity and leverage." In addition, a report by the Fed suggests Wall Street analysts "correctly predicted that a drop in real estate prices of 10 or 20 percent would imperil the market for subprime mortgage-backed securities", but severely underestimated the probability of this happening. (By now, errors in estimating probabilities are nothing new.) The article has many more nuggets of wisdom, which I will let you discover for yourself, but I'll end with this excellent quote by Columbia University Emanuel Derman: "To confuse the model with the world is to embrace a future disaster driven by the belief that humans obey mathematical rules."
"Bernanke's Models, and Their Limits." (New York Times, October 30, 2005) This article states that Bernanke, who was at the time the nominee to replace Alan Greenspan at the Fed, "has focused on the use of mathematical models to set monetary policy" and "has written repeatedly about ways of using mathematical models of a dauntingly complex economy to set monetary policy." His philosophy, according to the article, is "that the central bank should use a model, not just hunches, to decide about interest rates and the money supply."
A late economist at MIT, assessing one of Bernanke's models published in the literature, commented that "the interesting issue is not the gentle part of the trip but rather when it crashes;" the model apparently did not account for the fact that credit and liquidity could dry up. (And this was 2005.) But another professor, this time from Berkeley, supported Bernanke: "He of course understands that even in normal times, the best model is just a guide."
"The Anti-Macroeconomics Roar Grows Louder." (New York Times, June 3, 2009) Steven Levitt, of Freakonomics fame, argues that macroeconomics isn't about "writing down fancy mathematical models." Part of the problem, he says, is a lack of macro data, which makes it hard to measure the skills a good macroeconomist is supposed to have. He writes: "The single easiest way to make a mark in a modern macro paper is to solve a problem that is really, really hard mathematically. Even if it is not that relevant to anything, it is seen as a sign that the author has “impressive skills,” which is enough to get a job — and even tenure sometimes — at top universities."
While mathematical models are hopefully more relevant in real life than Levitt implies, he voices a valid concern, which is also illustrated in the chasm in my field between "hard operations research" (which is mathematics-driven) and "soft operations research" (which is non-mathematical). You can read more about that in OR/MS Today, especially "Taming Hard Problems with Soft O.R." (April 2009), "The Case for Soft O.R." (April 2009) and "Who's SORiors now?" (June 2009) The battle goes on.