In answer to your metacomment. The financial crisis is a strong indication that, yes financial firms can be terrible at math. Luckily, they have friends who can bail them out with taxpayer money when they fail at math.
Big Finance knew it was hustling rubes, and then was able to ride the Gub'mnt Gravy Train when it became unsustainable.
In brief, models were constructed of the complex behaviors of packages of loans - CDOs. These models, trained under benign market conditions, did not account adequately for correlations that might make all their component loans default at once.
You can elaborate the story with a lot of context and granular detail, but the core of the crisis did have a strong element of "bad mathematics" -- bad mathematical modeling.
For more, see: https://www.maths.ox.ac.uk/system/files/attachments/1000332....
and references therein.
The paper concludes that while there were deficiencies with the modelling method (as there are with any model), input manipulation was at greater fault than inherent failures of the model itself.
"These results support the arguments of Donnelly & Embrechts[4] and Mackenzie & Spears[12], that Li and the Gaussian copula were not to blame for the Crisis...Instead it appears that the gaming of the model beyond its original assumptions, the outsourcing of CDO risk management to credit rating agencies, and the failure to perform holistic risk assessment seem far more to blame."
"The simulation results in this paper show that it is more important to focus on parameter estimation than copula choice. This leads to the observation that when it comes to mathematical financial modelling: in order to avoid a disaster, the cooking is more important than the recipe."
My point is that mathematical models were indeed being used and followed in this case, and that the issue really was with overextension of the model, and not just generic volatility of any market, as claimed by the GP comment.
>poor mathematical modeling of the statistical properties of collateralized debt obligations (CDOs) was the underlying cause of the bottom falling out of that market.
The model is hardly to blame when falsified inputs yield poor results.
I'm not "blaming the model" - probably everyone recognizes that all models have limits.
I call your attention again to the point of my original comment - the GGP comment was claiming that the best mathematicians in the world could not have foreseen the kind of conditions that caused the 2008 market failure. I'm arguing that it was possible, and that it was clear (mostly in retrospect) that the model assumptions were being violated most promiscuously.
In fact, the real reason I chimed in is that I think this crisis was a really awesome example of the power that quite abstract mathematical constructs have over our lives. I felt that point was missed in the generic comment about "who could have known" that kicked this thread off, and I sort of wanted to rescue that underlying mathematical issue.