The Royal Society published a report on Science, Technology, Engineering and Maths impact on the service sector. They devote a whole chapter (3) to financial innovation, see Hidden Wealth. The report was covered in the FT.
I was contact by the Royal Society in mid-July, this is (their) summary of what I said:
1. The financial crisis was not a homogeneous events; some institutions did (much) better than thers.
2. The root of the problem is in banks mis-pricing assets. When pricing assets the banks were relying on mathematical models. Some banks had "engineered" their own models, others "bought in" models (either by buying "off the shelf" or by hiring individuals from the innovating banks). Banks who treated models as "black boxes" have done far worse than those that had a reputation or developing their own.
3. Many quants (the majority ?) have a background in physics and engineering (there is a factoid that the majority of engineering graduates from top UK universities go into finance rather than engineering - you could check this. Similarly The City is the largest employer of physics PhDs). They understand deterministic systems but only have a rudimentary understanding of modern probability theory (the majority of maths graduates are in a very similar position, I spoke to a maths teacher who had a degree from Glasgow who told me he had not done probability since he was 16).
4. Financial economics developed in the late twentieth century using relatively straightforward maths. The models it produced are "too simple" (see pp 4-12 in "An Engine, Not a Camera"), but are "elegant".
The physicists / engineers were given a simple framework in which deterministic approaches appeared to give definite results. This approach is related to the "Crash of 87" and "When genius failed" in '98.
5. Throughout the industry a belief emerged that maths, "rocket science" removed risk. In the 1990s, mathematicians began to investigate financial models and re-evaluate them. A more rigorous approach to financial economics revealed the naivety of the assumptions that led to the simple models.
6. Because the financial mathematics community is small and peripheral in British science, it lacks authority , and the theory (from the mathematicians) became disconnected from the practice in industry.
7. In Europe, because they approach probability as a branch of analysis rather than from the perspective of statistics, there seems to have been a better appreciation that simple models that fitted data were inadequate. This is a subtle point. The issue is whether the "quants"
really understand stochastic systems. Does the UK education system (schools to universities) produce the volume of people with (basic to advanced) skills in probability and statistics. There is a view that France & Germany are better at this, as demonstrated by the large number of continental scientists and engineers employed in London banks.
8. The credit crisis provides a tangible example and introduction to a wider problem about our poor understandings of complex and stochastic systems. The concern is that many of the global challenges we face involve these sorts of systems. Is our science up to the task?
9. There is a basic competency issue but also a need to develop new mathematics able to describe what Lord May describes as "ephemeral" systems, but in other areas relating to fundamental maths.