The quantitative schools of investing rely on very high powered mathematics (often drawing on physics and engineering graduate students). They tread on very dangerous ground (often engaging in complex and highly leveraged speculation) and make errors in assumptions about the market conditions upon which the mathematical models they use to invest are based. Fat Tails and Limitations of Normal Distributions describes one common mistake:
Stock market data clearly shows that a normal distribution does not provide a good model of the market. Not every system is defined by a normal distribution – it is common for distributions to be close to normal but there is no reason any system need be. Many statistical tools have as an underlying assumption that the system in question is a normal distribution (therefore to use the tools you need to determine if the system can be classified that way – if not some tools can’t be used).
Crazy as it seems, very smart people continually forget that the markets often experience panics, euphoria, behave in ways that models do not predict, seize up and fail to function… Against the Gods by Peter Bernstein provides a good picture of the chaotic nature of financial market risks. A good book on an example of a mathematical model failure, Long Term Capital Management: When Genius Failed. Another excellent book on financial market chaos is: Manias, Panics, and Crashes: A History of Financial Crises.
I keep thinking people will learn but so far the faith in numbers seems to outweigh the past examples of overconfident failures.