The Physics of Wall Street covers the history of math from Bernoulli through Mandelbrot and how we arrived at modern algorithmic trading.

http://www.amazon.com/The-Physics-Wall-Street-Unpredictable/...

It doesn't cover the actual math. Not sure if there's a good book for that.

For people who enjoy this video, I recommend this book:

http://www.amazon.com/The-Physics-Wall-Street-Unpredictable/...

Simons is mentioned but he refused to be interviewed for the book. However, it covers the history that leads up to the current day.

It's interesting that Simons' fund is pure algorithmic trading. No one decides that a position is too big, for example. Humans are out of the process after they write the algorithms.

In my opinion, there are probably some persistent quirks and patterns in human minds and computer programs (also written by humans) which may not be fully exploited by most market participants in some markets (esp. Emerging and Frontier markets). One well-known pattern is Momentum trading, which is also a basis of Market Crash prediction model by Prof. Sornette, with a history of several accurate predictions. [1]

> “a few funds that at any given moment outperform the indexes.” But over the years, he explains, their performances invariably decline..

There are a few hedge funds that, over decades, still beat the market. Medallion Fund, according to public knowledge, consistently generates above-market returns, never had a down year, and even returned 80% in 2008, when stock markets all over the world crashed. Its trading model is a highly guarded secret. It does not even let outsiders invest (with exceptions for a few).

The fund belongs to Renaissance Technologies, founded by a renowned Mathematical Physics professor, Jim Simons, and employs many PhDs in Physics and Math. (This book writes about it in fair detail. [2])

[1] How we can predict the next financial crisis: http://www.ted.com/talks/didier_sornette_how_we_can_predict_...

[2] The Physics of Wall Street: http://www.amazon.com/The-Physics-Wall-Street-Unpredictable/...

FYI The Physics of Wall Street gives a lot of reference to what type of trading James does, and chronicles a lot of James's history! The book also goes into a lot of the history of these types of traders! It is an insanely interesting read!

http://www.amazon.com/dp/0544112431