Reading Ian Ayres Book : Super Crunchers. Subtitled : 'Why Thinking by Numbers is the New Way to be Smart'. Steven Levitt, the coauthor of Freakonomics, last year's sort of how-to use quant methods to solve odd problems book, did something similar. I liked Freakonomics ... some of the examples are excellent ... but there was little background to the solutions, and I came away having a hard time understanding their depth and robustness.
Levitt is an economist, so his solutions are by their nature more idealistic ... addressing some form of 'homo economicus' that does not exist. Surprisingly Ian Ayres is in addition a lawyer, but his quant econometric background shows up in his also excellent examples. Levitt did not give you enough detail of what was done. I also come away with the impression that each solution is a tour-de-force, that needs special powers. Ayres makes the mistake of claiming that things are easier than they seem. His first set of examples, based on web date-matching site systems, is based on using various kinds of regressions to match people. He makes a very good case of why these kinds of approaches, using increasingly available mega data bases, can be used to generated classifications that are useful for all sorts of problems. He only hints at the fact that these methods can be harder than they appear.
As a quant guy I cringe a bit at both approaches. One giving no clue as to the underlying methods, the other not revealing that they do require rigorous methods. Bottom line: Super Crunchers is the more compelling argument, it sets up an optimistic view of how to solve tough problems by leveraging them with data. Ayres also systematically covers a number of useful methodologies that should be understood by all problem solvers. So if you only read one book, I suggest Super Crunchers, it can empower you with some powerful problem solving ideas.