They chose instead to develop two parallel themes. In one, they use mathematics—algebraic-looking stuff with formulas, equations, and numbers that are used to count things—to analyze Sudoku. In the other, they use Sudoku to explain the true nature of mathematics (or perhaps I should say mathematical thinking, since they obviously do not cover much of the vast content of modern mathematics).

So rich is the Sudoku puzzle, that it is perfectly adequate to achieve that second goal. The authors show vividly that mathematics is really about the power of abstraction, the push to explain as much as possible in the most compact form possible. Numbers and arithmetic are a part of that enterprise, but there is a lot more besides. "Taking Sudoku Seriously" is an excellent vehicle whereby devotees of the puzzle can come to understand the nature of mathematics. Whether it will work in the other direction, by turning mathematicians into Sudoku players, is another matter.