There are many places where mathematics and the world of government intersect. The book under review manages to find a way to touch on nearly all of these topics. There is an interview with former Israeli Prime Minister Ehud Barak, and a discussion of Kemal Atatürk's geometry text; optimization for finding shipwrecks, and sample simplex problems; the fight against misleading graphics, but also the PISA mathematics test. Surprisingly, though game theory comes up a bit as expected, there is nothing about different voting systems, and only a passing nod to redistricting/gerrymandering concerns.

The authors acknowledge that different sections require extremely wide differences in background, and suggest that it might be a good resource for illustrating courses with real examples of where mathematics can be useful in these settings. However, the organization is far more by the math, and it is often hard to discern what is a useful technique, what is a toy example far from reality, and where an interesting historical episode begins. (The index is not helpful here.)

To take one example, there is nontrivial detail given of the ellipsoid method for solving linear programs (marked with an asterisk for deeper mathematics), which was significant in the history of the P/NP problem as well as (according to the book) briefly notorious in Cold War politics. But there is not enough detail to actually teach with the example (nor is this the intent, since there are no exercises), and moreover this method is (in the words of a very qualified colleague I consulted) "completely irrelevant" for actual solving of linear programs. So, it's hard to know what to do with this example. Similar issues occur with topics as widely dispersed as activation functions in machine learning and cooperative game theory.

If you have this text in your library, you definitely could seek starting points for discussion on how politics influences who is allowed to do mathematics or why people in government care about it, especially in the first and last chapters. Also, careful reading can mine it for possible connections, such as how linear programming could be used for Iberian energy market regulation or separating planes can help decide the authorship of The Federalist Papers. But be ready to draw upon your own expertise, and other resources, to finish that task.

Karl-Dieter Crisman is Professor of Mathematics and Computer Science at Gordon College in Massachusetts. His primary research is in the mathematics of voting, but he also has significant interests in open source software, math history, and connections of all three to faith questions.