The Importance of Mathematics in Political Decision-making

Mathematics in Politics and Governance. By Francisco J. Aragόn-Artacho and Miguel A. Goberna. Springer Nature, Cham, Switzerland, April 2024. 220 pages, $49.99.

Let me be perfectly clear (as politicians like to say, while often doing quite the opposite): Mathematics in Politics and Governance is not a perfect book. Several things about it—not many, but a few—concerned me. And yet … if I had to select just one mathematics book to take with me on a two-week sea cruise—on a ship with no library of mystery novels to distract me—and I wanted a text that would be challenging, informative, and intimately connected to the real world, this would be the one. Written by Spanish academic mathematicians Francisco Aragόn-Artacho and Miguel Goberna, Mathematics in Politics and Governance offers numerous, quite specific examples (names are named!) of how the disparate worlds of hard-nosed, rigorous mathematical reasoning and soft, hand-wavy policymaking need not be mutually exclusive. To that end, the book is loaded with true-story politics, historical anecdotes, and lots of solid analyses that assume reader familiarity with college-level math.

The text opens with a story about U.S. President Abraham Lincoln. Lincoln admitted that he simply could not understand what it meant to demonstrate something during his early studies of the law; it wasn’t until he mastered Euclid’s geometry that he fully grasped the concept. The authors point out that most politicians typically remain in Lincoln’s earlier, limited state of understanding and only possess a minimal knowledge of mathematics. Of course, there are rare exceptions. U.S. President James Garfield discovered an elegant new proof of the Pythagorean theorem while he was still a congressman, and former German Chancellor Angela Merkel holds a doctorate in quantum chemistry.

At the other end of the mathematical literacy spectrum, Mathematics in Politics and Governance offers numerous examples of politicians who fail to comprehend mathematics (or, depending on one’s level of cynicism, seem to purposefully mislead). In one example, U.S. President Richard Nixon—whom Aragόn-Artacho and Goberna call a “master illusionist”—asserted in a formal speech that “the pace of inflation change is slowing.” As the authors observe, this claim is a subtle diversion from the actual price of goods to the third derivative of prices. Although Nixon was a Republican, the book has no particular axe to grind and we learn that Democratic U.S. President Barack Obama made similar mathematical missteps. Math illiteracy is a nonpartisan attribute.

The application of math to societal problems likely began with the development of geometry; for instance, people presumably needed to re-establish property boundary lines after the annual flooding of the Nile. While that particular example is not in the book, the authors do present an interesting alternative illustration with the ancient Dido’s problem: Given a city to be built on a river’s straight shoreline, what curve of a fixed length (with its endpoints on the shoreline) includes the greatest area? The answer is of course a semicircle, and Aragόn-Artacho and Goberna discuss Jakob Steiner’s famous 1842 proof that uses only simple geometric arguments. They also demonstrate that town planners actually knew about this solution much earlier, as evidenced by a map of the German city of Cologne along the Rhine that is dated to 1800. The semicircle boundary is clearly visible.

From this point on, the book’s math content becomes a bit more advanced. Commentary about various mathematical areas is embedded in specific examples of political scenarios that are generally presented as problems that optimize an objective function by some criteria. These scenarios span a broad swath of human concerns: healthcare, energy pricing, the allocation of scarce resources, and numerous other subjects where policy decisions are routinely made by politicians who may or may not understand the associated analytics. Linear programming and game theory in the context of nuclear war strategy lend themselves to particularly interesting dialogues. It may be asking too much for presidents to be familiar with such esoteric concepts, but we should all hope that several members of their support staff are math literate.

The appeal of Mathematics in Politics and Governance is greatly enhanced by numerous biographical sketches and photographs of the featured mathematicians. Also compelling is the authors’ willingness to comment on some less-than-flattering episodes, such as the 1975 Nobel Economics Prize committee’s outrageous snub of George Dantzig, despite his pioneering work on the simplex algorithm. Even the two men who shared the prize were stunned by the committee’s disregard for Dantzig, and both mentioned their missing colleague in their acceptance speeches. Up to three individuals can receive the prize, so Dantzig’s exclusion felt like a significant rebuff. It thus strikes me as somewhat ironic that Dantzig’s photo is missing from the book. Also missing is any mention of Richard Bellman and dynamic programming. I realize that it is unfair to criticize a small book of only 200 or so pages for not including everything, but Bellman’s omission seems like an oversight.

Finally, one glaring problem—which is particularly irritating because it would have been so easy to avoid—is the complete absence of proper names in an already anemic index. During the copyediting phase, Springer provides software support that automatically generates an index if authors simply submit a list of entries. Why Aragόn-Artacho and Goberna did not include proper names is a mystery to me.

Yet despite these minor grumblings, Mathematics in Politics and Governance is well worth a read. Just take my advice and pencil proper names into the index — the next time you read it and want to look up Dantzig or anybody else, you’ll be very glad that you did!