The Mathematics of the Gods and the Algorithms of Men: A Cultural History

Zellini (A Brief History of Infinity), a University of Rome math professor, provides an elegant but frustrating treatise about his discipline’s larger implications. Posing the question “Are numbers real entities?” he traces the ceaseless search for “the ultimate reality” of math, from the early Greeks, for whom “numbers were the last defense of an unfolding existence,” to Bertrand Russell, under whose scrutiny rational and irrational numbers, created as abstract mathematical tools, “inherited the actual and real nature of physical concepts.” However, discoveries about the inability of numbers to fully capture reality led in the early 20th century to a “crisis in the fundamentals” of math, further leading to the development of the algorithm as a “new kind of abstraction” allowing for “large, automatic calculations.” But beyond explaining that this proved useful in the digital revolution, he does not show how his discipline’s evolution influenced broader developments in world culture and history. At the most, he shows how mathematical concepts intersected with philosophy, such as L.E.J. Brouwer’s understanding of the human thought process as a temporal sequence similar to an iterative calculation. While mathematicians may savor this work, Zellini’s rendering of math as “cultural history” will leave most readers unconvinced. (May)