Synthetic Philosophy of Contemporary Mathematics

Synthetic Philosophy of Contemporary Mathematics is a unique and unprecedented book, and a much needed one. Fernando Zalamea (Professor of Mathematics at the Universidad Nacional de Colombia) offers a synthetic perspective on the vast spectrum of contemporary mathematics, together with an analysis of the new philosophical problems originating therein. The book makes available to the inquisitive non-specialist the conceptual transformations and intellectual orientations of modern and contemporary mathematics, and their significance for speculative philosophical thought. The first part of the text discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and offers an extensive review of how philosophy of mathematics addressed it (or failed to). In the second part, thirteen detailed case studies examine the greatest creators in the field, compiling a map of the central advances accomplished in mathematics over the last half-century. Drawing on these concrete examples, the third part proposes some generic outlines for synthesis. Zalamea's book serves as a conceptual introduction to mathematical themes rarely discussed outside specialist circles, and as a critical lens by means of which today's mathematics may aid us in the configuration of new cultural perspectives. If analytic philosophy was forged in the fires of set theory and classical logic at the beginning of the twentieth century, then today, at the dawn of the twenty-first, and around the scaffolding of category theory and the logic of sheaves, it is time for a complementary, synthetic philosophy to be built.