The history of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a history of ideas, mainly ideas that emerged from mathematical logic, an obscure and cult-like discipline that first developed in the 19th century. Mathematical logic was pioneered by philosopher-mathematicians, most notably George Boole and Gottlob Frege, who were themselves inspired by Leibniz’s dream of a universal “concept language,” and the ancient logical system of Aristotle.

Mathematical logic was initially considered a hopelessly abstract subject with no conceivable applications. As one computer scientist commented: “If, in 1901, a talented and sympathetic outsider had been called upon to survey the sciences and name the branch which would be least fruitful in [the] century ahead, his choice might well have settled upon mathematical logic.” And yet, it would provide the foundation for a field that would have more impact on the modern world than any other.