Giuseppe Peano

Peano is the secret ancestor of the machine age. Born on a farm near Cuneo in 1858 and trained at the University of Turin, he spent his career performing a single act of foundational audacity: taking the most familiar thing in human cognition—the counting numbers—and showing that all of it could be generated from a handful of symbols and a handful of rules. His 1889 pamphlet Arithmetices principia, nova methodo exposita stated five axioms from which the entire infinite tower of arithmetic follows, and in doing so made the founding gesture of the automatable view of thought. Everything downstream of his axioms—every claim that intelligence is “just” computation, every formal language a computer parses, every dream that reasoning might be fully mechanized—is a descendant of his discovery that a rich domain could rest on a sparse, explicit base. He also gave reasoning a written language: his symbolism for set membership, implication, and quantification became the notation Bertrand Russell adopted and built into Principia Mathematica, the book that