Peano, Giuseppe

(1858–1932)

   The son of a peasant family from a small village near Cuneo in Piedmont, Giuseppe Peano was one of the most important mathematicians of his day. He began his university career in 1876 at Turin, where he would continue to work and teach for the rest of his career. In 1884, he edited and published a new edition of a textbook on calculus written by his professor, Angelo Genocchi, who, with a most unacademic modesty, declared in the preface that most of the revisions and innovations in the book were to be attributed to “that outstanding young man Dr. Giuseppe Peano.” In 1889, Peano published (in Latin) what have since become known as the Peano axioms. These are a landmark in the history of mathematical logic, a field of which Peano, along with Gottlob Frege and Bertrand Russell, can justly claim to be the founder. Russell met Peano at the International Conference of Philosophy in Paris in 1900 and described the encounter as a “turning point” in his life. Russell recounts that in the discussions at the conference, Peano “was always more precise than anybody else” and always “got the better of any argument on which he embarked.” Russell and Alfred North Whitehead’s great work Principia Matematica was hugely indebted to Peano’s groundbreaking ideas. Peano was also responsible for other great discoveries, notably “space-filling” curves in 1890 and innovations in vector analysis and differential equations. Peano devoted many years of his life to working on the huge Formulario Matematico, a giant textbook containing over 4,000 theorems and formulae, which finally appeared in 1908. The book was published in Interlingua, a language Peano had invented whose grammar was based upon a simplified form of Latin. This did little for the work’s international appeal. Peano died of a heart attack in 1932.