Pieri was born in Lucca, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at University of Bologna where he drew the attention of Salvatore Pincherle. Obtaining a scholarship, Pieri transferred to Scuola Normale Superiore in Pisa. There he took his degree in 1884 and worked first at a technical secondary school in Pisa. When the opportunity to teach projective geometry at the military academy in Turin arose, Pieri moved there. By 1888 he was assisting in instructing that subject also at the University of Turin. In 1891 he became libero docente at the university, giving elective courses. Pieri continued teaching in Turin until 1900 when he won a competition for the position of extraordinary professor at University of Catania on the island of Sicily. Von Staudt's Geometrie der Lage was a much admired text on projective geometry. In 1889 Pieri translated it as Geometria di Posizione, a publication that included a study of the life and work of von Staudt written by Corrado Segre, the initiator of the project. Pieri also came under the influence of Giuseppe Peano at Turin. He contributed to the Formulario mathematico, and Peano placed nine of Pieri's papers for publication with the Academy of Sciences of Turin between 1895 and 1912. They shared a passion for reducing geometric ideas to their logical form and expressing these ideas symbolically. In 1898 Pieri wrote I principii della geometria di posizione composti in un sistema logico-deduttivo. It progressively introduced independent axioms: Pieri was invited to address the International Congress of Philosophy in 1900 in Paris. Since this was also the year he moved from Turin to Sicily, he declined to attend but sent a paper "Sur la Géométrie envisagée comme un système purement logique" which was delivered by Louis Couturat. The ideas were also advanced by Alessandro Padoa at both that Congress and the International Congress of Mathematicians also held in Paris that year. In 1900 Pieri wrote Monographia del punto e del moto, which Smith calls the Point and Motion memoire. It is noteworthy as using only two primitive notions, point and motion to develop axioms for geometry. Alessandro Padoa shared in this expression of Peano's logico-geometrical program that reduced the number of primitive notions from the four used by Moritz Pasch. The research into the foundations of geometry led to another formulation in 1908 in a Point and Sphere memoire. Smith describes it as This memoire was translated into Polish in 1915 by S. Kwietniewski. A young Alfred Tarski encountered the text and carried forward Pieri's program. In 1908 Pieri moved to University of Parma, and in 1911 fell ill. Pieri died in Andrea di Compito, not far from Lucca. In 2002 Avellone, Brigaglia & Zappulla gave a modern evaluation of Pieri's contribution to geometry: Giuseppe Peano wrote this tribute to Pieri upon his death: Mario Pieri's collected works were published by the Italian Mathematical Union in 1980 under the title Opere sui fondamenti della matematica.
