Legacy of Mario Pieri in Geometry and Arithmetic

by Ivor Grattan-Guinness One of the distortions in most kinds of history is an imbalance between the study devoted to major figures and to lesser ones, concerning both achievements and influence: the Great Ones may be studied to death while the others are overly ignored and thereby remain underrated. In my own work in the history of mathematics I have noted at least a score of outstanding candidates for neglect, of whom Mario Pieri (1860-1913) is one. A most able contributor to geometry, arithmetic and mathematical analysis, and mat- matical logic during his rather short life, his work and its legacy are not well known. The main reason is that Pieri worked 'in the shadow of giants,' to quote one of the authors 1 of this volume. Born into a scholarly family in Lucca, Pieri was educated briefly at the University of Bologna and principally at the prestigious Scuola Normale Superiore, in Pisa; under the influence of Luigi Bianchi (1856-1928) he wrote there his doctoral dissertations on al-braic and differential geometry. During his twenties came appointments in Turin, first at the military academy and then also at the university, where he fell under the sway of Corrado Segre (1863-1924) in algebraic geometry, and Giuseppe Peano (1858-1932) in the foundations of arithmetic, mathematical analysis, and mathematical logic. From 1900 to 1908 he held a chair at the University of Catania before moving to Parma, where he died from cancer.A list of errata can be found on the author Smith's personal webpage.