The Legacy of Mario Pieri in Geometry and Arithmetic de Elena Anne Marchisotto

The Legacy of Mario Pieri in Geometry and Arithmetic

Elena Anne Marchisotto

James T. Smith

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.

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"This book portrays Pieri as an individual of exceptional ability, who responded to the influence of many of his contemporaries; and they, in turn, acknowledged the quality of Pieri’s work. In fact, there is a sixty-page section in the first chapter containing biographical sketches of the lives and work of almost a hundred such mathematicians. Moreover, the general historical analysis and interpretative commentary, whilst focussing particularly upon the achievements of Mario Pieri, also extends to many of the general mathematical developments of his era. The book is very thoroughly documented and contains an abundance of photographic portraits. It culminates with an extensive bibliography and an accurately compiled index, and it will undoubtedly appeal to those concerned with the history of ‘modern mathematics’, as well as being of interest to the general readership specified by the authors." —MAA Reviews

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The Italian mathematician Mario Pieri (1860-1913) played an integral part in the research groups of Corrado Segre and Giuseppe Peano, and thus had a significant, yet somewhat underappreciated impact on several branches of mathematics, particularly on the development of algebraic geometry and the foundations of mathematics in the years around the turn of the 20^th century. This book is the first in a series of three volumes that are dedicated to countering that neglect and comprehensively examining Pieri’s life, mathematical work, and influence in such diverse fields as mathematical logic, algebraic geometry, number theory, inversive geometry, vector analysis, and differential geometry.
The Legacy of Mario Pieri in Geometry and Arithmetic introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints, placing his life and research in context and tracing his influence on his contemporaries as well as more recent mathematicians. The text also provides a glimpse of the Italian academic world of Pieri's time, and its relationship with the developing international mathematics community. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations—his postulates for arithmetic, which Peano judged superior to his own; and his foundation of elementary geometry on the basis of point and sphere, which Alfred Tarski used as a basis for his own system.
Combining an engaging exposition, little-known historical information, exhaustive references and an excellent index, this text will be of interest to graduate students, researchers, and historians with a general knowledge of logic and advanced mathematics, and it requires no specialized experience in mathematical logic or the foundations of geometry.

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Introduces readers to Mario Pieri’s career and his studies in foundations, from both historical and modern viewpoints First English translations, along with analyses, of two of his most important axiomatizations - his postulates for arithmetic; and his foundation of elementary geometry on the basis of point and sphere Combines an engaging exposition, little-known historical notes, exhaustive references and an excellent index

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