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 20th century. This book is the first in a series of three volumes that are dedicated to countering that neglect and comprehensively examining Pieria (TM)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 Pieria (TM)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 axiomatizationsa "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 knowledgeof logic and advanced mathematics, and it requires no specialized experience in mathematical logic or the foundations of geometry.

Alfred Tarski (1901-1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic and universal algebra. Throughout his career, he taught mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now. This self-contained book focuses on Tarski's early contributions to geometry and mathematics education, including the famous Banach-Tarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy. These themes are significant since Tarski's later research on geometry and its foundations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations and much newly uncovered social background of these works written during Tarski's years in Poland. Alfred Tarski: Early Work in Poland serves the mathematical, educational, philosophical and historical communities by publishing Tarski's early writings in a broadly accessible form, providing background from archival work in Poland and updating Tarski's bibliography. A list of errata can be found on the author Smith's personal webpage.

Alfred Tarski (1901-1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic and universal algebra. Throughout his career, he taught mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now. This self-contained book focuses on Tarski's early contributions to geometry and mathematics education, including the famous Banach-Tarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy. These themes are significant since Tarski's later research on geometry and its foundations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations and much newly uncovered social background of these works written during Tarski's years in Poland. Alfred Tarski: Early Work in Poland serves the mathematical, educational, philosophical and historical communities by publishing Tarski's early writings in a broadly accessible form, providing background from archival work in Poland and updating Tarski's bibliography. A list of errata can be found on the author Smith's personal webpage.