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The Legacy of Mario Pieri in Geometry and Arithmetic

Authors: Marchisotto, Elena Anne, Smith, James

  • 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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eBook 117,69 €
price for Spain (gross)
  • ISBN 978-0-8176-4603-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 155,99 €
price for Spain (gross)
About this book

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 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.

Reviews

"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


Table of contents (6 chapters)

Table of contents (6 chapters)
  • Life and Works

    Pages 1-122

  • Foundations of Geometry

    Pages 123-156

  • Pieri’s Point and Sphere Memoir

    Pages 157-288

  • Foundations of Arithmetic

    Pages 289-329

  • Pieri’s Impact

    Pages 331-371

Buy this book

eBook 117,69 €
price for Spain (gross)
  • ISBN 978-0-8176-4603-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 155,99 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
The Legacy of Mario Pieri in Geometry and Arithmetic
Authors
Copyright
2007
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4603-5
DOI
10.1007/978-0-8176-4603-5
Hardcover ISBN
978-0-8176-3210-6
Edition Number
1
Number of Pages
XIX, 494
Number of Illustrations
67 b/w illustrations
Topics