Alfred Tarski: Early Work in Poland-Geometry and Teaching

by Andrew McFarland, Joanna McFarland, James T. Smith, Ivor Grattan-Guinness

Overview

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.

Product Details

ISBN-13:	9781493951178
Publisher:	Springer New York
Publication date:	09/22/2016
Edition description:	Softcover reprint of the original 1st ed. 2014
Pages:	499
Product dimensions:	7.01(w) x 10.00(h) x (d)

Table of Contents

1 Tarski’s first paper.- 1.1 Introduction .- 1.2 Item 1 below (nearing completion).- 2 Papers on equidecomposibility of polygons.- 2.1 Introduction.- 2.2 Item 2 below (nearing completion).- 2.3 Item 6 below (old translation, needs redoing).- 2.4 Item 8 below (old translation, needs redoing).- 2.5 Exercise 31pc in item 11g below.- 3 Papers related to secondary teaching.- 3.1 Introduction.- 3.2 Item 4 below (meeting report).- 3.3 Item 7 below (on circles, nearing completion).- 3.4 Extract from Item 9 below (textbook).- 3.5 Remainder of item 11 below (exercises).- 4 Assorted contributions.- 4.1 Introduction.- 4.2 Item 3 below (on insurance).- 4.3 Item 5 below (abstract on truth).- 4.4 Item 10 below (Lukasiewicz abstract on definitions).- 4.5 Item 12 below (contributions to discussions).- 5 Bibliography.- 5.1 Introduction .- 5.2 List of Tarski works published since the Collected Works.- 5.3 List of biographical books and articles.- 5.4 List of summaries of Tarski’s scientific work.- 5.5 References for the present book .- Illustrations.- Young Tarski (frontispiece).- From the first paper .- From the 1924 paper.- Something from one of the teachers’ journals .- Index.

Editorial Reviews

The volume is richly illustrated with photographs, reproductions of artwork, copies of documents, and mathematical drawings. … the book will be warmly welcomed by readers interested in the history and philosophy of logic. Moreover, its many fascinating and informative commentaries on the publications it contains, on the people connected with the publications, and on the relevant social and political events in Poland during the pre-war period serve to make the volume of potential appeal to a wide spectrum of readers.” (Steven R. Givant, Mathematical Reviews, ams.org, January, 2016)

“This work sheds new light on mathematicians’ understanding of Tarski and his work. As a scholarly contribution, it provides translations of many of Tarski’s publications, especially those dealing with geometry and teaching. … Throughout the text, the editors serve as guides who provide relevant fascinating historical details, biographical asides for many logicians and mathematicians and thorough documentation, commentary, and references as necessary. This work is a gem. … Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty.” (J. Johnson, Choice, Vol. 52 (7), March, 2015)

“With its focal point being the life and work of Alfred Tarski, this big book provides an almost an encyclopaedic account of mathematical life in Poland in the period 1920 to 1945 … . one’s motivation to proceed through the extensive amount of material is enhanced by the liveliness of its presentation. In short, it should appeal to many readers and could form a reference work for those interested in the history of early 20th century mathematics.” (P. N. Ruane, MAA Reviews, January, 2015)

From the Publisher