David Hilbert’s Lectures on the Foundations of Geometry 1891–1902


Book Description

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study and contain many reflections and investigations which never found their way into print.







Alfred Tarski


Book Description

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.




Automated Deduction in Geometry


Book Description

This book constitutes the thoroughly refereed post-workshop proceedings of the 9th International Workshop on Automated Deduction in Geometry, ADG 2012, held in Edinburgh, UK, in September 2012. The 10 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement from the lectures given at the workshop. The conference represents a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction; the scope of the ADG 2012 moreover has been expanded to cover topics in dynamic geometry.




The Foundations of Geometry


Book Description

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.




Imagined Civilizations


Book Description

Roger Hart debunks the long-held belief that linear algebra developed independently in the West. Accounts of the seventeenth-century Jesuit Mission to China have often celebrated it as the great encounter of two civilizations. The Jesuits portrayed themselves as wise men from the West who used mathematics and science in service of their mission. Chinese literati-official Xu Guangqi (1562–1633), who collaborated with the Italian Jesuit Matteo Ricci (1552–1610) to translate Euclid’s Elements into Chinese, reportedly recognized the superiority of Western mathematics and science and converted to Christianity. Most narratives relegate Xu and the Chinese to subsidiary roles as the Jesuits' translators, followers, and converts. Imagined Civilizations tells the story from the Chinese point of view. Using Chinese primary sources, Roger Hart focuses in particular on Xu, who was in a position of considerable power over Ricci. The result is a perspective startlingly different from that found in previous studies. Hart analyzes Chinese mathematical treatises of the period, revealing that Xu and his collaborators could not have believed their declaration of the superiority of Western mathematics. Imagined Civilizations explains how Xu’s West served as a crucial resource. While the Jesuits claimed Xu as a convert, he presented the Jesuits as men from afar who had traveled from the West to China to serve the emperor.




What is a Mathematical Concept?


Book Description

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?




The Argument of Mathematics


Book Description

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​




Establishing Quantum Physics in Göttingen


Book Description

Quantum mechanics – the grandiose theory that describes nature down to the submicroscopic level – was first formulated in Göttingen in 1925. How did this come about and why is it that Göttingen became the pre-eminent location for a revolution in physics? This book is the first to investigate the wide range of factors that were pivotal for quantum physics to be established in Göttingen. These include the process of generational change of physics professors, the hopes of mathematicians seeking new fields of research, and a new understanding of the interplay of experiment, theory and philosophy. The other books in the four-volume collection address the beginnings of quantum physics research at Copenhagen, Berlin, and Munich. These works emerged from an expansive study on the quantum revolution as a major transformation of physical knowledge undertaken by the Max Planck Institute for the History of Science and the Fritz Haber Institute (2006–2012). For more on this project, see the dedicated Feature Story, The Networks of Early Quantum Theory, at the Max Planck Institute for the History of Science, https://www.mpiwg-berlin.mpg.de/feature-story/networks-early-quantum-theory.




The Cambridge Companion to Frege


Book Description

Offers a comprehensive and accessible exploration of the scope and importance of Gottlob Frege's work.