Author Description
Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth century ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecher, and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics.
Menrva's Summary
THE THESIS
This volume investigates the evolution of mathematical foundations from the late eighteenth century through the early twentieth century, specifically tracing the transition from Kantian philosophy to the formalist program of David Hilbert. William Bragg Ewald, a scholar of mathematical history, curates a comprehensive collection of primary source documents to illustrate how foundational concepts in algebra, geometry, and set theory were established. By presenting these seminal texts, the work argues that modern mathematics is the result of a continuous, interconnected dialogue between philosophers and mathematicians across several generations.
THE SCOPE MAP
What You Will Find
- Primary source translations of foundational works by mathematicians including Bolzano, Riemann, Hamilton, Dedekind, and Poincare.
- Original English translations of significant writings by Gauss, Cantor, Kronecker, and Zermelo.
- A thematic organization covering the development of algebra, geometry, number theory, analysis, logic, and set theory.
- Historical narratives that contextualize the links between nineteenth-century mathematical ideas and the formalist approach of David Hilbert.
THE AUTHORITY PERSPECTIVE
Experts and historians of mathematics recognize this collection as a foundational resource for accessing difficult-to-find primary source material in reliable translations. Readers frequently note the academic density of the prose, which is intended for students and researchers interested in the rigorous history of mathematical thought.
Page Count:
712
Publication Date:
2007-10-12
Publisher:
Oxford University Press
ISBN-10:
0198505361
ISBN-13:
9780198505365
Philosophy
Reference
Logic
Mathematics
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