The Mathematical Works of Bernard Bolzano [Hardcover]

Steve Russ (Author)

Book Description

Publication Date: February 17, 2005 | ISBN-10: 0198539304 | ISBN-13: 978-0198539308

Bernard Bolzano (1781-1848, Prague) was an outstanding thinker and reformer, far ahead of his times in many areas, including philosophy, ethics, politics, logic, theology and physics, and mathematics. Aimed at historians of mathematics, philosophy, ethics and logic, this volume contains the first English translations of some of his most significant mathematical writings, which contain the details of many celebrated insights and anticipations: clear topological definitions of various geometric extensions, an effective statement and use of the Cauchy convergence before it appears in Cauchy's work, remarkable results on measurable numbers (a version of real numbers), on functions (the construction of a continuous, non-differentiable function around 1830) and on infinite collections.

Editorial Reviews

Review

"The conclusion is clear: no self-respecting library will be without this book. History fanatics may want their won copies. And let's hope that Russ's expectation tht his book will stimulate further work will be fulfilled."
-MAA Online

Product Details

• Hardcover: 728 pages
• Publisher: Oxford University Press, USA (February 17, 2005)
• Language: English
• ISBN-10: 0198539304
• ISBN-13: 978-0198539308
• Product Dimensions: 9.3 x 6.5 x 2 inches
• Shipping Weight: 2.8 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,752,156 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

5.0 out of 5 stars A welcome edition, November 12, 2011

By 

Craig Smorynski (Westmont, IL USA) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: The Mathematical Works of Bernard Bolzano (Hardcover)

Had Bolzano published more of his mathematics, his reputation today would be much greater. As it was, much of what he did was independently reproduced by later mathematicians and he is not placed as highly in the mathematical pantheon as he deserves. This book, which belongs in the library of any college with a pretense of being a university and on the shelf of any mathematician with an interest in the history of the field, is a real eye opener. In the past few years I have become interested, through the works of van Rootselaar, Gericke, and Laugwitz, in Bolzano's foundations of the real numbers, a work left unfinished and marred by errors which gave me the impression that Bolzano understood the foundational problems better than any of his contemporaries, but was too weak technically to carry out the necessary work. Thanks to this book I have revised my opinion. True, he made some errors--like everyone else he did not realise the necessity of uniform convergence for various results, and in his foundations of the real numbers he didn't think things through enough to complete the project. However, he was heading in the right direction and his work on functions, with the construction of a nowhere differentiable function reveals great technical skill.

I would have liked more annotations and explanatory material. Knowing before reading which parts were in error would be a time saver. And I would have thought any Bolzano fan would have relished in debunking Hahn's claim that the proof of the convergence of the geometric series in Paradoxes of the Infinite was "not grounded on anything". These minor faults aside this book is one of my most valued recent acquisitions.