- Paperback: 390 pages
- Publisher: Oxford University Press; 1 edition (March 1, 1990)
- Language: English
- ISBN-10: 0195061357
- ISBN-13: 978-0195061352
- Product Dimensions: 8.9 x 0.8 x 5.9 inches
- Shipping Weight: 1.6 pounds (View shipping rates and policies)
- Average Customer Review: 15 customer reviews
- Amazon Best Sellers Rank: #331,777 in Books (See Top 100 in Books)
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter your mobile phone number.
001: Mathematical Thought from Ancient to Modern Times, Vol. 1 1st Edition
Use the Amazon App to scan ISBNs and compare prices.
Fulfillment by Amazon (FBA) is a service we offer sellers that lets them store their products in Amazon's fulfillment centers, and we directly pack, ship, and provide customer service for these products. Something we hope you'll especially enjoy: FBA items qualify for FREE Shipping and Amazon Prime.
If you're a seller, Fulfillment by Amazon can help you increase your sales. We invite you to learn more about Fulfillment by Amazon .
Frequently bought together
Customers who bought this item also bought
"I have always had great regard for this book as the one which relates the development of modern mathematical ideas in a readable fashion."--Michael F. O'Reilly, University of Minnesota in Morris
"Outstanding scholarship and readability. One of only a couple of books available in English for in-depth historical studies at the fourth year/graduate level."--Charles V. Jones, Ball State University
"The consistently high quality of presentation, the accuracy, the readable style, and the stress on the conceptual development of mathematics make [these volumes] a most desirable reference."--Choice
"Without a doubt a book which should be in the library of every institution where mathematics is either taught or played."--The Economist
"What must be the definitive history of mathematical thought....Probably the most comprehensive account of mathematical history we have yet had."--Saturday Review
About the Author
Morris Kline is Professor of Mathematics, Emeritus, at the Courant Institute of Mathematical Sciences, New York University, where he directed the Division of Electromagnetic Research for twenty years.
Author interviews, book reviews, editors picks, and more. Read it now
Top customer reviews
There was a problem filtering reviews right now. Please try again later.
This work was written in a more innocent time. It is not the result of in-depth historical scholarship, but of compilation of information. As such it often has a rather sophomoric ring to it. Consider for example this passage:
"It was Wallis and Newton who saw clearly that algebra provided the superior methodology [to geometry]. Unlike Descartes, who regarded algebra as just technique, Wallis and Newton realized that it was vital subject matter." (p. 392)
No further evidence or references are given for this claim here. It is simply stated as if it was a straightforward fact. In my opinion this vague and simplistic statement is half vacuous and half false, but let's put that aside and look only at Kline's text. Indeed, in the very same paragraph we also read:
"It is true that excessive reverence for Newton's geometrical work in the Principia … caused English mathematicians to persist in the geometrical development of the calculus. But their contributions were trivial compared to what the Continentals were able to achieve using the analytical approach." (p. 392)
So even though Newton "clearly saw" that algebra was the "vital subject matter" of mathematics, his magnum opus nevertheless conveyed the exact opposite sentiment, namely an emphasis on geometry, whence analytical mathematics was advanced most by precisely those who did not see clearly its significance. A serious attempt at coherent historical understanding would attempt to resolve this apparent paradox; a sophomoric compilation of "facts" would not. Kline does not.
It is much the same with Kline's claim that Descartes "regarded algebra as just technique." Here too we find Kline stating virtually the exact opposite in other places:
"Algebra, for Descartes, precedes the other branches of mathematics. It is an extension of logic useful for handling quantity, and in this sense more fundamental even than geometry." (p. 280)
This is a rather anachronistic point of view, which also mars Kline's very poor account of Descartes's Geometrie, where we read this confusing nonsense:
"Descartes rejects the idea that only the curves constructible with straightedge and compass are legitimate and even proposes some new curves generated by mechanical constructions. He concludes with the highly significant statement that geometric curves are those that can be expressed by a unique algebraic equation … All other curves … he calls mechanical." (p. 312)
On this account it indeed seems that "algebra, for Descartes, precedes the other branches of mathematics," but in reality it is the exact opposite: algebraic curves are accepted as geometrical (i.e., exact and rigorous) by Descartes precisely *because* they can be generated by his construction method. Thus Descartes does not "propose some new curves generated by mechanical constructions"---on the contrary, he proposes constructions which he considers *geometrical*, and thus *not mechanical*, which he claims generates not "some new curves" but rather *all geometrical curves*, a class which, he claims, turns out to be coextensive with the class of all algebraic curves.
This is all essential to the intrinsic logic of Descartes's works, but it is incidental to it as precursor of the modern analytic geometry of today, which explains why Kline's discussion is so hopelessly botched.
This is a typical instance of Kline's anachronistic perspective: Kline is reliable-ish when it comes to precursors of modern ideas, but often very inadequate in terms of holistic and sympathetic understanding of past mathematics when the original motivations and contexts differed greatly from our own.
For a reader who wants an accessible and reliable general history of mathematics I recommend Victor Katz's "A History of Mathematics". Kline covers European mathematics in more detail than Katz does, but Katz is a better one volume work, and I suggest that anyone who wants more detail than what Katz gives should use one of the following references instead of turning to Kline.
The two volume "Abrégé d'histoire des mathématiques" edited and partially written by Dieudonne, Moritz Cantor's "Vorlesungen über Geschichte der Mathematik", and the two volume "Companion Encyclopedia" edited by Ivor Grattan-Guinness are all reliable and cover in detail much material. Dieudonne's Histoire is not comprehensive, but it is excellent for the material it does cover, mostly in function theory and the theory of numbers.
For a mathematically knowledgeable reader who wants a structural history of certain parts of mathematics, I recommend Bourbaki's "Elements of the History of Mathematics". That book however is not meant to be a comprehensive history of mathematics, and really should be thought of as a history of the parts of mathematics that interested Bourbaki, written from their point of view. It is however reliable and specific in its details.
For the history of Greek mathematics one cannot do better than to read Heath's books and translations. A one volume summary of Greek mathematics is given in Heath's "A Manual of Greek Mathematics", available from Dover.
The best book to use for the number theory of Fermat and Euler is Weil's "Number Theory: An Approach Through History". It is exhaustive, completely reliable, and has excellent analysis of the material.
A reader who wants to know anything about Newton's mathematics needs to consult Whiteside's "The Mathematical Papers of Isaac Newton". This will probably never be improved on and Whiteside gives extremely good comments on the papers. However, the commentary is given as footnotes to papers, and the book is hard to jump into. It would probably be hard casually to use Whiteside's edition. Joseph E. Hofmann's "Leibniz in Paris" is a good first place to turn for questions about the mathematics of Leibniz. Finally, for any question about the history of rational mechanics, you should see what Clifford Truesdell has to say, especially in his "Rational Mechanics of Flexible or Elastic Bodies", published as part of Euler's Opera omnia.