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Mathematical Thought from Ancient to Modern Times, Vol. 1 1st Edition

4.3 out of 5 stars 8 customer reviews
ISBN-13: 978-0195061352
ISBN-10: 0195061357
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Editorial Reviews

Review


"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.
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Product Details

  • 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: 4.2 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #311,673 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
As one might expect from a 3-volume history, _Mathematical Thought_ is comprehensive; Kline covers basically all the important mathematical developments from ancient times (e.g. the Babylonians) until about 1930. Note that (as Klein himself mentions) the coverage of ancient mathematics, while taking up a good half of the first volume, is necessarily modest, and if that is the reader's primary interest, s/he would do best to seek out specific histories on the Greeks, Chinese, etc. [Kline gives several useful references, as always].
The reader interested in the 18th and 19th centuries will find plenty of food for thought. For example, the story of non-Euclidean geometry is covered well, and Kline does a good job of putting the discoveries in the light of the times. One notable thing I learned is that Lobachevsky and Bolyai were not the discoverers of non-Euclidean geometry, nor were they the first to publish material on that subject. Others before had expressed the opinion that non-Euclidean gometry was consistent and as viable a geometry as Euclidean (e.g. Kluegel, Lambert...even Gauss!) It remained for Beltrami to later show that if Euclidean geometry were consistent, so is non-Euclidean. Of course, important events like the invention of Galois theory are also mentioned. Really, if it's a major mathematical development before 1930, Kline will have it somewhere in these 3-volumes.
Incidentally, Kline advances the interesting theory that Lobachevsky and Bolyai somehow learned of Gauss' work on non-Euclidean geometry (which he kept secret and was not learned of until after his death) through close friends of Gauss: Bartel (mentor to Lobachevsky) and Bolyai's father, Farkas.
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Format: Paperback
The only reader I think Kline's book would be right for is one who wants a single source for the history of mathematics and who is not willing to use more specialized books. I have had Kline's history for years and I sometimes look something up in it, am disappointed by his presentation, and then look for the topic in another book.

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.
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Format: Paperback
I've been learning more about the history of analytic geometry and the mathematization of physics, so I consulted the last chapters of Vol. 1. Kline explains very clearly the innovations Descartes made but also his misunderstanding of Galileo's mathematization of physics. For example, Galileo (and Newton) described motion and gravity mathematically, but they did not attempt to explain WHY; Descartes mistakenly criticized Galileo's work because of that.

There was an incredible change in thinking about science during the seventeenth century. Kline explains clearly how that unfolded mathematically.

I only gave the book four stars because of others' critique of the early part of the book, which I didn't read.
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Format: Paperback
if flawed. Not only do you have to wade through the gentleman amateur flavour of the first couple of hundred pages or so, but Kline manages to describe William Hamilton as 'the greatest English theoretical physicist after Newton'; even an Irishman would concede that the greatest English theoretical physicist after Newton was Maxwell - Hamilton was third. However with the first impact tremors announcing the approach of Leonard Euler, when the technical issues start to thicken, things improve enormously. Kline is clearly in awe of Euler, and does a good job of communicating why awe is appropriate.

It is nevertheless fortunate that the history of mathematics, unlike that of science, is a discipline essentially invulnerable to whiggish prejudice.
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