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Mathematical Thought from Ancient to Modern Times, Vol. 1 [Paperback]

by Morris Kline
4.0 out of 5 stars  See all reviews (6 customer reviews)

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Book Description

March 1, 1990 0195061357 978-0195061352 New Ed
This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

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Editorial Reviews


"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.

Product Details

  • Paperback: 390 pages
  • Publisher: Oxford University Press; New Ed edition (March 1, 1990)
  • Language: English
  • ISBN-10: 0195061357
  • ISBN-13: 978-0195061352
  • Product Dimensions: 9 x 5.8 x 0.8 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #384,092 in Books (See Top 100 in Books)

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Customer Reviews

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44 of 44 people found the following review helpful
5.0 out of 5 stars Very thorough July 22, 2002
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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8 of 12 people found the following review helpful
5.0 out of 5 stars pretty good November 4, 2005
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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2 of 3 people found the following review helpful
3.0 out of 5 stars I've had it for years and always use something else October 2, 2013
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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