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Mathematical Thought from Ancient to Modern Times, Vol. 1 1st Edition
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"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.
Top Customer Reviews
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.Read more ›
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.Read more ›
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.
It is nevertheless fortunate that the history of mathematics, unlike that of science, is a discipline essentially invulnerable to whiggish prejudice.
Most Recent Customer Reviews
Morris Kline's "history" is a disappointment. I have no doubt that Kline knows his mathematics, but he either does not know his history, or prefers to distort it so that it fits... Read morePublished on December 24, 2004 by Demetrios Vakras