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Revolutions in Mathematics Paperback – December 14, 1995

ISBN-13: 978-0198514862 ISBN-10: 0198514867

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Product Details

  • Paperback: 368 pages
  • Publisher: Oxford University Press (December 14, 1995)
  • Language: English
  • ISBN-10: 0198514867
  • ISBN-13: 978-0198514862
  • Product Dimensions: 6.1 x 0.9 x 9.1 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #4,638,097 in Books (See Top 100 in Books)

Editorial Reviews


"Some of the major historical developments in mathematics are considered at length, enriching the overall quality of the presentation. . . . a good reference for those who are interested in the history of mathematics." --Science Books and Films

"The insightful contributions found in this book prove that the tools of Kuhnian analysis, in particular the idea of a revolution, may be applied usefully to produce history of the sort that goes beyond description in the logical presentation of ideas, to reveal what is at the heart of the process of discovery." --Science

About the Author

Donald Gillies is at King's College London.

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Most Helpful Customer Reviews

5 of 8 people found the following review helpful By Viktor Blasjo on March 15, 2008
Format: Paperback
These articles quibble about whether one should paste the label 'revolution' on this or that or any development in the history of mathematics. This is a boring pseudo-problem. The reason Kuhn and others studied scientific revolutions was not to produce a list of them or to concoct a definition, but rather to reach insights into the development of science. Nothing of that sort is achieved here.

Mancosu's article proves that it is ahistorical to consider Descartes' Géométrie revolutionary (although Mancosu himself is to polite to draw this conclusion). Foolish people like Cohen have claimed that it is a big deal to think of x^3 as an algebraic object instead of an actual cube, and that "Descartes' conception of such powers or exponents as abstract entities" was a "breakthrough," and that "Descartes' freeing of algebra from geometric constraints constituted a revolutionizing transformation," and so on (pp. 109-110). This is an ahistorical view. Nobody at the time considered this a revolution. Cohen claims they did, but his only proof is that Glanvill once "printed Descartes's name in a very large bold-faced type that bespoke his greatness" (p. 109). Instead there is compelling evidence to the contrary. "None of the mathematicians who could have have given a sound opinion of [the Géométrie] speak of Descartes as the mathematician who had revolutionized geometry. For example, Barrow mentions the analytic method of Viète and Descartes only as one of the many novel things in seventeenth century mathematics, but significantly he praises most of all Cavalieri's method of indivisibles as 'the most fruitful mother of new inventions in geometry'.
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