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Greek Mathematical Thought and the Origin of Algebra (MIT Press Classics) [Paperback]

Jacob Klein
4.8 out of 5 stars  See all reviews (6 customer reviews)

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Book Description

September 15, 1976 0262610221 978-0262610223

Historians of science have usually assumed that the mathematicians of the Renaissance took up where prior mathematicians had left off. This important work argues that during the sixteenth century, a crucial change in the concept of number took place which distinguishes ancient and modern mathematics once and for all.The author regards Francois Vieta as "the true founder of modern mathematics" and demonstrates that to this development of symbolic algebra corresponds a fundamental change in the concept of the number.

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Editorial Reviews


"Historians of ideas will be reminded of numerous struggles in other fields paralleling these attempts to overcome or accommodate vestiges of the traditional but no longer useful concept of the number. The thoroughness of this work will ensure that it will remain a standard reference for a long time to come." British Journal for the Philosophy of Science

"It is to be hoped that someone before long will make searching a study of Arabic algoristic impulsion toward modern algebra as Klein has made of Greek philosophical stimuli. Historians... will be grateful... for the very welcome inclusion of a long-desired English translation of Vieta's Introduction to the Analytical Art." Science

Language Notes

Text: English (translation)
Original Language: German --This text refers to an alternate Paperback edition.

Product Details

  • Series: MIT Press Classics
  • Paperback: 376 pages
  • Publisher: The MIT Press (September 15, 1976)
  • Language: English
  • ISBN-10: 0262610221
  • ISBN-13: 978-0262610223
  • Product Dimensions: 7.9 x 5.1 x 0.8 inches
  • Shipping Weight: 14.9 ounces (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #14,083,254 in Books (See Top 100 in Books)

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Customer Reviews

4.8 out of 5 stars
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Most Helpful Customer Reviews
30 of 33 people found the following review helpful
5.0 out of 5 stars On 'arithmos' and 'general magnitude' June 29, 2002
It's hard to say something about this wonderful book without sounding pompous. Generally, I try to avoid terms like 'classic' and 'essential', but they keep coming to mind.
The original was written in the mid 1930s. As Klein writes in this version's preface, "This study was originally written and published in Germany during rather turbulent times."
The late Jacob Klein spent his post war years teaching Platonic philosophy at St. John's College. There, he was known as something of a lovable elitist. Professors tell a story about Klein being partial to the number 12. He claimed that there were an exclusive 12 philosophers, 7 Greek and 5 German. The word got out and he soon received a letter from 4,000 American philosophers begging to differ with his opinion.
While many might call this book 'philosophy of math,' I doubt Dr. Klein would agree. The book is without much in the way of serious math. It is more concerned with the symbols of math and how they are used. Quoting from the first paragraph of the introduction:
"Creation of a formal mathematical language was of decisive significance for the constitution of modern mathematical physics. If the mathematical presentation is regarded as a mere device, preferred only because the insights of natural science can be expressed by "symbols" in the simplest and most exact manner possible, the meaning of the symbolism as well as of the special methods of the physical disciplines in general will be misunderstood.
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34 of 40 people found the following review helpful
By A Customer
Klein's work examines the generally unsuspected foundations of modern algebraic mathematics. He charts the development of a new kind of intentionality which lies at the heart of modern mathematical practice, with an explicit affirmation that this mode of intentionality is exemplary for all of modern thought. Beginning from the classical foundations of mathematics, he follows the subject carefully through every turn of ideation until he has completed his thesis. On the basis of this thorough-going evaluation and exegesis of mathematical thought, he identifies Francois Viete as the true founder of this modern symbolic intentionality. But he does not rest with this, proceeding to show how Descartes, Stevin, and Wallis each draw out of this foundation conclusions which are familiar to the modern thinker. This reader knows of no other work of this kind that has so deeply penetrated the foundations of what we call modernity.
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3 of 3 people found the following review helpful
By R. Ross
I have returned to this book after a number of years and still find something of value in every page and sometimes every paragraph.

My interest comes through music. The use of ratios and proportion is something the Greeks understood intimately. Prior to the nineteenth century musicians were generally more aware of this. But in the Renaissance, a decline started to take place. This decline is linked with an alienation of ancient math within the corpus of modern thought.

It is essential that a truer knowledge of Greek math, musical theory, and philosophy be restored. Klein knows intimately how the late Renaissance and early age of Reason did a great disservice to the place and important of ancient Greek mathematical thought and its philosophic foundation.

Buy this book. Heath's History of Greek Mathematics is just as important but does not tackle the philosophical issues the way Klein's book does. It demands attention but you will be amply rewarded.
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