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Greek Mathematical Thought and the Origin of Algebra (Dover Books on Mathematics) Paperback – September 11, 1992

by Jacob Klein (Author)

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Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Greek Mathematical Thought and the Origin of Algebra (Dover Books on Mathematics)

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Editorial Reviews

Review

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) --This text refers to an alternate Paperback edition.

Language Notes

Text: English (translation)
Original Language: German

Series: Dover Books on Mathematics
Paperback: 384 pages
Publisher: Dover Publications; Reprint edition (September 11, 1992)
Language: English
ISBN-10: 0486272893
ISBN-13: 978-0486272894
Product Dimensions: 5.5 x 0.8 x 8.5 inches
Shipping Weight: 14.9 ounces (View shipping rates and policies)
Average Customer Review: 9 customer reviews
Amazon Best Sellers Rank: #913,436 in Books (See Top 100 in Books)
- #764 in Books > Science & Math > Mathematics > History
- #1546 in Books > Science & Math > Mathematics > Pure Mathematics > Algebra

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Slo***dollarz

Interesting but unnecessarily difficult to read.

December 21, 2014

Format: PaperbackVerified Purchase

Good thoughts but the writing style is very difficult. At the beginning, there is a guide to about 30 Greek words that are used throughout the book. You'd better memorize all of them or else be ready to turn back to the front of the book two or three times on every page. Sentences are long, rambling, and broken up by Greek sentences in the same font in the middle of sentences. One paragraph can last two pages. As a double major in mathematics and philosophy, I thought I would be able to read this without too much difficulty. I was wrong. Maybe the second time through when I am more aware of what he is trying to say. It sounds really interesting; I just have a hard time getting past all the stumbling blocks.

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B. Style

Not light weight

August 20, 2008

Format: PaperbackVerified Purchase

The scholar or academic may find this book quite engaging -- I'm just an amateur mathematician with an added mild interest in the history. For me, it's rather pedantic (over my pay grade as it were).

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Franklin Ransom

A work of scholarly genius

August 6, 2015

Format: PaperbackVerified Purchase

What Klein does in this book is nothing short of genius. The section on Plato's Forms is by itself a good enough reason to read it; the story afterwards about the historical development of algebra from the Forms is nothing short of remarkable. As Klein himself notes, the book is very assiduous in its scholarship to a fault, as it can be tedious in the quotes. But still, it leaves very little room for doubt that Klein's analysis of the historical development of algebra is right on target. If the reader wishes to understand Plato's Forms better and the influence of his idea of ideas, this is the book to read.

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Rossharmonics

Indispenble for understanding how important Greek Mathematics still is in understanding music

December 17, 2012

Format: Paperback

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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Jordan Bell

The ontology of numbers in Greek mathematics

November 21, 2015

Format: Paperback

Roughly, this book is to Greek mathematics as Lewis's The Discarded Image: An Introduction to Medieval and Renaissance Literature (Canto Classics) is to medieval natural philosophy. (However, Lewis's book is a tighter work and Lewis writes more clearly than Klein does.) To understand what how mathematicians think about the objects they talk about, Klein should have given close readings on a few theorems and problems from Euclid, Archimedes, Diophantus, Apollonius, and instead refers overwhelmingly to statements of theorems and definitions and commentaries and scholia.

Klein explains how Greek mathematicians thought about the objects with which they worked. What Klein says reminds me of the notion of a theory (in mathematical logic) being "categorical" when it has a model that is unique up to isomorphism. Talking about objects that are determinate but have only some general property, like "a red thing" being a fixed object that only has those properties which are entailed from being red, reminds me for different vague reasons of equivalence classes and universal objects. (One usually speaks about "the tensor product", and thus works with something that is not fixed but merely unique up to unique isomorphism.)

I think I would have understood this book more deeply if I were familiar with Aristotle's Metaphysics and Organon, and ideas from Scholastic logic like the first and second intentions of terms, and the metaphysical problem of universals, and it would also help to know ancient Greek. I would like to have a stock of examples for the various technical Greek terms that Klein uses. Klein does not work out the helpful pedestrian examples that let a reader feel familiar with a subject, and without having meaning beyond their dictionary meaning attached to, say, eidos, aisthesis, noesis, dianoia, I often became confused or frustrated. But because this book has so much value and is unique, my complaints are small, and I would be delighted if another work like this is published some day. Most of what non-mathematicians write about mathematics seems shallow to a mathematician (for example, there is much more to say about the ontology of universal objects in category theory or the indeterminateness of the sample space in probability theory than there is about "what is a number", but getting to these more substantial questions requires more command of mathematics than most philosophy graduate students have, and likewise someone with meager mathematical training will ask shallow questions about general relativity and quantum physics, missing the substantial questions that tend not to be asked by initiates), and Klein is an exception to this. Even though I have not fully connected with Klein's book I feel that his thoughts are deep and are based on long reading of the original writings.

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Most recent customer reviews

Superb treatment of its subject.

Mark Mills gives a good precis of the argument of the work as a whole.

I would like to emphasize the particular value of the first section, concerning the ancient Greek...Read more

Published on May 17, 2012 by Undecided

The Inner Workings of the Modern "Abstraction" of Experience from Nature

While Klein's LECTURES & ESSAYS contains accounts of the distinctive features of the modern world (from modern science to the rise of capitalism) that are likely to appear as more...Read more

Published on May 26, 2008 by M. Andreacchio

On 'arithmos' and 'general magnitude'

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.Read more

Published on June 29, 2002 by Mark Mills

Klein's work is a masterpiece of philosophical exegesis.

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...Read more

Published on July 29, 1998

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