Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) [Hardcover]

Serafina Cuomo (Author)

Book Description

ISBN-10: 0521642116 | ISBN-13: 978-0521642118 | Publication Date: March 13, 2000

This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. This is one of very few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus' text as part of a wider context and relates it to other contemporary cultural practices and opens new avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity.

Editorial Reviews

Review

"All in all, the publication provides a meaningful and insightful treatment of the mathematics of late antiquity." Mathematical Reviews

"Readable, interesting, and an eye-opener for those who have only met Greek mathematics at a superficial level. This little book in the 'Cambridge Classical Series' is one that mathematicians interested in the history of their subject will want to read." MAA Online

"This book contains an abundance of interesting historical material... Cuomo shows that we can learn much from looking at Pappus's Collection in its own right. Her book deserves careful study." Ali Behboud, ISIS

"The book is well written, in a pleasant style. The argument is based throughout on a wide range of sources, and the pertinence of the source and the leap from source to interpretation is always made clear. The reviewer felt well treated and entertained while reading and quite a bit wiser when closing the book." British Jrnl for the History of Science

Book Description

This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. This is one of very few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus's text as part of a wider context and relates it to other contemporary cultural practices and opens new avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity.

Product Details

• Hardcover: 248 pages
• Publisher: Cambridge University Press (March 13, 2000)
• Language: English
• ISBN-10: 0521642116
• ISBN-13: 978-0521642118
• Product Dimensions: 8.8 x 5.6 x 0.7 inches
• Shipping Weight: 15.2 ounces (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #6,450,904 in Books (See Top 100 in Books)

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4 of 5 people found the following review helpful:

3.0 out of 5 stars Interesting project, May 26, 2003

By 

Mark Mills (Glen Rose, TX USA) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) (Hardcover)

Cuomo starts this book by suggesting we don't understand the late-classical era, that great confusing muddle which starts around 300 AD when Constantine transferred the capital of the Roman Empire to Constantinople and legalized Christianity. It ends with the Muslim conquest of Alexandria. In crude terms, it is what Gibbon called the 'fall of the Roman Empire.' Cuomo uses the 'Arch of Constantine' as a metaphoric reference. For most contemporary art historians, the arch is a pastiche of scavenged sculptures from earlier and finer artistic efforts. Scavenged is the key word here. The late-antiquity (according to Gibbon) was the moral equivalent of Sodom and Gomorrah.

I don't know how many people still take "Rome's Fall' as a moral litmus test, but I suspect the story still holds a lot of weight. It's this icon that Cuomo targets.

In general terms, I couldn't be more pleased with the project. Unfortunately, it doesn't really get off the ground. Cuomo isn't very forth coming on what she makes of the era. It seems she simply likes pastiche.

She starts her iconoclastic journey well, suggesting the subject of her book might never have existed. It is hard to argue the point. We know almost nothing about Pappus, the man. Unfortunately, the fictional Pappus concept seems to have been mentioned for shock value, and not pursued seriously. I would have been interested in hearing details on the process of putting mathematic lectures on scrolls for academic, social or bureaucratic purposes. Maybe ghost writing was a common practice. This emphasis on the 'media' itself seems critical to Cuomo's case (a role the Arch of Constantine served), but it is entirely ignored.

Cuomo then takes us down an entertaining bunny hole involving legal torture and highly paid astrologers. By taking this route, she hopes to convince us that mathematics was about as important to our late-classical delinquents as, well, ourselves. The legal discussion shows mathematical knowledge put one socially above those who could expect torture during any legal cross-examination. The astrological references show desperate young parents prayed for their off-spring to become mathematicians.

So far, so good, but Cuomo then launches into a book by book deconstruction of the works ascribed to Pappus (whoever he was), and in this the reader starts to wonder just what she wants to say. The less than stunning conclusion is that Pappus had careerist interests and said different things to target groups in hopes of enhancing his authority.

I was less than impressed.

One might surmise Cuomo has a bigger goal, but if it exists, it is very subtle. Of these subtle arguments, the chief seems to be that the standard historiography associates the development of Greek mathematics exclusively with Plato's philosophy (the Proclus (411-485) perspective). Cuomo points out contradictions in this line of reasoning made by Pappus (? 320 ?) and Iamblichus (250?-330?). In this, Cuomo hints at disputing the role of the Neo-Platonic synthesis. Proclus, as the heir to Plato's academy, plays a pivotal role in this. Cuomo seeks to uncover the real mathematician hidden by Proclus and later Neo-Platonic Christians.

If this is really what she hints at, I would be surprised. I am just grasping at straws... The unfortunate fate of the interested reader.

3 of 4 people found the following review helpful:

3.0 out of 5 stars Run-of-the-mill sociology of science, May 13, 2010

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) (Hardcover)

This predictable book betrays the author's eagerness to conform to the academic fashions of the day. Its predictable thesis is that "Pappus was not operating in a vacuum" (pp. 89-90); rather he had an "agenda" (e.g., p. 169) to "augment his prestige" (p. 200), etc., etc. In other words, the usual staple thesis of the pomo generation of historians. One impatiently awaits the day when the sterility and mediocrity of such flavour-of-the-month scholarship will be recognised. A typical passage may illustrate its futility:

"It is remarkable, I think, that in the case of book 4 the reader is left to fend for himself through a text difficult to understand even for skilled mathematicians ... while, in the case of book 5, the reader is not even expected to be acquainted with one of Archimedes' most famous discoveries ... These marked double standards ... can only be explained on the basis of two different kinds of intended readership." (p. 73)

There you have it---groundbreaking revelations of cutting-edge science-studies research: some guy wrote for different audiences in different styles. If you find this "remarkable" then you're in for a treat.

As an additional illustration of Cuomo's tasteless catering to the establishment, we may quote the very first sentence of a section called "Mathematics and the stars":

"That astrological texts could be fruitfully used by ancient historians was an idea first put forwards by Lynn Thorndike, revived by Ramsay MacMullen and later applied with interesting results by Tamsyn Barton." (p. 10)

I for one would prefer if Cuomo put substance first and incestuous scholarly accolades and pedigrees second. But since Cuomo is clearly more concerned with fitting in with her peers than with addressing interesting and important historical questions, her backwards approach makes perfect sense.