Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) by Serafina Cuomo (PDF)

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’ 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.

User’s Reviews

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 A study of the work of a fourth-century AD mathematician and its cultural setting.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book was of more historical interest than mathematical significance. I found its discussion of the problem about duplicating the cube to be an interesting treatment of proportional means, but the substance of this book is an academic interpretation of Pappus’ historical context. It’s too bad that no one has prepared a good english edition of Pappus’ Collections (or Synagogue); I found a French edition when I had library privileges as a graduate student long ago, and it’s really important. Pappus was true to his criticisms about how many mathematicians make things difficult in an effort to show off; his theorems really get to his points to simplify by reducing the number of terms rather than complicating forms toward simplistic conclusions.

⭐You will be disappointed if you want a survey of mathematics in late antiquity. Cuomo has little to say about music and astronomy, or about what texts people learned from, how much of Euclid people knew, why Nicomachus’s “Introduction to Arithmetic” became popular, etc. The book is instead about the professional self-image of people who called themselves mathematicians. There is a detailed presentation of the construction of two mean proportionals, and anyone studying the history of that problem should use this book.Some ancient sources are cited that might not be familiar to students of the history of mathematics, especially the writings of the Roman land surveyors. Unfortunately Cuomo does not say anything about the level of mathematics in those texts. Some of these texts have been translated in Brian Campbell’s “The Writings of the Roman Land Surveyors”. Another source of technical writings is on war machines, and for that see E. W. Marsden, “Greek and Roman Artillery: Technical Treatises”.I would indeed like to know about the level of mathematical knowledge in the ranks below Archimedes, Euclid, Eratosthenes, Apollonius, etc., but like many current writings by people in history of science departments, this work spends more time exhorting us to recognize that mathematics was done by those of the second ranks than actually talking about that mathematics in detail. (A common operation in astronomy and surveying is taking the square root of a non-square number, or computing the area of regular polygons, but this is not mentioned by Cuomo, although several pages are spent on the virtue of bees for making hexagons without art.)

⭐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.

Keywords

Free Download Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) in PDF format
Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) PDF Free Download
Download Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) 2000 PDF Free
Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) 2000 PDF Free Download
Download Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies) PDF
Free Download Ebook Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge Classical Studies)