The Exact Sciences in Antiquity by O. Neugebauer (PDF)

Description

Based on a series of lectures delivered at Cornell University in the fall of 1949, and since revised, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy, and their transmission to the Hellenistic world. Entirely modern in its data and conclusions, it reveals the surprising sophistication of certain areas of early science, particularly Babylonian mathematics. After a discussion of the number systems used in the ancient Near East (contrasting the Egyptian method of additive computations with unit fractions and Babylonian place values), Dr. Neugebauer covers Babylonian tables for numerical computation, approximations of the square root of 2 (with implications that the Pythagorean Theorem was known more than a thousand years before Pythagoras), Pythagorean numbers, quadratic equations with two unknowns, special cases of logarithms and various other algebraic and geometric cases. Babylonian strength in algebraic and numerical work reveals a level of mathematical development in many aspects comparable to the mathematics of the early Renaissance in Europe. This is in contrast to the relatively primitive Egyptian mathematics. In the realm of astronomy, too, Dr. Neugebauer describes an unexpected sophistication, which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical apparatus. The transmission of this early science and its further development in Hellenistic times is also described. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods.Dr. Neugebauer has long enjoyed an international reputation as one of the foremost workers in the area of premodern science. Many of his discoveries have revolutionized earlier understandings. In this volume he presents a non-technical survey, with much material unique on this level, which can be read with great profit by all interested in the history of science or history of culture.

User’s Reviews

Editorial Reviews: About the Author Otto Neugebauer: Exacting History Neugebauer’s The Exact Sciences in Antiquity became an instant unique classic of scientific literature when first published in 1951 in the United States and in Copenhagen where he had lived and worked for some years after having been forced out of Germany because of his opposition to National Socialism. At the start of World War II, Otto Neugebauer (1899–1990) left Europe for Brown University where he founded the History of Mathematics Department. Years later a colleague at Brown recalled Neugebauer’s eloquent summary of the dark years in Germany: “If you never heard the sound of Nazi boots below you in the street, you cannot understand the history of the period.” In the 1980s he moved to the Institute for Advanced Study in Princeton. He wrote several books and many articles in addition to The Exact Sciences in Antiquity. His monumental three-volume History of Ancient Mathematical Astronomy (1975) is the definitive work on the subject. Dover reprinted The Exact Sciences in Antiquity in 1969. Critical Acclaim for Otto Neugebauer:”Otto Neugebauer was the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age. He began as a mathematician, turned first to Egyptian and Babylonian mathematics, and then took up the history of mathematical astronomy, to which he afterward devoted the greatest part of his attention. In a career of sixty-five years, he to a great extent created our understanding of mathematical astronomy from Babylon and Egypt, through Greco-Roman antiquity, to India, Islam, and Europe of the Middle Ages and Renaissance. Through his colleagues, students, and many readers, his influence on the study of the history of the exact sciences remains profound, even definitive.” ― N. M. Swerdlow

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

⭐Neugebauer explains how ancient math and astronomy worked. This is done very well, although I’d argue that he doesn’t always make it very clear what he’s talking about if you don’t already know (his treatment of the Almagest and Ptolemy’s map projections take a lot of definitions for granted). In order to understand the explanations of many of the steps, you will have to reread them many times and stare at the figures (just like you have to for any math/physics books with derivations that aren’t trivial). Still, the explanations are there, and Neugebauer in the main of the text gives good information about the history of science, his opinions, and I thought his Babylonian math explanations were much clearer than the geometric ones.Overall, I think it is definitely worth reading just to get a sense of the achievements of ancient cultures, and to know what ancient math and astronomy consisted of.

⭐Other reviews are correct when they describe this book as the classic textbook for how ancient cultures approached mathematics and scientific calculations. The examples are well explained and illustrative of the mindset of each culture at the time. It’s fascinating seeing “normal” calculations like trigononetry written in cuneiform or ancient Egyptian. As a data analyst I approached this book from the perspective of how numbers are stored and how the arrangement / structure affects the mathematical thought / steps necessary to solve a problem using them. The only thing to be aware of is that the prose is very dry and a little outdated, but if you’re curious enough to buy a book about ancient math, you are probably accustomed to it.

⭐Rather than the endless tomes containing nothing but what individuals think the ancients did this one actually shows pictures of some of the source tablets and mathematical tables the concepts in the book were translated from. The sources are direct, well researched, well documented, and extremely reliable. I first bought this book a couple of decades ago but discovering it missing from my library after a move I still treasured it enough to purchase it again. For someone in search of a time when the mathematics of music, time, and space were one it is most rewarding and worthwhile.

⭐Very satisfied with this purchase.

⭐This was a second edition hardback, a Barnes and Noble copy. I was disappointed that it did not include photos of the source document tablets which the original book apparently had.

⭐Old book, of course is Neugebauer, but very good introduction to mathematics in the antique babylonian and greek civilization.

⭐This book is incredible! It is really dense with information that I don’t quite understand, but the history presented by the author is intriguing nonetheless. I honestly don’t understand anything besides base 10 maths 🙂 Definitely buy this book…and then read it.

⭐This particular edition (the dover edition) does not have the plates; the plates are very helpful for understanding the argument.

⭐Per chi capisce bene l’inglese ottima lettura, altrimenti meglio prendere l’edizione in italiano. L’autore è uno dei maggiori studiosi sull’argomento.

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⭐Aunque publicado hace ya muchos años, mantiene su interés por estar basado en datos obtenidos personalmente por el autor en los textos que sirven de fuente al estudio.

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