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A New History of Greek Mathematics
The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created.
540 pages, Hardcover
Published November 24, 2022
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Displaying 1 - 5 of 5 reviews
February 22, 2023
Brilliant, but not for the faint-hearted.
September 13, 2023
First of all, this is a scholarly work, well into "hour a page" territory if you want fully to understand it. Given that, the "chatty" style is a little jarring at first but it does convey the author's enthusiasm for his subject.
Many of those picking up this book will have been put in mind of A History of Greek Mathematics, Vol. 1: From Thales to Euclid. Netz is conscious of that and goes on to point out how he is building upon the work of Thomas Little Heath and Neugebauer O. (Otto).
This is an account set in a very broad and deep cultural and sociological context. His spiritual home is clearly somewhere around The Structure of Scientific Revolutions and Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life. This history of Greek mathematics starts in the ethnomathematics of pre-literate times and ends with Galileo Galilei. It is a work of spectacular ambition. And, unlike Heath, he's kept it down to one volume. 500 pages with footnotes rather than endnotes (good) but no bibliography.
Given that scope it's full of interesting material. He's very good on Roman engineering and the influence of Greek mathematics there. I got a lot out of that, a subject on which I'd often speculated. In fact, this was rather more rewarding on the subject than The Oxford Handbook of Engineering and Technology in the Classical World. In fact, he's very strong on the Greek cultural influence in late antiquity in general.
Another of his insights is on the turn from enquiry to commentary and rise of neo-Platonism. In The Closing of the Western Mind: The Rise of Faith and the Fall of Reason, Freeman blames this in Christianity. Netz gives a much more critical analysis here.
I think non-mathematicians interested in Greek cultural influence can get a lot out of this book, even if they skip the mathematics.
Many of those picking up this book will have been put in mind of A History of Greek Mathematics, Vol. 1: From Thales to Euclid. Netz is conscious of that and goes on to point out how he is building upon the work of Thomas Little Heath and Neugebauer O. (Otto).
This is an account set in a very broad and deep cultural and sociological context. His spiritual home is clearly somewhere around The Structure of Scientific Revolutions and Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life. This history of Greek mathematics starts in the ethnomathematics of pre-literate times and ends with Galileo Galilei. It is a work of spectacular ambition. And, unlike Heath, he's kept it down to one volume. 500 pages with footnotes rather than endnotes (good) but no bibliography.
Given that scope it's full of interesting material. He's very good on Roman engineering and the influence of Greek mathematics there. I got a lot out of that, a subject on which I'd often speculated. In fact, this was rather more rewarding on the subject than The Oxford Handbook of Engineering and Technology in the Classical World. In fact, he's very strong on the Greek cultural influence in late antiquity in general.
Another of his insights is on the turn from enquiry to commentary and rise of neo-Platonism. In The Closing of the Western Mind: The Rise of Faith and the Fall of Reason, Freeman blames this in Christianity. Netz gives a much more critical analysis here.
I think non-mathematicians interested in Greek cultural influence can get a lot out of this book, even if they skip the mathematics.
December 25, 2023
Initial disclaimer: I am no historian and can not judge any controversial claims the author makes about history.
Many textbooks in mathematics contain a historical discussion, and for elementary textbooks in subjects like geometry and number theory this often means references to ancient Greek authors. For anyone inspired by these references to dig deeper, and to verify how correct the history taught in math books is, this is a good resource. In particular, Netz takes care to treat ancient sources more critically than an earlier generations of math historians always did. (Historians who probably influenced writers of math textbooks.) Apparently, there is no reason to think Pythagoras or Thales did any real mathematics, while the usual presentation of the achievements of later authors like Euclid and Archimedes is essentially correct.
Many mathematical arguments are presented in detail. Mostly the theorems and proofs discussed are geometrical, both results well-known from school textbooks and more obscure (but interesting) results. Someone with a keen interest in Euclidean geometry will likely enjoy this book. Its not for the mathematical uninclined however.
The reception of ancient Greek mathematics in Byzantine, Arabic and European cultures are discussed. It ends with Newton's Principia. That may be when Western science liberated itself from Greek sources, but in mathematics I would suggest the engagement with ancient Greek texts lasted longer.
Be forewarned that the book was not given the proof-reading it should have been. The proof-reader seems to have been sloppy, or perhaps mathematicially illiterate. Because while I discovered only one purely grammatical error, there are several mistakes in references to diagrams (mistaken letters or referring to the "right side" when the left is means) and the like, that could result from a proof-reader who is unable to follow the arguments anyway, so can't catch the errors. There are also mathematical errors when dealing with modern mathematics. Thus in the discussion of Khayyam–Saccheri quadrilaterals it is incorrectly asserted one can get a consistient geometry by allowing them to have obtues angles, but in fact only right-angles (in Euclidean geometry) or acute angles (in hyperbolic geometry) are possible.
A minor point which amused me is that we get some pious platitudes to politically correctness, such as a brief disclaimer that the Greeks did not invent mathematics because they are white, which are poorly integrated in the text. Perhaps they were felt necessary because the book is in large measure a celebration of the uniqueness of Greek mathematics as compared to anything that came before or anything contemporary.
Many textbooks in mathematics contain a historical discussion, and for elementary textbooks in subjects like geometry and number theory this often means references to ancient Greek authors. For anyone inspired by these references to dig deeper, and to verify how correct the history taught in math books is, this is a good resource. In particular, Netz takes care to treat ancient sources more critically than an earlier generations of math historians always did. (Historians who probably influenced writers of math textbooks.) Apparently, there is no reason to think Pythagoras or Thales did any real mathematics, while the usual presentation of the achievements of later authors like Euclid and Archimedes is essentially correct.
Many mathematical arguments are presented in detail. Mostly the theorems and proofs discussed are geometrical, both results well-known from school textbooks and more obscure (but interesting) results. Someone with a keen interest in Euclidean geometry will likely enjoy this book. Its not for the mathematical uninclined however.
The reception of ancient Greek mathematics in Byzantine, Arabic and European cultures are discussed. It ends with Newton's Principia. That may be when Western science liberated itself from Greek sources, but in mathematics I would suggest the engagement with ancient Greek texts lasted longer.
Be forewarned that the book was not given the proof-reading it should have been. The proof-reader seems to have been sloppy, or perhaps mathematicially illiterate. Because while I discovered only one purely grammatical error, there are several mistakes in references to diagrams (mistaken letters or referring to the "right side" when the left is means) and the like, that could result from a proof-reader who is unable to follow the arguments anyway, so can't catch the errors. There are also mathematical errors when dealing with modern mathematics. Thus in the discussion of Khayyam–Saccheri quadrilaterals it is incorrectly asserted one can get a consistient geometry by allowing them to have obtues angles, but in fact only right-angles (in Euclidean geometry) or acute angles (in hyperbolic geometry) are possible.
A minor point which amused me is that we get some pious platitudes to politically correctness, such as a brief disclaimer that the Greeks did not invent mathematics because they are white, which are poorly integrated in the text. Perhaps they were felt necessary because the book is in large measure a celebration of the uniqueness of Greek mathematics as compared to anything that came before or anything contemporary.
December 28, 2023
I found the sections about intersections with Arabic and European sciences more interesting than the all-Greek sections. It did make me briefly think about mathematics as a candidate for a Fermi Paradox Great Filter since math’s invention was fairly unitary but that seems unlikely given the timescales involved.
April 13, 2023
What a terrible book! Any reader that checks the claims in this book using the works cited will find that some claims are clearly false. While this is bad enough, (no good mathematician would make claims so easily shown to be false) there are also claims made with no citation or proof provided. The author seems to try to bully the reader into believing what they say (proof by intimidation I suppose).
Displaying 1 - 5 of 5 reviews