The Mathematics of Plato's Academy: A New Reconstruction

Rating:
Summary: A new landmark
Review: "THE MATHEMATICS OF PLATO'S ACADEMY"
Second Edition
Fowler.

The first impression on receiving this book in your hands is the heavy weight. But this is not only true physically, due to the high quality of the cartridge paper, it is also true intellectually. Thus the second impression reinforces the first. The caliber of the scholarship exhibited in this tome is of the highest order, doing full justice to an investment in so expensive a paper.

Nothing less than the most complete exposition possible of ancient Greek mathematics as taught at the Platonic Academy in Athens, is presented, based on all currently available sources.

The author labors to guide the reader with diagrams, definitions, explanations, cross-references, commentaries and modern mathematical symbols to provide a clear, detailed and thorough account. He even starts from the photographic plates of Greek papyri. This is a major work of scholarship that itself deserves to become a classic; a model of its kind.

Just in case amazon readers accuse me of obsequious flattery, abject servility and distasteful onesidedness, allow me one criticism. The influence of the Ionian philosopher-mathematicians, Thales, Anaxagoras, Anaximander and Anaximenes on Plato's Academy is not covered.

A magnificent twenty-one page bibliography testifies to the author's detailed background research, and whets the reader's appetite for further reading.

Finally, three separate indexes show that the author is making every effort to help his reader as much as he can. Could one ask for more ?

Rating:
Summary: A new landmark
Review: "THE MATHEMATICS OF PLATO'S ACADEMY"
Second Edition
Fowler.

The first impression on receiving this book in your hands is the heavy weight. But this is not only true physically, due to the high quality of the cartridge paper, it is also true intellectually. Thus the second impression reinforces the first. The caliber of the scholarship exhibited in this tome is of the highest order, doing full justice to an investment in so expensive a paper.

Nothing less than the most complete exposition possible of ancient Greek mathematics as taught at the Platonic Academy in Athens, is presented, based on all currently available sources.

The author labors to guide the reader with diagrams, definitions, explanations, cross-references, commentaries and modern mathematical symbols to provide a clear, detailed and thorough account. He even starts from the photographic plates of Greek papyri. This is a major work of scholarship that itself deserves to become a classic; a model of its kind.

Just in case amazon readers accuse me of obsequious flattery, abject servility and distasteful onesidedness, allow me one criticism. The influence of the Ionian philosopher-mathematicians, Thales, Anaxagoras, Anaximander and Anaximenes on Plato's Academy is not covered.

A magnificent twenty-one page bibliography testifies to the author's detailed background research, and whets the reader's appetite for further reading.

Finally, three separate indexes show that the author is making every effort to help his reader as much as he can. Could one ask for more ?

Rating:
Summary: A brilliant, sprawling book
Review: Two things are certain if you really want to know what mathematics was done in Plato's Academy, and before Euclid: Your heart will break at the lack of evidence, and you will have to read this book.

Fowler details how thin the surviving evidence is, even for such basics as when Euclid's ELEMENTS were written. Drawing on other careful classicists he demolishes now traditional stories about the Pythagoreans and the irrational, Plato's Academy, even Euclid's own style in the Elements. He shows them coming from heavy interpretations of extremely vague (and often late) sources. Plates in the book show how desperately scanty are the physical remains of any mathematical writing within centuries of Plato's death. Even the first and second century AD leave us only a few scraps of Euclid.

On the positive side, Fowler gives a persuasive account of a method of reciprocal subtraction which he calls "anthyphairesis". It lay within the grasp of Athenian geometers, and suits some remarks Plato makes on mathematics, and suits traditions on geometers Plato knew, and goes far to unify and explain much of Euclid. It was apparently cited by Aristotle (under the name "antanairesis"). Probably, it really was used in the period. It also makes some very pretty geometry. Regular pentagons make a lot of sense anthyphairetically. Anyone trying to read the later books of Euclid, especially books X and XIII, will get tremendous help from this book. Conversely, you can hardly read much of this book without reading Euclid.

The book is not well organized. It spends many pages at a time on mathematical reconstructions that could not possibly have been used by the Greeks, so as to show beyond question that they could not have been. And it probably pushes its point too far. That is what classicists do. They push a point for all it is worth and perhaps more. These flaws are inevitable when you work on such important questions on so little evidence. Fowler assembles enormous amounts of classical textual evidence and later scholarship. He gives some nice mathematics including an appendix on the later arithmetized incarnation of anthyphairetic methods as continued fractions.

If you are determined to ask what math Plato knew and promoted, and what existed before Euclid--and so you are determined to break your heart--then you must read this book.