David Fowler (mathematician)
Encyclopedia
David Herbert Fowler was a historian of Greek mathematics
who published work on pre-Eudoxian
ratio theory (using the process he called anthyphaeresis). He disputed the standard story of
Greek mathematical discovery, in which the discovery of the phenomenon of incommensurability
came as a shock.
His thesis was that, not having the real numbers, nor division, the Greeks
faced difficulties in defining rigorously the notion of ratio
. They called ratio 'logos
'. Euclid
Book V is an exposition of Eudoxus's theory of proportion, which Eudoxus discovered about 350BC, and which has been described as the jewel in the crown of Greek mathematics. Eudoxus showed by a form of abstract algebra how to handle rigorously the case when two ratios are equal, without actually having to define them. His theory was so successful that, in effect, it killed off perfectly good earlier theories of ratio, and Fowler's aim had been to find the evidence for the rediscovery of these previous theories.
In particular Thaetetus (c 414-369BC) introduced a definition of ratio using a procedure called anthyphairesis, based on the Euclidean subtraction algorithm
. Fowler developed his ideas in a series of papers, culminating in the book The Mathematics of Plato's Academy: A New Reconstruction, which was published in 1987. This book is based on a study of the primary sources and on their assimilation and transformation.
Greek mathematics
Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 7th century BC to the 4th century AD around the Eastern shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to...
who published work on pre-Eudoxian
Eudoxus of Cnidus
Eudoxus of Cnidus was a Greek astronomer, mathematician, scholar and student of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy...
ratio theory (using the process he called anthyphaeresis). He disputed the standard story of
Greek mathematical discovery, in which the discovery of the phenomenon of incommensurability
Commensurability (mathematics)
In mathematics, two non-zero real numbers a and b are said to be commensurable if a/b is a rational number.-History of the concept:...
came as a shock.
His thesis was that, not having the real numbers, nor division, the Greeks
Greeks
The Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....
faced difficulties in defining rigorously the notion of ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
. They called ratio 'logos
Logos
' is an important term in philosophy, psychology, rhetoric and religion. Originally a word meaning "a ground", "a plea", "an opinion", "an expectation", "word," "speech," "account," "reason," it became a technical term in philosophy, beginning with Heraclitus ' is an important term in...
'. Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
Book V is an exposition of Eudoxus's theory of proportion, which Eudoxus discovered about 350BC, and which has been described as the jewel in the crown of Greek mathematics. Eudoxus showed by a form of abstract algebra how to handle rigorously the case when two ratios are equal, without actually having to define them. His theory was so successful that, in effect, it killed off perfectly good earlier theories of ratio, and Fowler's aim had been to find the evidence for the rediscovery of these previous theories.
In particular Thaetetus (c 414-369BC) introduced a definition of ratio using a procedure called anthyphairesis, based on the Euclidean subtraction algorithm
Euclidean algorithm
In mathematics, the Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, also known as the greatest common factor or highest common factor...
. Fowler developed his ideas in a series of papers, culminating in the book The Mathematics of Plato's Academy: A New Reconstruction, which was published in 1987. This book is based on a study of the primary sources and on their assimilation and transformation.
External links
- Bibliography
- Book Review of The Mathematics of Plato's Academy
- Memorial symposium organized in his honor at Warwick, 9 November 2004.