David Fowler

Who was David Fowler?

David Herbert Fowler was a historian of Greek mathematics who published work on pre-Eudoxian ratio theory. 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 Theaetetus 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.