David Fowler: Obituary of the British Historian of Mathematics

Steve Russ, Eleanor Robson, Rona Epstein, and David Epstein in the London Independent (May 24, 2004):

AS THE first Manager of the Mathematics Research Centre at Warwick University, from 1967, David Fowler played an important part in establishing, through the research symposia organised at the centre, the outstanding international reputation that Warwick now enjoys in many branches of mathematics. As a distinguished scholar of the history of mathematics he has left a wonderful legacy in the form of a series of papers and books presenting, in rich detail, a far-reaching, original and inventive re-interpretation of early Greek mathematics....

Not so long ago, a mathematician was sent a book to review. It was a dense and learned tome on ancient Greek mathematics that he was about to return when he noticed the price. Intrigued that a book could be both so incomprehensible and so expensive, he took it home out of sheer curiosity and ended up becoming a historian of Greek mathematics himself. The year was 1975, the book Wilbur Knorr's The Evolution of the Euclidean Elements, and the mathematician David Fowler. This was the story he liked to tell of his origins as a historian, although ironically the whole of his subsequent career was spent in refuting the accepted story of the origins of Greek mathematics and arguing, very engagingly and persuasively, for another one.

Here, first, is the standard account. In fifth-century Athens, Greek mathematics was all about numbers, just like mathematics in other ancient cultures. Then the Greeks discovered incommensurability: that some ratios of lengths or areas could not be expressed in terms of whole numbers. An example, discovered by the Greeks, is the square root of 2, equal to 1.414213562373095... . This caused such a shock to the Greek mathematicians that they abandoned numbers altogether and instead invented the Euclidean geometrical tradition that describes and explores only the properties and relationships of mathematical objects, not their numerical values. The most famous of these de-arithmetised formulations is Euclid's Elements book II, proposition 12: The square on the hypotenuse of a right triangle is equal to the sum of the squares on its two shorter sides.

But, asked Fowler, where is the evidence for this story? Early, pre-Euclidean mathematics suggests nothing of the sort. It is all in the works of later Greek commentators on mathematics and its history, who had no better access to the very ancient sources than we do. In fact, there is no direct evidence at all for the mathematics of the fifth century BC; the earliest extant source is Plato's dialogue Meno from 385 BC.