David Fowler

Historian of ancient mathematics

David Herbert Fowler, historian of mathematics: born Blackburn, Lancashire 28 April 1937; Lecturer in Mathematics, Manchester University 1961-67; Lecturer in Mathematics, Warwick University 1967-80, Senior Lecturer 1980-90, Reader 1990-2000 (Emeritus); married Denise Stroh (one son, one daughter); died Warwick 13 April 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.

While at Rossall School near Fleetwood, Lancashire, in the early 1950s he was taught and influenced by a particularly dedicated mathematics master, R.K. Melluish. He decided to read that subject at Gonville and Caius College, Cambridge, where he also went on to do research in analysis. Fowler's first academic post was as Lecturer in Mathematics at Manchester University, from 1961 to 1967.

In 1967, he began lecturing in analysis at Warwick, having been invited there by (Sir) Christopher Zeeman, his former tutor at Cambridge. Zeeman was then setting up the Mathematics Institute at the newly established university and Fowler was appointed to manage the Mathematics Research Centre.

Fowler brought many special and unusual abilities to the task. His great interest in people, and in mathematics, and his mastery of many practical issues in the maintenance of good living conditions, enabled him to provide, with colleagues, conditions under which distinguished visitors created much new mathematics and proved many new theorems. As a result, there were, in almost every year during Fowler's first 25 years at Warwick, more mathematicians visiting the university's Mathematics Department than there were mathematical visitors to all other English universities combined - a remarkable record for a new university.

In the midst of so much administrative activity, and interaction with leading scholars, Fowler did not neglect the students. He formed good relationships with his many undergraduate tutees, some of whom became lifelong friends. He was an outstanding teacher, concentrating on helping students to think things out for themselves instead of just listening to a lecturer. He pioneered different ways of university teaching long before such experimentation became fashionable, encouraging students to learn mathematics by doing: by solving problems and by sharing work.

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.

In it, Socrates teaches Meno's slaveboy about the mathematics of ratio and proportion, not by lecturing but by questioning him in such a way that he allows the slaveboy to discover the results for himself. Through treating these early sources seriously, as both textual and material evidence, Fowler argued instead that Euclidean mathematics evolved naturally from a Greek tradition that was deeply concerned with ratio, proportion, and approximation in several different ways.

The book that resulted, The Mathematics of Plato's Academy (1987), is as dense and learned as Knorr's, but sparkles with humour, originality, and a concern for the reader that is as rare as hens' teeth in most academic writing. Academic authors are often at a loss to know exactly who, and how many, read and use particular books or manuscripts. In Fowler's case it seems that philosophers, classicists, papyrologists, and historians of mathematics, as well as mathematicians themselves, have all found value in his work: there are no less than 15 copies of it circulating in Oxford's university libraries alone.

In January 1994, Fowler sought medical advice for what he described as a "strange collection of sensations". He was given a devastating diagnosis, a brain tumour inaccessibly deep in the left frontal lobe. He faced this with amazing fortitude. Those around him were always struck by the grace and good-humour with which he bore his illness. It was typical of the man that he wrote a letter to all his colleagues, telling them of his illness and reassuring them that he understood their sympathy and that there is "no need to attempt to say anything if you would prefer not to do so".

In the British Medical Journal of 23 December 1995, David Fowler wrote of his experiences and his philosophy under the title "A Case for Non-intervention", explaining his choice to refuse an intrusive biopsy, and his and his wife Denise's decision to "get on with our lives". Which is exactly what they did. David himself continued with his teaching and research for a further six years. Denise completed a PhD in history that was awarded at the same ceremony in 1999 in which David was awarded a DSc from Warwick.

Throughout his life, a natural expression of his compassion and humanity was the thoughtful and active support David Fowler gave to numerous social causes. These ranged from those on a wide scale such as human rights and comprehensive education, to more local issues of traffic congestion, and being active in his local community.

His broad social interests naturally included capitalising on any academic gathering. Running throughout Fowler's mathematics teaching at Warwick, as well as his later historical writing, was a deep concern with Socratic dialogue between teacher and student. He was a marvellous listener.

Steve Russ, Eleanor Robson, Rona Epstein and David Epstein

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