## David Fowler

### A leading expert on the history of early Greek mathematics and head of Warwick University's Mathematics Research Centre

David Fowler, who has died aged 66, was an eminent historian of mathematics at Warwick University. He was one of the top half dozen leading experts in the world on early Greek mathematics, notably of pre-Euclidean ratio theory. He was a well-known figure in the British Society of the History of Mathematics, and was regarded as a father figure by many of the younger members. He always attended meetings of the BSHM, gently and wisely contributing to the discussions of all the papers presented there. Among historians he was looked up to as an authoritative mathematician, and among mathematicians he was looked up to as an authoritative historian; he managed to straddle both worlds.Born in Blackburn, he went to Russell school near Morecambe Bay. When he was 13, he designed and built himself a television set, but his real love was always for mathematics. In 1955 he entered Gonville and Caius College, Cambridge, to read mathematics, and I first met him there as his tutor. We remained close friends for nearly half a century.

He used to come for tutorials with fellow student John Conway, which guaranteed the wit flying around, and I remember them as the most exciting tutorials I have ever been party to. David was generous and thoughtful, enthusiastic and sensitive to the feelings of others, and seldom angry. He was always interested in what you had to say to him, and his replies were always stimulating and often very amusing. He graduated with a first, and then stayed on to do research in analysis for two years before accepting a lecturership at Manchester in 1961. Meanwhile I moved to the new University of Warwick to begin the Mathematics Institute there. When the Nuffield Foundation gave Warwick the money to found a Mathematics Research Centre in 1967, I realised it needed a person of very special qualities to manage it, and I knew that David was that person. He chose Elaine Shiels (now Coelho) to be the Centre secretary and, during the next 20 years they welcomed more than 1,000 long-term senior visitors to the annual year-long research symposia held at Warwick. They found housing for all the visitors, solved all their problems, talked maths with them and made them happy.

They dealt with all the difficulties that arose with amazing patience, generosity and compassion. In many ways it was a horrendous task, occupying much of his time; many of the staff would have balked at it, but Fowler's love of people made it rewarding for him. Warwick benefited academically from all the visitors, and became famous throughout the mathematical world for its symposia. This fame and success was due in no small measure to the skill and devotion of David helped by Elaine.

Meanwhile, mathematically Fowler lectured on analysis, and published a popular undergraduate textbook *Introducing Real Analysis* (1973) and a graduate course on global analysis and its applications.

In 1972, he and his French wife, Denise, translated into English René Thom's famous book *Structural Stability And Morphogenesis*, thus making catastrophe theory accessible to the English-speaking world.

Fowler's initial venture into history began in 1979 with a ground-breaking paper *Ratio In Early Greek Mathematics*, published in the Bulletin of the American Mathematical Society. The history of mathematics then became his major research interest, and indeed his passion.

His thesis was as follows: not having the real numbers, nor division, the Greeks faced difficulties in defining rigorously the notion of ratio. They called ratio *logos* (the word whose nobility is apparent from its use in the first verse of the Gospel according to St John). 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 lucid papers, culminating in a challenging and highly original book *The Mathematics of Plato's Academy: A New Reconstruction*, which was published in 1987. This book is based on a deep study of the primary sources and on their enthusiastic assimilation and transformation. Although parts of his work have been considered controversial by some, his contribution to the history of Greek mathematics has been substantial and is of lasting value.

David Fowler was a cultured man with wide interests. He made himself a clavichord, which he played softly, and he contributed a chapter to *Music And Mathematics* (2003). He was also a quiet but unwavering supporter of human rights, environmental and educational organisations and campains.

He was loved by all his students and colleagues, and he will be greatly missed. He is survived by his wife Denise and their children Stephan and Magali.

**Christopher Zeeman**

*David Herbert Fowler, historian of mathematics, bom April*28 1937;

*died April*13 2004

Monday May 3 2004 © Guardian Newspapers Limited