## Rollo Davidson: 1944-1970

Rollo Davidson was born on 8 October 1944 in Bristol, and spent his childhood at Thornbury, Gloucestershire. Like his father, his father's father, both his mother's brothers and his own younger brother, he took a Scholarship to Winchester. Here his career was characterized by breadth (Ancient History as well as Mathematics at A level) and speed (he won the Senior Mathematical Prize at the age of 16). One of his school papers which has been preserved is a Stewart McDowall Essay (1962) on 'The Appeal of Science to the Victorian Intelligentsia'.

He matriculated as a Scholar of Trinity College at the University of Cambridge in October 1962. He was awarded the Percy Pemberton prize as the Trinity undergraduate most distinguished in his studies in his first year, and at the end of his second year he was already a Wrangler. It would have been normal at that time to spend the third year working for Part III of the Mathematical Tripos, but with characteristic independence Davidson chose to take the course for the Diploma in Mathematical Statistics instead (in which he duly received, with distinction). It was this choice which determined the way he was to spend the next 5 years, in which brief period he made profound contributions to Probability Theory, a circumstance perhaps without parallel. It is idle to speculate on what he might have achieved, had he lived to attain full maturity in years and in his profession, but to his friends and colleagues there can be no doubt of the immense loss to learning, and to the society of scholars, occasioned by his tragically early death in 1970. By this time he had become a Smith's Prizeman (1967), a Research Fellow of Trinity College (1967), Ph.D. (1968), Assistant Lecturer in the Department of Pure Mathematics and Mathematical Statistics (1968), Lecturer in the Statistical Laboratory in the same Department (1969) and Fellow-elect of Churchill College (1970).

It is so usual for prodigies to be sophisticated, and perhaps even intolerable, that one must stress how far Davidson was from following this familiar pattern. Extremely diffident, overcoming a natural shyness by power of will alone, and far from self-confident in his mathematical powers, he did not at all realize until the last year or two that he had the capacity not merely to solve hard problems but to create new fields of enquiry, and to take the undisputed lead in them. In his work on Delphic semigroups he was the problem-solver, cracking one hard nut after another, but in his work on Stochastic Geometry, with which his name will always be linked, he quickly became, as Klaus Krickeberg has written, `the reader one wrote for':

'I have systematized, made precise and generalized many things, but most of the basic intuitive ideas are his. I always assumed that we would go on like this for some time to come, pushing each other ahead and complementing each other, and while writing the article I thought of him as the reader of it, and imagined how he would be surprised and pleased with certain things.

Davidson had an unpredictable variety of special interests outside mathematics, and any visitor to his rooms at Trinity would be struck by these. He was interested in trains, in physical geography, in old books (a 'regular' at David's stall on Saturday mornings, he collected especially old Alpine books), and above all things he adored mountains. Mathematical excursions quickly became the passport to mountain wanderings. In June 1969 a 'Tagung' at Oberwolfach was devoted to 'Integral Geometry and Geometrical Probability'; Krickeberg and D.G.K. organized it, but it was the existence of Davidson's thesis which inspired the project. There were many happy rambles over the Black Forest hills during that week, which proved scientifically very fruitful, for it was followed by three weeks of collaboration in Heidelberg between Davidson and Krickeberg, which led to many advances.

We mention 'physical geography' because Davidson's papers contain a correspondence with the Hydrographer of the Navy on the existence (or not) of bores on certain Chinese rivers. This may have been linked to conversations with Trinity colleagues, although his own interest in bores undoubtedly came from growing up (by the Severn) near such a good one. But he may well have been equally interested in the observer of the Chinese bores, Commander W. Usborne Moore, R.N. (H.M.S. Rambler) in 1888-92, and he would certainly have leaped at the chance of an antiquarian contribution to physical science; he would have delighted in D.E. Cartwright's 'Tides and waves in the vicinity of Saint Helena' (Phil. Trans. Roy. Soc. A, 270 (1971), 603-649) and in the utilization there of observations cited from 'Maskelyne, N. (1762b)'.

In August 1969 Davidson went to Canada to participate in the Twelfth Biennial Seminar of the Canadian Mathematical Society which was held in Vancouver. Here he went to the Cascade Pass with Daryl Daley, and on one of the weekends took a party to climb The Lions (getting within a few hundred feet of the summit). At about this time he was discussing the possible truth of the Riemann hypothesis with Littlewood, and lending a hand with Littlewood's psychophysical experiments and their statistical analysis.

From this point onwards Davidson's mathematical and mountaineering notes get rather mixed up. There is a 1969 entry of a visit to Snowdon (probably at Easter time) in characteristic style:

`0th day ... Bangor:Cod and Chips, Tea, Buns, 6s 9d. Buns OK.

5th day ... Pen yr Olewen, C.D., C.L., F.Grach, down into cwm below Craig Ysfa, up to Bwlch, Pen Helig ... very fine: sun on tops of rocks'.

Rollo Davidson In June 1970 he went to Skye with E.F.H., climbing Sgurr Alasdair `by something like Collie's route'. Later 'on the 15th we moved over to Sligachan and did the classic expedition: S.nan Gillean by the Pinnacle and West ridges. Very pleasant scrambling ... The new Guide recommends descent on the right (W.) side of the 3rd Pinnacle, but this appears to be dictated by a desire to stop the holds on the usual route getting too smooth'. By avid reading he had absorbed the spirit of early British mountaineering, and in the Coolins, he almost ritually enacted for himself the legendary traditions. The climbing apart, it was finding in the Glen Brittle Post Office log-book a Cambridge entry of the 1920s (with such names as Adrian, R.H. Fowler, Littlewood and many others) that perhaps more than anything closed the link with the old days. Agile, swift and light as an elf on the mountains, and totally untroubled by 'exposure', he had advanced in skill and achievement in climbing as in everything else: his climbs at home were also stages in the symbolical ascent to the great peaks abroad, and he now had the Alps clearly in his sight.

By now, also, Davidson was preparing for a Royal Society sponsored visit to Erevan, in the Armenian Soviet Socialist Republic. Here he hoped especially to meet again and work with R.V. Ambartzumian, a distinguished young mathematician sharing both his mathematical and his mountaineering interests, but of course he had intended as well to visit the probabilists in Moscow, Leningrad and Kharkov. His notes on the proposed visit include the postscript: `I'd like to cross a pass or two in the Caucasus'. But this expedition was not to take place.

In July he went to the Alps with the Cambridge University Mountaineering Club, accompanied by a Russian grammar and Paul-Andre Meyer's ProbabilitÃ©s et Potentiel, the latter decorated by mathematical comments in the margin and climbing notes on the fly leaf. After a very successful meet, the party broke up to go their several ways, Davidson remaining with Michael Latham (a gifted young mathematician from Gonville and Caius College) near Pontresina, to climb the Piz Bernina.

On 29 July 1970, while they were descending from the summit, an accident cost them both their lives.

David Williams expressed all our feelings at the time when he wrote in a letter to one of us:

`I feel so angry - if `angry' is the word, (but anger that he died, not at how) - at such a loss for parents, friends, Cambridge, but, above all, for himself.'

From such feelings this book emerged. In the years that have gone to the making of it one has learned to see things in a slightly different perspective. Rollo's was a magnificent life; a flawless blend of personal relations, mathematics and mountain adventure. The hazards of the latter, never wholly to be avoided, are familiar to all, and to rail at its folly is to invite a reply which he himself might have made, in the words of one of the more sympathetic characters in contemporary fiction:

`If you always look over your shoulder, how can you still remain a human being?'

**E.F.Harding and D.G.Kendall**

Reproduced with the permission of the copyright holder John Wiley & Sons Ltd.

Obituary published in the Volumes in honour of Rollo Davidson.