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Department of Applied Mathematics and Theoretical Physics

Address given at Professor David Crighton's Memorial Service

Delivered on 3 June 2000 in Great St. Mary's Church, Cambridge

David George Crighton, whose year-long battle with cancer was lost on 12th April this year was Master of Jesus College and one of the country's most influential applied mathematicians. He passionately believed that mathematics provided the best way of understanding complex systems and that a good mathematical education was the best route for enabling the most able people to address really important practical problems. He also believed, and amply demonstrated throughout his career, that the practical problems provided one of the best incentives for developing the subject - a subject he really cared about and enjoyed. It was fun to do mathematics with Crighton.

What made David remarkable was the consistency with which he applied a very good memory and a great natural intelligence to very hard work without ever appearing stressed. He had the highest standards of intellectual integrity and a natural humility: qualities that made him approachable and warm and very easy to like and to trust. He rose to the top of his profession and was greatly admired.

His parents saw little in David's background that pointed to mathematical brilliance. Their natural courtesy and charm, which David certainly inherited, made it difficult to be certain that they weren't being modest. He insisted that being born in Wales during wartime did not make him Welsh - I thought him overly-modest on that point.

He seemed to be good at everything at Watford Grammar School and spoke with affection about being spurred into mathematics by a teacher's challenge. He took Firsts in both parts of the Mathematics Tripos at St John's, but did not stay at Cambridge to do Part III, the normally preferred route into research and an academic career. I never really found out why he left Cambridge so abruptly. He was a very private person, despite his warmth of character.

David Crighton became a lecturer in mathematics at Woolwich Polytechnic and within a year was made Senior Lecturer, a post paying at that time a salary much higher than those available at universities. Woolwich provided night school courses on the London University External Degree Programme, that were much in demand, with the students being older, more streetwise, and rougher than we see here. David's rapid promotion reflected the fact that lecturers capable of teaching such classes at the Honours level were very difficult to find. He was at the top of the Polytechnic's career grade within a year of starting, and he was 23 years old. He needed a bigger challenge. He was interested in research, very interested in applications of mathematics to real problems, but he did not want to come back to Cambridge.

He became my Research Assistant in 1967 and registered as a research student at Imperial College, where the application of mathematics to understand and control the noise of unsteady flow was a lively research issue. Concorde's take-off noise problem and the need to limit the underwater sound by which submarines could be detected provided the context for the work. It also provided a most stimulating research environment in which really bright people tackled very hard problems. David was in his element.

For the next nine years David was at the heart of the most vibrant attack ever mounted on the aircraft noise problem and its underwater counterpart. Unravelling the intricate complexity of experimental results by correlating them with the predictions of theoretical models was the best approach and he was superb at it, his analytical skills being matched by his ability to find new techniques through extensive reading and through collaboration with others. His judgement on what techniques to use and on who to collaborate with was impeccable.

I still recall with a thrill the dawning of our realisation that the fine bubbles about to be introduced to give water the features of a sound-absorbing foam, would actually amplify underwater noise by a very large factor indeed. Those bubbles made possible a completely new and better way of sound creation - a fact we were encouraged to keep quiet at the time!

David's interaction with Frank Leppington was especially fruitful in this phase. Together they made brilliant advances by bringing together the subjects of wave diffraction and aeroacoustics to solve definite new types of problems using clever mathematical methods. The singular perturbation and matched asymptotic expansion techniques they harnessed so effectively were to become a solid foundation for much of David's future research. Their involvement in the British Navy's amusingly titled ‘Baffle Panel' provided access to the practical problems in a very agreeable way.

David served on Concorde's noise research panel and made fundamental contributions to its work. He was quick to appreciate how much of the take-off noise problem was caused by features outside the classical models and he was very good at extending their scope. Some of the problems lay in the coupling of instability waves to sound, now an important and much-studied subject for which David Crighton laid reliable foundations, and some of the problems lay in the non-linear effects by which very loud sounds change their character as they travel. That again was a subject that David expanded enormously and was indeed the subject he made largely his own in later years.

When the Concorde noise research programme moved to Cambridge in 1972, David was reluctant to move with it. He had many opportunities to become a university lecturer, chances I encouraged him to ignore. Brilliant research work would be bound to suffer were he to join the academic ladder at its lower rungs and it was completely obvious to me that he would soon be sought after for a senior position. But it wasn't obvious to him, and his confidence began to falter. He eventually accepted a research post in the Concorde programme at our Engineering Department, but hardly visited the place before he was appointed to succeed T. G. Cowling as Professor of Applied Mathematics at Leeds University. That was exactly what both David and Leeds needed.

David threw all his energy into raising academic standards and staff morale at Leeds. His qualities of charismatic leadership soon became evident and he brought about a veritable transformation of the Department. He knew how to attract funds and how to motivate his team. He led from the front making major contributions to the modelling of non-linear waves and extending significantly the scope of asymptotic methods. He wrote about these with great clarity and authority. He lectured extensively, travelling a great deal and earning international acclaim.

Everyone who knew David knew how he really cared for his students, but it took a tragedy for that care to be expressed in any public way. David dedicated his lecture to the first European/American Aeroacoustics Conference to the memory of Alex Cargill, his brilliant student who died suddenly and unexpectedly; the warmth and compassion in that dedication is an elegant expression of what David really was.

It is one of Cambridge's greatest strengths that it is able to attract outstanding scholars. It's ability to attract outstanding leaders is less apparent but equally important, and might well rest on the reputation of its top professors. David enormously admired George Batchelor, founder of the Department of Applied Mathematics and Theoretical Physics, and Founding Editor of what David regarded as the finest scholarly journal in his subject, The Journal of Fluid Mechanics. David was appointed into George Batchelor's Chair and became Editor of JFM, a fantastic realisation of things he would never have expected. Though he survived George by less than a month he had held the reins long enough for both the Department and the Journal to surge forward under his leadership. He seemed to do everything right. He brought the same inspiration to Cambridge that had transformed Leeds and very soon his influence could be seen to be benefiting the University and inspiring his colleagues. He chaired the Funding Councils' mathematics committees, founded and chaired their non-linear systems initiative and chaired also the NATO non-linear science panel. Through things like these his reputation grew, but that of his department grew more. Cambridge Applied Mathematics stands today the equal of the very best in the world and David was amongst their most influential leaders.

And still he made friends and continued to collaborate with scholars and students on new mathematical matters. He was remarkable. His genius was happily married to very hard work and like all happy marriages it seemed easy. His achievement of the rare five-star grade for the Department of Applied Mathematics and Theoretical Physics was a bit of an anti-climax. He had left no stone unturned and spared no effort in presenting the Department in the best possible light. But everyone knew the five-star was right and everybody, apart from him, expected it.

DAMTP's contribution to industry grew steadily under David's leadership. Research funding followed and students flourished, confident of their place in the world and in their ability to contribute by solving really worthwhile problems. DAMTP was being looked upon as a natural source of answers, an attitude that was really David's legacy. He had, so to speak, made as good friends with corporations as he had with people, a step that brought large-scale industrial support. He believed Cambridge needed the best equipment and he was able to persuade industrial sponsors to provide it. He brought some of the world's most powerful computing equipment to Cambridge and there are many here today who can testify to the advantage that provided.

It seemed natural that Jesus College should choose David as Master. That appointment provided a challenge for him and an opportunity that brought his wife Johanna into the centre of his professional life. They both loved it. Jesus has a tradition of achievement and scholarship and sparkle that drew David to its heart. He threw as much energy into the College as most men are capable of, but it hardly dented David's commitment to DAMTP. From nearby I could observe the waves he made, and could see and hear how much he was appreciated. David was a star and College duties seemed to add to rather than detract from his mathematical life. At Jesus he was a new inspiration. Everybody seemed to know and love him. That was no surprise to his friends, of course. He and Johanna had made the Master's Lodge a friendly and hospitable place and David was happy in it. He was also very very busy and being busy was what he wanted most. But, just over a year ago, it all fell apart. He became ill, initially with a breathing problem; then complications and secondary cancer was diagnosed in the liver. That was awful. He knew what it meant and with friends and family he preferred to ignore it. He worked it out. His love of work kept him stable. That is what he wanted to do.

Here was a man at the height of a wonderful career; Master of Jesus College, Head of the most wonderful mathematics department, with friends and admirers from all over the world, trapped in a mandatory decline. It was tragic. I thought he worked too hard. He thought about details of University and professional life more than was necessary. He deserved a rest, and I told him so. He protested that continuing with work on things, and in a place that he loved, was what he wanted to do, and who could protest at that?

I have said little about David's musical interests and that is deliberate because though I was very close to him and appreciated his doings more than most, I never could understand his music. I couldn't actually understand his enthusiasm for matched asymptotic expansions either. We often bantered about these things. I recall with particular pleasure the visit we made together with Lothar Kramer, the acoustical genius behind Berlin's Philharmonic Hall to hear a wonderful concert in two parts. In the first, Tortellier played Elgar's Cello Concerto; the second featured a modern Czechlosvakian piece by a composer unknown to me. Tortellier was absolutely marvellous, holding his audience spellbound well after the finish of the piece - in fact well into the interval that followed. David, who knew much more about the music and the performer was much less moved than I was, reflecting on the absence of any association with the Malvern Hills that should have been evident in the Concerto. He predicted a fantastic second half, and enjoyed it immensely and enthused about it. I was amazed. The performance had made me reflect on chaos and cacophony. We often reflected about that concert. We saw some things differently but never differed on important things.

As I look back on his life I recall with delight the evening in a North-American restaurant where I had gone for a private discussion with Janos Laufer, a close friend with shared interests in fluid mechanics - and food. We had ordered a very fine meal. The first course had been enjoyed, and we had relaxed away from the pressures of scientific discussions with conference colleagues. Our second course had just been served, but not started, when there was a commotion from the kitchen and a rush of chefs to our table. Something was clearly wrong. The wine was whisked away and the food removed from our table with abject apologies from the man wearing the biggest hat. All very alarming, until we smelt something fishy - the chefs were too agitated and it dawned slowly on us that we were the subject of a practical joke. Professor Karamchety from Stanford was the Head Chef and David Crighton his fussing assistant.

David, internationally acknowledged for his leadership of applied mathematics, was much honoured in his profession. A Fellow of the Royal Society, and editor of its proceedings he won many medals, chaired the most influential committees and boards. The Gauss Medal in Braunschweig gave him particular pleasure, as did his membership of the Academia Europea and his honorary degrees. He had even been welcomed at Clinton's White House and was soon to have been honoured by Majesty the Queen. The Queen had approved the offer of an award of the CBE just before he died, but he never knew it. There were many wonderful things ahead of him, and he would have rejoiced in them all.

He will be remembered with enormous gratitude by his College, whose portrait of David, which was painted at a desperate phase of his illness, gives a remarkable and wonderful insight into a marvellous man held in very great affection. He will be remembered by very many others, unsure of whether they admired him more for his genius or for the friendship that he offered so freely and so warmly.

Prof. J.E. Ffowcs Williams