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" I think the subject I became interested in above all was mathematics. I am a mathematician fundamentally, although I have done many other things. I became very interested in mathematics at a very young age. I can never remember not being interested in mathematics, certainly at the age of three or thereabouts."¹ Sir M. James Lighthill

Sir M. James Lighthill (1924-1998) like many mathematicians, was fairly precocious and was always ahead of his age group. Fortunately, the schools he attended allowed him to learn alongside people who were considerably older. He went to one of Britain's famous schools, Winchester College, winning a scholarship there at the age of twelve. Another boy there of the same age was Freeman Dyson. The two boys studied together, and again managed to persuade the teachers to allow them to study differently from their age group. Studying mainly from books, they won major scholarships to Trinity College, Cambridge, at the age of fifteen. This was much younger than normal Cambridge practice, and Cambridge did not want them to enroll until the age of seventeen. In some respects this was good for both of them. They continued to study mathematics with great enthusiasm, but it gave them time to study many other subjects. Lighthill developed a strong interest in languages at that time. Both were able to pursue the study of humanities as well as mathematics because they had that extra time before going to the university. They had continued to do mathematics, so when they arrived at Cambridge, it was not necessary to study the undergraduate material at all.

During the war in 1941, there was a rule that no one could have more than two years of university education. After that, students were expected to engage in the war effort. Bright students were managing to get the bachelor's degree in the two years. There were very few other people going to the postgraduate lectures that Lighthill and Dyson attended. As a result, Lighthill and Dyson had some of the greatest mathematicians almost to themselves. Sometimes there were only five students in classes given by G. H. Hardy, J. E. Littlewood, P. A. M. Dirac, A. S. Besicovitch, and many other top mathematicians. The ones that taught him most were Hardy and Littlewood, both great mathematical analysts. Both believed that their work was only of importance for its own sake and because it was pure mathematics, incapable of being used for anything. A famous book by Hardy, called A Mathematician's Apology, was written to make this point.² Throughout his career in applied mathematics, Lighthill found that the training in basic analysis was endlessly valuable and important. He remembered telling Hardy that he found what Hardy taught him to be valuable in applied mathematics, but he did not think Hardy believed him.

After his two years at Cambridge Lighthill entered the war effort. Joining the aerodynamics division of the National Physical Laboratory (NPL), he was put under the charge of Sydney Goldstein, an applied mathematician. Goldstein was typical of the applied mathematicians Lighthill would have studied under at Cambridge had it not been for the war. Lighthill had not encountered such first-rate applied mathematics while he was at Cambridge, with the exception of Dirac. In 1943, Goldstein told Lighthill that the authorities believed that the war would go on for such a long time that the British would end up having to have supersonic aircraft to fight the Germans. Lighthill was given the task of finding out everything known about supersonic aerodynamics and take it on from there. He read the works that had been done by German (Prandtl, Busemann), Italian (Crocco) and Swiss (Ackeret) scientists.

Lighthill wrote many papers on supersonic aerodynamics in the first year that developed ideas about what supersonic aircraft might be like in the future. There is a tenuous link between the ideas that were coming out then and the ultimate shape which the Concorde finally took. Lighthill was deeply involved when the Concorde came about because at the time he was director of the Royal Aircraft Establishment. While he was working on other things with Goldstein, the war abruptly ended.

Lighthill had learned a lot during the two years in the war effort in applied mathematics, but he had felt terribly frustrated because he wanted to be a pure mathematician. When the war was over, he thought to himself, "Now why don't I go back and do what I was meant to do?" All his life he had wanted to do mathematics, especially pure mathematics. He returned to Cambridge, submitting to Trinity College the twelve papers he had written while at the NPL. He was granted a fellowship at Cambridge which allowed him to do research. He spent only a short time pursuing pure mathematical research, because he found people were writing him letters about the papers he had written while at the NPL. For example, G. I. Taylor, one of Britain's great mechanical scientists, had questions to ask him, as did Goldstein himself.

Lighthill received the biggest challenge of his life in 1949, when the Ministry of Aviation asked him to determine if jet aircraft developed originally for military purposes, could be used for civilian purposes. The problem was whether they could be made tolerable to communities living near airports. This has turned out to be one of the abiding preoccupations: how jets can be made quieter and more powerful at the same time. Lighthill started working on that problem and the resulting paper published in 1952 is one of the most cited papers in aerodynamics. In it, Lighthill reports his Eighth Power Law of Jet Noise that says there is a tendency for the acoustic energy emitted from the jet engine to vary as the eighth power of the jet exit velocity. This knowledge made quieter engines possible. Since those early days, jet aircraft have become increasingly quiet, making the whole development of jet transport possible. This is one area of his work where Lighthill is still involved.

When Goldstein became professor of applied mathematics at Manchester University, Lighthill joined him and continued with this work. Goldstein put together a splendid team of people, then suddenly Goldstein was taken by the call to Zionism. In 1950, he moved to Israel, where he assumed the top academic post at the Technion, the technical university at Haifa, and Lighthill was chosen to succeed him as the professor of applied mathematics. For the next nine years Lighthill headed this group of applied mathematicians. He had a first-rate laboratory called the Fluid Motion Laboratory, which had good supersonic wind tunnels, shock tubes and low turbulence tunnels. It was well equipped, with separate people to run the experimental equipment.

Lighthill returned to the study of fluids, starting new work. He had already worked with incompressible aerodynamics, or low Mach number aerodynamics, and with supersonic aerodynamics, but he had done nothing in between. He started some pioneering work in transonic aerodynamics, an interesting and more difficult field. Subsonic aerodynamics utilizes Laplace's equation, boundary layers and such concepts. Supersonic aerodynamics utilizes purely hyperbolic equations and boundary layers, but transonic aerodynamics utilizes equations of mixed type. Lighthill invented a new method based on certain hodograph transformations and mapping the problem onto a different problem which could be solved. He worked on that and on more extensions of the supersonic work to more complicated problems, like delta wings.

At the end of the 1950s, Lighthill was unexpectedly invited to direct the Royal Aircraft Establishment at Farnborough, an enterprise with about 8,000 employees. Its mission was like that of NASA Langley, a sort of overall aeronautical research establishment with out stations and a main base located at Farnborough. There was an important airfield at Bedford with large supersonic wind tunnels.

The RAE had departments covering everything from chemistry to electronics, but its main work was centered on aerodynamics and structures. The Harrier, the vertical take-off aircraft (VTOL), was at the development stage, as was the Concorde. Britain was moving forward as fast as possible into space science. While he was there, he could not actually do research himself, but it was perfectly feasible for him to write long review articles, because good bibliographical services were at his disposal. These review articles were not just summaries of other people's work, but rather his own view of it. Some of his best reviews were written during this period. After about five years, he felt that the time was right to move on into other subjects. One was oceanography, which has gradually expanded to become the science of the earth's fluid envelope. He likes that phrase because it includes the atmosphere, the oceans, the groundwater, the rivers and the lakes.

Then out of the blue came this offer to him to be a candidate for the Lucasian Chair when Dirac retired. He thought the people in fluid dynamics at Cambridge felt they would like him to be a candidate, because Sir George Gabriel Stokes had been a great Lucasian professor. Dirac had been professor for almost forty years, but Stokes had been Lucasian professor even longer. Lighthill was elected in April 1968, although Dirac was not due to retire until October of 1969. Lighthill considers these years to have been a splendid ten years, when he could concentrate entirely on research. There were no administrative or other duties attached to the post, except to generally reside during the term within five miles of the great St. Mary's Church.

Lighthill mainly concentrated on fluid dynamics research and writing books. His major book, Waves and Fluids, includes acoustics, oceanography, water waves and atmospheric science, and internal waves in the atmosphere. He has also a book on mathematical biofluiddynamics. His best seller is an eighty page book published in 1958 on generalized functions.

An important new thing happened to him while he was at Cambridge: he met a marvelous zoologist, named Torkel Weis-Fogh, a Dane, who succeeded Sir James Grey as professor of Zoology. He was an expert on insect flight. There were other people at Cambridge who were experts on bird flight, so he worked with all of these people and discoveries were made in insect flight. Whereas the bigger insects fly like a smaller version of a bird, the smaller insects fly quite differently. They use what is now known as the Weis-Fogh mechanism of flight generation, where they clap their wings. This was just one of many studies that Weis-Fogh and he did together on insect flight.

Lighthill is working with NASA today, because although Europe was technically successful with the Concorde, there have not been many Concordes flying. Success can be measured by its consistently good performance, it has not had accidents, and has done everything it was promised to do. It was expected that the first generation of supersonic transport would not be economical. There are never good economics with any first generation aircraft. It is enough if they are technically correct. It was always anticipated the second generation would be the one to show good economics. Because Lighthill does not think Europe will do it, he is concentrating on helping NASA on their high speed civil transport project, the HSCT.³

The HSCT is specially designed to minimize the level of supersonic boom noise, which he thinks is a good objective, although his own feeling about Concorde is that the supersonic boom level on the ground is not terribly objectionable. It would be more acceptable to fly it over ground if the overpressure of the supersonic boom could be brought down by a factor of four or so. That looks quite feasible with the HSCT design, but the real problem will be getting the engine noise reduced, and this involves a high Mach number jet. The Mach number of the jet can not be lowered, requiring some other method, a subject that he is working on at the moment.

Lighthill is proud of his aero-acoustical contributions, because they have clearly influenced the whole development of civil aviation, and because they made it possible for jets to be more powerful and quieter. It was mathematically difficult to solve the problem. Turbulence is difficult enough, but then coupled with deciding what noise it generates makes the problem even more difficult. Turbulence is in a way a vortex phenomenon, an incompressible phenomenon. Somehow the noise is a by-product. Working out how the noise is generated as a by-product of the turbulence involved some of the subtleties of what he regards as the essence of applied mathematics: Taking a problem where there is no recognized mathematical formulation and trying to work a good mathematical formulation.

Lighthill is also fond of his biofluiddynamics, understanding that not everyone would be, but to him it is quite important. He gave the Rayleigh lecture to the American Society of Mechanical Engineers (ASME) in the United States on the biomechanics of hearing sensitivity. The topic was his latest biofluiddynamics work about the inner ear and the fluid mechanics in the cochlea. Here again it is quite a problem to formulate the problem. He thinks that most people in hearing regard that lecture as a good summary of what they know of the subject.

After retiring from the Lucasian Chair, he accepted the position as provost of University College of London. It was an exciting period, a challenge to keep a good place good in difficult times and to make it even better by making good appointments. When he retired, he was able to look back on a college which had been positively changed as a result of his efforts. It was a great challenge to run UCL. When he took it over, they were just beginning to merge with University College Medical School. He realized that the clinical side of the university was not nearly as strong as the scientific side, but Lighthill managed a merger between the medical school and the neighboring Middlesex Hospital Medical School. Now they are the University College Middlesex School of Medicine, a powerful school.

While looking back over his life is satisfying, Lighthill doubts if there is much he can say about the future, especially the future of the Lucasian Chair. He has a general interest in the past, wishing to emphasize his almost boundless enthusiasm for Sir George Stokes. He loves the nineteenth century writers, calling them writers because, although they were wonderful researchers, they wrote up their research well. He considers Stokes' papers an absolute joy to read, brilliant writing, a characteristic he shares with Rayleigh. As an acoustics person, he is interested in almost every aspect of acoustics, including hearing. He regards Rayleigh's theory of sound as one of the great books on sound.

Concerning other previous Lucasian professors, he has taken a strong interest in Newton, and therefore an interest in Barrow as well, because they interacted. Saunderson was interesting because he was blind and was a good mathematician.

"There is no doubt that there was a stagnation in scholarship in Cambridge throughout the eighteenth century, this unreformed Cambridge was really bad. A great pity really. Airy was very good, an interesting man doing interesting things, his analytical works, the Airy Functions and so on, were great. Of course, Stokes was this grand genius, tremendously varied. What he did for viscous flow theory, for compressible flow theory, for water waves, and everything, was in no doubt unsurpassed."

Lighthill often finds that he solved problems whose solutions people have forgotten, and then forgotten that they were solved at all. Lighthill believes that for

"elderly professors like me, it's almost one of our jobs to keep reminding people of the wonderful things that were really discovered long ago by some of these people. You have to keep somehow the collective memory of science alive."

From 1946 to 1950 he was Senior Lecturer in Mathematics at the University of Manchester. In 1950 he was named Beyer Professor of Mathematics. He was elected a Fellow of the Royal Society in 1953. The Royal Aeronautical Society Bronze Medal was awarded to him in 1955 for "contributions to theoretical high speed aerodynamics which recently had included outstanding work on the source of noise, from jets in particular." In 1958 he was made a Foreign Member of the American Academy his of Arts and Sciences. Lighthill was elected a Fellow of the Royal Aeronautical Society in 1961 and is a Fellow of the American Institute Aeronautics and Astronautics. Lighthill has received numerous other awards, among them the first G. I. Taylor medal (1984) given by the Society of Engineering Science. That same year the Division of Fluid Dynamics of the American Physical Society awarded him the Otto Laporte Memorial Lecture, a division lectureship prize which recognizes outstanding contributions to fluid dynamics and to honor Otto Laporte. He continues to actively pursue his research, still publishing and speaking at an international level.

Sir M. James Lighthill tragically drowned Friday July 17, 1998 while swimming in rough seas at 74 years of age.

Footnotes

1. 1 This section is based upon an interview with Sir M. James Lighthill in December 1992. At the time of the interview, he was the only living Lucasian professor other than the current holder of the chair, Stephen Hawking.
2. 2 Godfrey Hardy, A Mathematicians's Apology (Cambridge: Cambridge University Press, 1967).
3. 3 Robert Rosen,"The Rebirth of the Supersonic Transport," Technology Review 96(2) (1993): 22-29.