James was educated at Winchester College and, at the age of 15, he won a scholarship to Trinity College, Cambridge. However, he chose to wait until he was 17 years old before entering Trinity College which he did in 1941. He graduated with a BA in 1943, after taking a course shortened because of World War II.
While at Cambridge, Lighthill met Nancy Dumaresq who was studying mathematics at Newnham College. Lighthill tried to get a job in the Royal Aircraft Establishment at Farnborough after he graduated, since Nancy already had a job there. However, he was offered a job in the Aerodynamics Division of the National Physical Laboratory at Teddington. Lighthill married Nancy in 1945, the year he finished his job at the National Physical Laboratory.
Lighthill was elected a fellow of Trinity College in 1945 and he held this fellowship until 1949. In 1946 he was appointed as a Senior Lecturer at Manchester University and there he set up a very strong fluid dynamics group which soon dominated research in fluids. In 1950 Lighthill was promoted to Beyer Professor of Applied Mathematics at Manchester University.
In 1959 Lighthill moved from Manchester to become director of the Royal Aircraft Establishment at Farnborough. In the early 1960s he formed links between the Royal Aircraft Establishment and the Post Office to develop commercial television and communications satellites. He was also involved in plans for a manned space craft which would return to earth. His work at this time on supersonic aircraft proved to be vital in the development of the joint French-UK project for the Concorde supersonic passenger aircraft.
In 1953 Lighthill had been elected as a fellow of the Royal Society of London and, in 1964, he became Royal Society Research Professor attached to Imperial College in London. Also at this time Lighthill, who had become unhappy with the support given to applied mathematics from government sources, founded the Institute of Mathematics and its Applications, becoming its first president in 1965-67.
In 1969 Paul Dirac retired as Lucasian professor of Mathematics at the University of Cambridge and Lighthill was appointed to succeed him. Lighthill held the Lucasian chair for 10 years and was proud to hold the chair once held by Newton. He became Provost of University College London in 1979, Stephen Hawking succeeding him as Lucasian Professor of Mathematics at Cambridge, and Lighthill held this administrative post for 10 years until he retired in 1989. In this post Lighthill was much involved in fund raising but, despite a heavy administrative load, he continued his mathematical work studying chaotic systems, methods of extracting wave energy, and human hearing on which topic he gave the lecture Acoustic streaming in the ear itself at a conference on fluid dynamics in biology at Seattle in 1991.
After Lighthill retired in 1989 he took on the position as chairman of the Special Committee on the International Decade for Natural Disaster Reduction which was sponsored by the International Council of Scientific Unions. He held this position from 1990 to 1995. He spoke on a topic related to this Large scale hazards - tropical cyclones, earthquakes, risk, mathematics at the ICIAM 95 Conference in Hamburg in 1995.
Lighthill's mathematical publications began in 1944 with publications such as Two-dimensional supersonic aerofoil theory, The conditions behind the trailing edge of the supersonic aerofoil, and Supersonic flow past bodies of revolution. Crighton, in , describes his work during his time at Manchester where he:-
... worked extensively on gas dynamics, including effects important at very high speed, in his studies of ionisation processes, and the diffraction of shock and blast waves. He also launched two major new fields in fluid mechanics.The first of these new fields was aeroacoustics which proved to be of vital importance in the reduction of noise from jet engines. He introduced this topic in two fundamental papers On sound generated aerodynamically. I. General theory and On sound generated aerodynamically. II. Turbulence as a source of sound which appeared in the Proceedings of the Royal Society of London in 1952 and 1954 respectively. On this topic he gave Lighthill's eighth power law which states that the acoustic power radiated by a jet is proportional to the eighth power of the jet speed.
The second new field introduced by Lighthill during his time at Manchester was nonlinear acoustics which :-
... was initiated by a famous 100-page article written in 1956 in honour of the 70th birthday of another great mechanics scientist Sir Geoffrey Taylor. This field is again represented now by many thousands of papers, and applications include kidney-stone-crushing lithotripsy machines and, with the same mathematics, flood waves in rivers and traffic flow on highways.Another new field introduced by Lighthill during his time as Royal Society Research Professor at Imperial College London was mathematical biofluiddynamics. In his important text Mathematical biofluiddynamics (1975) he writes:-
The present author as a lifelong devotee of fluid dynamics has attempted in this book to demonstrate that during the past two decades there has come of age a new major division of the subject: biofluiddynamics.The first part of the book covers topics such as: swimming and flying of animals for high Reynolds number, and ciliary and flagellar propulsion in low Reynolds number. It studies the theory of fish locomotion and the flight of birds and insects. The second part of the book deals with respiratory flow and pulse propagation. It also considers blood flow, arterial disease, and microcirculation.
During his time as Lucasian Professor of Mathematics, Lighthill :-
... widened his range yet further with work on control systems; on active control of sound, or antisound; more and more on waves; on oceanography and atmospheric dynamics, including monsoon prediction and propagation; and on biological mechanics at the microscopic level.Lighthill's classic text Waves in fluids was published in 1978. In it he writes:-
This book is designed as a comprehensive introduction to the science of wave motions in fluids (that is, in liquids and gases), an area of knowledge which forms an essential part of the dynamics of fluids, as well as a significant part of general wave science, and, also has important applications to the sciences of the environment and of engineering. The [book] has two principal aims. First ... it allows an analysis in depth of four important and representative types of waves in fluids (sound waves, one-dimensional waves in fluids, water waves, internal waves)... At the same time, the subject matter ... is chosen so that ... all the most generally useful fundamental ideas of the science of waves in fluids can be developed at length, one after another.It should not be thought from this brief summary of Lighthill's work that he was interested only in applications of standard mathematical techniques. He did considerable work developing new mathematical tools particularly in the area of Fourier analysis and generalised functions.
Lighthill certainly attracted attention in many ways such as in 1959 when he was fined £1 in a very public court case in which he was accused of jumping off a moving train. He had discovered that the train he was on did not stop at Crewe and he persuaded the guard to have the train slow down enough for him to jump out!
Several times he was accused of speeding in his car. Many others would plead guilty to such an offence and pay the fine but not so Lighthill. He would successfully contest the charge by telling the magistrate that :-
... as Lucasian Professor, he was fully seized both of the laws of mechanics and of his duty to society not to waste energy, the latter compelling him to desist from applying the brake on any downhill section of road.Swimming was one of Lighthill's joys in life. In the early 1970s he was a main speaker at the British Theoretical Mechanics Colloquium in St Andrews and on the afternoon off he chose not to go on the conference bus trip. Instead he went swimming in St Andrews bay where he was spotted far out to sea. The rescue helicopter was called out but when one of the crew was winched down to rescue him, he refused to be rescued saying that he was only out for a few miles swim and not in any trouble.
In 1973 Lighthill became the first person to swim round the Channel Island of Sark :-
He spent two weeks studying the hazardous currents before setting off one sunny morning at 10am. Using a 'two-arm, two-leg backstroke, thrusting with the arms and legs alternately' he reached Grande Grève after two and a half hours, and shared a picnic lunch there with Lady Lighthill. He then continued the swim, completing it by 7pm. He modestly called the nine mile swim 'a pleasant way to see the scenery'. He repeated the achievement half a dozen times before the accident that claimed his life.The accident which claimed his life was another attempt to swim around Sark. The accident was reported in :-
Sir James Lighthill was found in rough seas off the island's rocky coast more than nine hours after he stepped into the waves for the nine mile swim. ... Before his death, he was staying at a hotel on Sark with his wife of 53 years, Nancy, and their son. He had nearly completed his swim around the island when people on the shore realised he had stopped swimming and alerted someone with a boat.Many honours from all parts of the world were bestowed on Lighthill during his distinguished career for his outstanding mathematical contributions. We noted above that he was elected a fellow of the Royal Society of London in 1953, at the age of only 29. He was awarded the Royal Medal of the Royal Society in 1964, then, between 1965 and 1969, he served the Society first as its Secretary and then as its Vice-President. He also served as president of the International Union of Theoretical and Applied Mechanics from 1984 to 1988.
Among other medals and prizes he was awarded are the Gold Medal of the Royal Aeronautical Society in 1965, the Harvey Prize for Science and Technology, Israel Institute of Technology in 1981, and the Gold Medal of the Institute of Mathematics and its Applications in 1982.
In 1961 Lighthill was elected a fellow of the Royal Aeronautical Society. He was also elected to the American Academy of Arts and Sciences (1958), the American Institute of Aeronautics and Astronautics (1961), the American Philosophical Society (1970), the French Academy of Sciences (1976), the US National Academy of Science (1976), and the US National Academy of Engineering (1977).
Many universities have awarded Lighthill honorary doctorates including Liverpool (1961), Leicester (1965), Strathclyde (1966), Essex (1967), Princeton (1967), East Anglia (1968), Manchester (1968), Bath (1969), St Andrews (1969), Surrey (1969), Cranfield (1974), Paris (1975), Aachen (1975), Rensselaer (1980), Leeds (1983), Brown (1984), Southern California (1984), Lisbon (1986), Rehovot (1987), London (1993), Compiègne (1994), Kiev (1994), St Petersburg (1996), and Tallahassee (1996).
Lighthill received the Commander Order of Léopold in 1963 and was knighted in 1971. Sir Eric Ash writes in  about Lighthill's period as Provost of University College London and his words provide a fitting tribute:-
James Lighthill was indeed a brilliant scientist; but he was also a polymath, with knowledge, insight and enthusiasm for the arts and humanities. He would invariably take the chair at inaugural lectures and, in thanking the speaker, provide an erudite coda - for any discipline - be it Egyptology, literature (illuminated by his ability to read in most modern European languages), medicine, or our own field of engineering. He was able to inspire his colleagues over the whole range of academic disciplines. Without the slightest doubt, during his watch, Lighthill succeeded in raising academic standards and in enhancing the international recognition accorded to University College.
Article by: J J O'Connor and E F Robertson