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James Lighthill was acknowledged throughout the world as one of the great mathematical scientists of this century. He was the prototypical applied mathematician, immersing himself thoroughly in the essence and even the detail of every engineering, physical or biological problem he was seeking to illuminate with mathematical description, formulating a sequence of clear mathematical problems and attacking them with a formidable range of techniques completely mastered, or adapted to the particular need, or newly created for the purpose; and then finally returning to the original problem with understanding, predictions, and advice for action.
His published legacy, of six books and some 150 papers (most of them republished in four volumes in 1997 by Oxford University Press) show at every stage a well-nigh perfect correspondence between a clearly identified physical process or mechanism and its expression and description in mathematical terms. His presentations, in papers or lectures, often emphasized the physical aspects, and gave the mathematics almost as a throw-away for those who like everything formalised; but in fact his style of working was usually the reverse.
In one of his most celebrated works, his first paper on "Sound generated aerodynamically, by jet aircraft and the like", he developed the essential mathematical structure completely in two weeks, but felt that the users (aeroengine designers) would not be able to grasp the implications, and so he delayed submission of his manuscript for sixteen months, in which time he worked backwards from the conclusions, isolating the meaning at each stage and refining and simplifying the mathematics as he did so.
He was in no sense simply the deployer of existing mathematics against a rich range of practical problems. To be sure, his earliest papers on supersonic flight already showed brilliant mastery and exploitation of classical techniques. But much more powerful techniques were needed for problems such as those of how waves in fluids are generated and propagated, and for this Lighthill made great developments in the theory of Fourier analysis, generalized functions and asymptotics all set out with elegance and economy, and full rigour, in a delightful 1958 book. Rather different ideas were needed for nonlinear problems, such as the propagation and focusing of sonic booms, and here Lighthill provided equally original and elegant new techniques, permanent and frequently-used additions to the armoury.
Michael James Lighthill was born in Paris, on 23 January 1924, and excelled across the board at Winchester before going up to Trinity College Cambridge in 1941 for a two-year wartime B.A.. He worked on supersonic flight at the National Physical Laboratory, Teddington, for the rest of the war, publishing his first paper before he was 20. He then went as Senior Lecturer to the University of Manchester at age 22, before taking the Beyer Professorship of Applied Mathematics there at age 26, in succession to Sydney Goldstein. In his thirteen years, 1946-59, at Manchester, Lighthill ran one of the most powerful and inventive fluid dynamics groups ever formed anywhere.
He had many Ph.D. students there, and his students often rose to considerable heights themselves. Indeed, there was a period in which no fewer than 17 of his Manchester students held Chairs in the UK, and that at a time when the number of universities was no more than a third of its present number. Although prepared to share the credit on a paper with a colleague, Lighthill almost never allowed his name to appear as author on any paper written by a student. And he was, then and since, tireless in his support for young scientists of any promise and for scientists working in disadvantaged circumstances.
During these Manchester years, Lighthill worked extensively on gasdynamics, including effects important at very high speed, in his studies of ionization processes, and the diffraction of shock and blast waves. He also launched two major new fields in fluid mechanics. The first of these, "aeroacoustics", or "sound generated aerodynamically", was announced in a remarkable paper published by the Royal Society in 1952. Unusually, but significantly, that paper neither contains nor needs so much as a single reference to any prior work. This work has remained, over nearly fifty years, the progenitor of all subsequent work in the field, and has been cited in many thousands of later papers.
It had immediate implication for noise reduction in jet aeroengines, motivating the trend begun later in the 1950s and still continuing, to engines with higher bypass ratio, greater diameter and lower exhaust speed, as mandated by Lighthills famous eighth power law for jet noise. Remarkably, the Lighthill theory was sufficiently versatile for it to be applied also to problems as diverse as the heating of the suns corona and the noise heard under water due to breaking surface waves and splashing drops.
The second, "Nonlinear acoustics", was initiated by a famous 100-page article written in 1956 in honour of the seventieth 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.
From Manchester, Lighthill went in 1959 to be Director of the Royal Aircraft Establishment Farnborough, where his leadership extended to the critical examination of every report emanating from RAE. The six years to 1964 saw him again in his element (`wouldnt change it for anything!), working on the aerodynamics of the slender delta wing for Concorde, on spacecraft, and on short-haul aircraft. He also worked with the Post Office in developing commercial use of television and communications satellites, while managing in unusual detail the work of the 8000 RAE staff, of whom 1400 were professional scientists and engineers. Towards the end of his RAE time he became dissatisfied with the support in national societies for applied mathematics, and founded the Institute of Mathematics and its Applications, of which he was the first President 1965-67.
From 1964 to 1969 Lighthill held a Royal Society Research Professorship at Imperial College, and here he began his great development of mathematical biofluiddynamics -- the quantitative understanding of the flow of blood in mammalian cardiovascular systems, of air in the human airways, and of the flying of birds and insects and the swimming of fish. Mastery of the biology was, he insisted, thesine qua nonfor entry into this field. He revelled, in lectures, not only in the articulation of all the Latin names, but in his ability to perform the appropriate gymnastics to illustrate certain flying characteristics in particular the `clap and fling mechanism employed by the tinyencarsia formosato endow it with a lift coefficient far above that obtainable from the ordinary aerodynamics in which the component parts of the body do not break apart.
In 1969 he succeeded Paul Dirac, founder of much of quantum mechanics, in the Lucasian Professorship of Mathematics at Cambridge though when he referred to `his predecessor in the Chair one sensed he was thinking primarily of Newton. Here he taught indefatigably, and with enormous gusto, six days of the week at nine in the morning. He widened his range yet further with work on control systems; on active control of sound, or anti-sound; more and more on waves; on oceanography and atmospheric dynamics, including monsoon prediction and propagation; and on biological mechanics at the microscopic level. He sat on many national and international committees, in academic, industrial and governmental circles, and took a serious interest in issues of mathematical education in schools.
From 1979 to 1989 Lighthill was Provost of University College London, much engaged in fundraising, in new developments in the College, particularly in the biology and biotechnology sides, and in dramatically improving the representation of women in senior posts. He still maintained his scientific work, with studies on the unpredictability of large systems, on wave energy extraction devices, and on features of the human auditory system. After retirement he took up Chairmanship of the Special Committee on the International Decade for Natural Disaster Reduction, and travelled and lectured world-wide.
His achievements have been widely recognized – through election to FRS at age 29, through award of 24 Honorary Doctorates, through Foreign Membership of the most prestigious academies, through receipt of many medals and prizes, and through knighthood in 1971.
Stories about Lighthill are legion, as would be expected with such a larger-than-life figure, and no amount of discounting for exaggeration makes them less amusing or less essentially accurate. It is well known that he was fined 1 for jumping from a train as it passed to his dismay without stopping through Crewe; and that on more than one occasion he successfully defended himself on charges of speedy driving, turning the full spotlight of his presence, charm and authority on the magistrates as he explained how, 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.
He saw everything as a challenge to his brain, or to his physique, or to the co-ordination of the two. And if no challenge were obviously to hand he would create one – mastering Portuguese in three weeks to the extent that he could give a (long) after-dinner speech in the language, for example. He listed his leisure interests as music and swimming, to which surely literature, poetry (especially Portuguese) and languages (French, German, Russian, Portuguese) should be added.
His swimming exploits were legendary careful in their homework on tides and local currents, bold in their ignoring of everything else. On countless occasions he came home safely, against the odds. Last Saturday he almost completed a nine-hour swim round Sark (he was the first ever to do this, at age 49) against high winds and huge waves, before dying close to the shore.
His published legacy, of six books and some 150 papers (most of them republished in four volumes in 1997 by Oxford University Press) show at every stage a well-nigh perfect correspondence between a clearly identified physical process or mechanism and its expression and description in mathematical terms. His presentations, in papers or lectures, often emphasized the physical aspects, and gave the mathematics almost as a throw-away for those who like everything formalised; but in fact his style of working was usually the reverse.
In one of his most celebrated works, his first paper on "Sound generated aerodynamically, by jet aircraft and the like", he developed the essential mathematical structure completely in two weeks, but felt that the users (aeroengine designers) would not be able to grasp the implications, and so he delayed submission of his manuscript for sixteen months, in which time he worked backwards from the conclusions, isolating the meaning at each stage and refining and simplifying the mathematics as he did so.
He was in no sense simply the deployer of existing mathematics against a rich range of practical problems. To be sure, his earliest papers on supersonic flight already showed brilliant mastery and exploitation of classical techniques. But much more powerful techniques were needed for problems such as those of how waves in fluids are generated and propagated, and for this Lighthill made great developments in the theory of Fourier analysis, generalized functions and asymptotics all set out with elegance and economy, and full rigour, in a delightful 1958 book. Rather different ideas were needed for nonlinear problems, such as the propagation and focusing of sonic booms, and here Lighthill provided equally original and elegant new techniques, permanent and frequently-used additions to the armoury.
Michael James Lighthill was born in Paris, on 23 January 1924, and excelled across the board at Winchester before going up to Trinity College Cambridge in 1941 for a two-year wartime B.A.. He worked on supersonic flight at the National Physical Laboratory, Teddington, for the rest of the war, publishing his first paper before he was 20. He then went as Senior Lecturer to the University of Manchester at age 22, before taking the Beyer Professorship of Applied Mathematics there at age 26, in succession to Sydney Goldstein. In his thirteen years, 1946-59, at Manchester, Lighthill ran one of the most powerful and inventive fluid dynamics groups ever formed anywhere.
He had many Ph.D. students there, and his students often rose to considerable heights themselves. Indeed, there was a period in which no fewer than 17 of his Manchester students held Chairs in the UK, and that at a time when the number of universities was no more than a third of its present number. Although prepared to share the credit on a paper with a colleague, Lighthill almost never allowed his name to appear as author on any paper written by a student. And he was, then and since, tireless in his support for young scientists of any promise and for scientists working in disadvantaged circumstances.
During these Manchester years, Lighthill worked extensively on gasdynamics, including effects important at very high speed, in his studies of ionization processes, and the diffraction of shock and blast waves. He also launched two major new fields in fluid mechanics. The first of these, "aeroacoustics", or "sound generated aerodynamically", was announced in a remarkable paper published by the Royal Society in 1952. Unusually, but significantly, that paper neither contains nor needs so much as a single reference to any prior work. This work has remained, over nearly fifty years, the progenitor of all subsequent work in the field, and has been cited in many thousands of later papers.
It had immediate implication for noise reduction in jet aeroengines, motivating the trend begun later in the 1950s and still continuing, to engines with higher bypass ratio, greater diameter and lower exhaust speed, as mandated by Lighthills famous eighth power law for jet noise. Remarkably, the Lighthill theory was sufficiently versatile for it to be applied also to problems as diverse as the heating of the suns corona and the noise heard under water due to breaking surface waves and splashing drops.
The second, "Nonlinear acoustics", was initiated by a famous 100-page article written in 1956 in honour of the seventieth 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.
From Manchester, Lighthill went in 1959 to be Director of the Royal Aircraft Establishment Farnborough, where his leadership extended to the critical examination of every report emanating from RAE. The six years to 1964 saw him again in his element (`wouldnt change it for anything!), working on the aerodynamics of the slender delta wing for Concorde, on spacecraft, and on short-haul aircraft. He also worked with the Post Office in developing commercial use of television and communications satellites, while managing in unusual detail the work of the 8000 RAE staff, of whom 1400 were professional scientists and engineers. Towards the end of his RAE time he became dissatisfied with the support in national societies for applied mathematics, and founded the Institute of Mathematics and its Applications, of which he was the first President 1965-67.
From 1964 to 1969 Lighthill held a Royal Society Research Professorship at Imperial College, and here he began his great development of mathematical biofluiddynamics -- the quantitative understanding of the flow of blood in mammalian cardiovascular systems, of air in the human airways, and of the flying of birds and insects and the swimming of fish. Mastery of the biology was, he insisted, thesine qua nonfor entry into this field. He revelled, in lectures, not only in the articulation of all the Latin names, but in his ability to perform the appropriate gymnastics to illustrate certain flying characteristics in particular the `clap and fling mechanism employed by the tinyencarsia formosato endow it with a lift coefficient far above that obtainable from the ordinary aerodynamics in which the component parts of the body do not break apart.
In 1969 he succeeded Paul Dirac, founder of much of quantum mechanics, in the Lucasian Professorship of Mathematics at Cambridge though when he referred to `his predecessor in the Chair one sensed he was thinking primarily of Newton. Here he taught indefatigably, and with enormous gusto, six days of the week at nine in the morning. He widened his range yet further with work on control systems; on active control of sound, or anti-sound; more and more on waves; on oceanography and atmospheric dynamics, including monsoon prediction and propagation; and on biological mechanics at the microscopic level. He sat on many national and international committees, in academic, industrial and governmental circles, and took a serious interest in issues of mathematical education in schools.
From 1979 to 1989 Lighthill was Provost of University College London, much engaged in fundraising, in new developments in the College, particularly in the biology and biotechnology sides, and in dramatically improving the representation of women in senior posts. He still maintained his scientific work, with studies on the unpredictability of large systems, on wave energy extraction devices, and on features of the human auditory system. After retirement he took up Chairmanship of the Special Committee on the International Decade for Natural Disaster Reduction, and travelled and lectured world-wide.
His achievements have been widely recognized – through election to FRS at age 29, through award of 24 Honorary Doctorates, through Foreign Membership of the most prestigious academies, through receipt of many medals and prizes, and through knighthood in 1971.
Stories about Lighthill are legion, as would be expected with such a larger-than-life figure, and no amount of discounting for exaggeration makes them less amusing or less essentially accurate. It is well known that he was fined 1 for jumping from a train as it passed to his dismay without stopping through Crewe; and that on more than one occasion he successfully defended himself on charges of speedy driving, turning the full spotlight of his presence, charm and authority on the magistrates as he explained how, 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.
He saw everything as a challenge to his brain, or to his physique, or to the co-ordination of the two. And if no challenge were obviously to hand he would create one – mastering Portuguese in three weeks to the extent that he could give a (long) after-dinner speech in the language, for example. He listed his leisure interests as music and swimming, to which surely literature, poetry (especially Portuguese) and languages (French, German, Russian, Portuguese) should be added.
His swimming exploits were legendary careful in their homework on tides and local currents, bold in their ignoring of everything else. On countless occasions he came home safely, against the odds. Last Saturday he almost completed a nine-hour swim round Sark (he was the first ever to do this, at age 49) against high winds and huge waves, before dying close to the shore.