# Clive William Kilmister

### Quick Info

Epping, Essex, England

Lewes, East Sussex, England

**Clive Kilmister**was an applied mathematician who had broad interests including the history of mathematics, philosophy of mathematics and teaching of mathematics. He wrote several books on relativity, Arthur Eddington and Eddington's fundamental theory.

### Biography

**Clive Kilmister**was the son of William Kilmister (1898-1973) and Doris Cookson (1900-1992). William Kilmister, born in Harlow, Essex, on the 31 January 1898, became an engineers pattern maker, working in wood. He was a skilled craftsman who made patterns for the iron foundry which, at that time, was the largest employer in Epping. William had served in the Royal Navy during World War I, serving on HMS President II, the accounting base at Chatham, from 5 June 1916, then serving on the HMS Queen II at Malta in October 1917. He married Doris Cookson in 1922 at Steyning, Sussex and their only son, Clive Kilmister, the subject of this biography, was born in Epping.

After primary education in Epping, Kilmister, after taking the scholarship examination, attended Leyton County High School for Boys, a selective grammar school taking pupils from 11 to 18. The Headmaster was Dr Leonard Couch, nephew of the author Arthur Thomas Quiller-Couch. The masters at the school were good teachers who aimed to have their pupils take the University of London's General Schools Certificate which gave the best pupils automatic entry to the University of London. Kilmister was fifteen years old and in the middle of his secondary education at the school when World War II broke out. This was a particularly difficult time, especially in London where there were evacuations of children to safer parts of the country. Kilmister graduated from the High School in 1942 and gained entry to Queen Mary College, London.

The Principal of Queen Mary College had quickly arranged for the College to be evacuated to King's College, Cambridge, soon after war was declared in 1939. By the time that Kilmister began his university studies in 1942 the arrangement was working well with Queen Mary College students allowed to enter the King's College clubs and societies. RAF soldiers were also billeted at the College and students were able to undertake military service while taking shortened university courses. Kilmister graduated in 1944 with first class honours having completed his studies in two years and at the same time having undertaken military service with the Royal Artillery. He was awarded a University of London Sherbrooke Studentship.

C P Snow, who had trained as a physicist but is now better known as an author, was looking for talented students to undertake war related projects. He was particularly involved in the training of scientists for radar work and he recommended Kilmister to the Plessey Company who, among many other wartime projects, were working on developing radar. Kilmister spent the three years, 1944-47, working on developing radar at Plessey before returning to Queen Mary College, now back in London, to continue his education which had been disrupted by the war. His first postgraduate study was for an M.Sc. degree and for this he took courses on complex functions and on electromagnetic theory. The M.Sc. was by examination, not by dissertation, and he was awarded the degree in 1948. He then began research for his Ph.D. advised by George McVittie. McVittie had begun research in Edinburgh with Edmund Whittaker and continued at Cambridge under Arthur Eddington. He had been on the staff at the University of London from 1936, first as a reader at King's College, and from 1948 as a professor at Queen Mary College. Kilmister's [26]:-

... research topic ... dealt with some of Eddington's ideas and included the writing of Eddington's E-numbers in terms of quaternions. This was a rather surprising area of research. McVittie had long thought that Eddington had lost touch with real physics. According to Kilmister, McVittie considered Eddington's last works "scandalous", and he hoped Kilmister would "get rid of this scandal" ...Also in 1948 Kilmister met Peggy Joyce Hutchins (1927-2012) who at that time was reading English at Queen Mary College. Peggy, born in Wembley, London, was the daughter of Cyril Edmund Hutchins (1898-1965) and Rebecca Elizabeth Isaacs (1899-1948). Cyril began a career with the Post Office in November 1914 but in 1916, when he reached the age of eighteen, he was called up for military service during World War I. He did not report for war service and was brought before a Court Martial on 4 December 1916 at Newton Abbot. He was registered as a Conscientious Objector and sentenced to 112 days hard labour in Dartmoor Prison. Clive and Peggy Kilmister were married in Kensington, London in March 1955; they had three children: Andrew, Sally and Penny.

Let us return to Kilmister's research at Queen Mary College. In 1949, before submitting his Ph.D. thesis, he had three publications. The paper

*The use of quaternions in wave-tensor calculus*was published in 1949 in the

*Proceedings*of the Royal Society of London. The Abstract states:-

Quaternions are used to obtain some of Eddington's results in a general affine space, and a more convenient notation for E-numbers is suggested. As an example, Dirac's equations are derived, their connexion with the affine space of distant parallelism is explained, and Eddington's views on their 'Euclidean' nature are discussed.At the end of the paper, Kilmister acknowledges the help from his advisor George McVittie:-

The author wishes to thank Professor G C McVittie for suggesting this subject to him, and for helpful advice and encouragement in the course of the work.Also in 1949,

*A note on minimum integrals in field theory*was published in the

*London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science*. The Abstract states:-

A unification of the minimum energy theorems encountered in electromagnetic theory has been stated, and the extension of the theorem to non-isotropic dielectrics and conductors has been made. An application of the theorem to the magnetic field suggests a modified form for the density of the magnetic force-function which agrees which Livens's expression for this quantity.A third publication in 1949 is a joint one by Kilmister and Edward William Bastin, namely the letter

*Physics Tomorrow*. E W Bastin (1926-2011), who was known as "Ted" and even published as "T Bastin", was a research student in mathematics at Queen Mary College. His interests were very similar to those of Kilmister and the two published joint papers and books for the whole of their careers. Their first joint publication

*Physics Tomorrow*[14] contains ideas they would continue to develop throughout their careers; you can read a version at THIS LINK.

In 1950 Kilmister was awarded a Ph.D. for his thesis

*The use of quaternions in wave-tensor calculus.*This contained results from the 1949 paper with the same title we mentioned above, but he published a further paper,

*Tensor identities in wave-tensor calculus*, in 1951 which also appeared in the

*Proceedings*of the Royal Society of London. The Abstract states:-

The quaternion methods of a previous paper are used to formulate clearly the problem of Eddington's 'tensor identities' in both single and double frames. As examples, the single-frame theory is used to calculate the well-known gyromagnetic ratio of the electron, and the double-frame to deduce a complete set of equations, of which Eddington has given a few, which include equations having the form of the field equations of general relativity. A discrepancy with Eddington's results is noted, and reasons given for preferring the present equations.At the end of the paper, Kilmister acknowledges the help from his advisor George McVittie:-

Most of the results of this paper are to be found proved by longer, but more elementary methods in a thesis (Kilmister 1950). This work was undertaken at Queen Mary College and the author wishes to thank Professor G C McVittie for constant advice, and interest in the course of the work.Kilmister was appointed as an assistant lecturer in King's College, London in the autumn of 1950. This was a temporary, three or four year, appointment. Before its end, however, he was appointed to a lectureship in King's College, London in 1953 and he continued to work there for the rest of his career. John Silvester writes [29]:-

In later years Clive recalled the small department he joined as being a very happy place. Departmental bureaucracy was essentially confined to a half hour meeting after the summer examinations although, as he said, it did sometimes run over to nearly three quarters of an hour. In 1954 Hermann Bondi joined the Department and, together with Clive and Felix Pirani, established the gravitational theory group. The King's group quickly became internationally renowned. It was one of a small number largely responsible for the post-war renaissance of research into Einstein's theory of general relativity. He had broad interests, and his publications range over Eddington's work and applications of his algebraic approach in other fields, and also general relativity and unified field theories, special relativity, mechanics (including quantum mechanics) both in relation to teaching and foundations, history and philosophy of science, and applications of mathematics in the social sciences. With his long-term collaborator Ted Bastin he was involved in attempts to construct an abstract approach to physics, and they were founding members of the Alternative Natural Philosophy Association. This latter work he regarded as his most important and the most likely to endure, though perhaps also his most heterodox. He was author of more than a dozen books ...David C Robinson writes [27]:-

Kilmister was delighted when Bondi and Pirani were appointed. "Everything changed" he later said although his personal work on gravity was never more than a small part of his research. The latter did include explorations of alternatives to general relativity. For example he undertook one of the early investigations of what later tended to be called Yang's theory of gravity ... Kilmister was elected to the committee of the International Society on General Relativity from 1971 to 1974 but by then his many other activities were crowding out his interest in general relativity ..Some of these "other activities" involved, as mentioned in the previous quote, writing "more than a dozen books." These books, some of which are co-authored, are:

*Special Relativity for Physicists*(1958);

*Eddington's statistical theory*(1962);

*Hamiltonian Dynamics*(1964);

*The Environment of Modern Physics: Study in Relativistic Mechanics*(1965);

*Rational Mechanics*(1966);

*Men of Physics: Sir Arthur Eddington*(1966);

*Lagrangian Dynamics: An Introduction for Students*(1967);

*Language, Logic and Mathematics*(1967);

*Physical Applications of Vectors and Tensors*(1969);

*The Nature of the Universe*(1971);

*General Theory of Relativity*(1973);

*Eddington's Search for a Fundamental Theory: A Key to the Universe*(1994);

*Combinatorial physics*(1995); and

*The origin of discrete particles*(2009). For more information about these books such as extracts from Prefaces, Introductions, Contents, and reviews, see THIS LINK.

In many ways

*Eddington's Search for a Fundamental Theory*is an account of a major aspect of Kilmister's life-long research. We give a substantial extract from the Preface at THIS LINK.

Here let us give a short extract to illustrate our comment in the last paragraph:-

It is half a century since I first succumbed to the Eddingtonian magic ... in 'Relativity Theory of Protons and Electrons', which Eddington had published ... in 1936. I had already enjoyed his authoritative 'Mathematical Theory of Relativity' with no more difficulty than that produced by the complex mathematical techniques which were new to me. Looking back on it, it surprises me that I could take in without a qualm so many of the unorthodox philosophical views in that book. But 'Relativity Theory of Protons and Electrons' was a different matter. Another clutch of mathematical techniques was not enough to obscure a radically new position. ...Research in mathematical physics was not the only thing to occupy Kilmister's interests. He was an active member of the Mathematical Association, being a member of a committee in 1962 which reported on the teaching of modern mathematics and a committee in 1965 which reported on the teaching of mechanics in secondary schools. He was elected President of the Mathematical Association, serving in 1979-80, and delivered his Presidential Address entitled

In 1941 much of [the] background was unknown to me and I was just fascinated by the book on its own terms. As time went on I learnt more and more of the difficulties and the task became that of reconstructing Eddington's work in such a way as to avoid them. In 1945 'Fundamental Theory' appeared after Eddington's death. It was a disappointment to me, for it did not seem to address the real obscurities of the earlier book. I spent a good deal of time clearing up the algebraic aspects of the theory but when this had been done the basic ideas were not much clearer. Yet they continued to dazzle: flashes of insight grouped round a frame of numerical results. I kept returning to Eddington's work and puzzling over it between the other enterprises that filled my working life. I owe a debt of great gratitude to Ted Bastin who often gave me guidance and help over Eddington during this forty-five years.

*Zeno, Aristotle, Weyl and Shuard: two-and-a-half millenia of worries over number*was delivered on 9 April 1980. We give a version of his Address at THIS LINK.

Let us mention his involvement with the Logistics Research Project, sponsored in part by the Office of Naval Research with ran at the George Washington University in Washington D.C. from 1950 to 1968. Kilmister participated in this project flying from Manchester, England, to New York on 5 December 1958.

He was also much involved with the British Society for the Philosophy of Science serving on its committee during 1963-66 and serving as President during 1981-83. He was a founder member of the British Society for the History of Mathematics in 1971 and served as its second President in 1974-76. He was a great enthusiast for the history of mathematics and wrote in [15]:-

Years ago books on the history of mathematics, especially those addressed to the general public, were written by second-rate mathematicians who had turned themselves into something less than second-rate historians. More recently things have improved greatly and there are first-rate historians producing works of real scholarship.He was promoted reader at KCL in 1959, and professor in 1966. From 1972-1988, he was Gresham Professor of Geometry. He took on many administrative tasks including Dean of the Faculty of Natural Science, and Chair of the Department of Mathematics. He writes [16]:-

In 1967 I was appointed to the Chair of Mathematics (which had been vacant for a year). I found a Department of 11, or rather 10 and 2 halves, one post being shared with the Institute of Computer Science and one with the Philosophy Department. In the course of the next few years both were converted to full posts, giving us a strength of 12. Professor John S Griffith left in 1968 to take up a split appointment between Bloomington and the CSIRO in Sydney (he died only 5 years later). He was succeeded in 1969 by R F Streater, an applied mathematician with very broad interests in pure mathematics. During the next dozen years, when lecturers were relatively scarce, there was a turnover of about one staff member per year, and we were usually able to get people whose interests were represented in the Department, with the result that distinct research groups could be formed, in algebra, logic and quantum field theory. This was also reflected in the growing number of research students, research fellows and the steady stream of overseas visitors to the Department. At the same time the interests of the undergraduates were not forgotten; the syllabus had become more 'algebraic', but efforts were made to provide a balanced fare. In the third year it was possible to attend courses at other colleges, and there was a (2-way) interchange with both University College and Westfield College, and to a lesser extent King's College. At the postgraduate level there was the M.Sc. which was truly intercollegiate, and it could easily happen that the class for an M.Sc. course was larger than one for an optional second year course.John Silvester writes in [29] about working with Kilmister:-

I have many reasons to be grateful to Clive. As a young lecturer I quickly realised that he was among the most approachable, generous and helpful of my senior colleagues, and I picked his brains and benefited from his advice on innumerable occasions. He encouraged me early on to take an interest in what went on in schools by arranging for me to be involved in examining for the London Teaching Certificate and, much later, by suggesting I might like to become Admissions Tutor. And, knowing that I lived a long way out from London, year after year he so organised the timetable that I could avoid too often having to travel uncomfortably and expensively in the rush-hour. Clive was a devoted husband and family man. He and Peggy shared interests in theatre, opera, art, and music, in particular lieder.After he retired in 1984, Kilmister and his wife went to live permanently in a cottage in Lewes, East Sussex, which had previously been their weekend retreat. He continued to undertake research and write papers and books [29]:-

He sometimes suffered from insomnia, and would do mathematics to pass away the hours of darkness ...In 2090 he began to suffer from cancer and died a year later in his home in Lewes.

### References (show)

- R E Berendzen, Review The Nature of the Universe, by C W Kilmister,
*Journal of College Science Teaching***2**(1) (1972), 54-55. - F Chorlton, Review: Hamiltonian Dynamics, by C W Kilmister,
*The Mathematical Gazette***49**(368) (1965), 226. - F Chorlton, Review: Rational Mechanics, by C W Kilmister and J E Reeve,
*The Mathematical Gazette***51**(378) (1967), 370-371. - Clive Kilmister,
*London Mathematical Society Newsletter***394**(July 2010), 11. - Clive Kilmister,
*Sussex Express*(14 May 2010). - E Deeson, Review The Nature of the Universe, by C W Kilmister,
*Phys. Bull.***23**(1972), 295-296. - A S G, Review: Language, Logic and Mathematics, by C W Kilmister,
*Current Science***37**(10) (1968), 299. - General Relativity in the Department of Mathematics, Department of Mathematics, King's College, London.

https://www.kcl.ac.uk/mathematics/about/history - B Jeffreys, Review: Langrangian Dynamics, by C W Kilmister,
*The Mathematical Gazette***53**(383) (1969), 106-107. - B Jeffreys, Review: Physical Applications of Vectors and Tensors, by H Teichmann and C W Kilmister.
*The Mathematical Gazette***56**(397) (1972), 254. - T Jordan, Review: Eddington's Search for a Fundamental Theory: A Key to the Universe, by C W Kilmister,
*The British Journal for the History of Science***29**(3) (1996), 377-378. - D Kaiser, Review: Eddington's Search for a Fundamental Theory: A Key to the Universe, by C W Kilmister,
*Isis***86**(4) (1995), 675. - C W Kilmister, Zeno, Aristotle, Weyl and Shuard: two-and-a-half millenia of worries over number,
*The Mathematical Gazette***64**(429) (1980), 149-158. - C W Kilmister and E W Bastin, Physics Tomorrow,
*Physics Today***2**(3) (1949), 3; 5. - C W Kilmister, Review: Number theory: An Approach through History from Hammurapi to Legendre, by AndrĂ© Weil,
*Nature***310**(1984), 168. - C W Kilmister, The teaching of mathematics in the University of London,
*Bull. London Math. Soc.***18**(1986), 321-337. - P T Landsberg, Review: The Environment of Modern Physics, by C W Kilmister,
*The Mathematical Gazette***50**(374) (1966), 442-443. - P T Landsberg, Review: General Theory of Relativity, by C W Kilmister,
*The Mathematical Gazette***58**(405) (1974), 243. - J Merleau-Ponty, Review: Eddington's Search for a Fundamental Theory: A Key to the Universe, by C W Kilmister,
*Revue d'histoire des sciences***50**(1/2) (1997), 225-226. - D J Montgomery, Review: Hamiltonian Dynamics, by C W Kilmister,
*Physics Today***18**(3) (1965), 74-75. - E Palm, Review: Langrangian Dynamics, by C W Kilmister,
*Nordisk Matematisk Tidskrift***16**(4) (1968), 160. - Pictorial Representation: Why Geometry?, Professor Clive Kilmister,
*Gresham College*(1986).

https://www.gresham.ac.uk/lectures-and-events/why-geometry - Pictorial Representation: Nomography, Professor Clive Kilmister,
*Gresham College*(1987).

https://www.gresham.ac.uk/lectures-and-events/pictorial-representation-nomography - Pictorial Representation: The Twentieth Century, Professor Clive Kilmister,
*Gresham College*(1987).

https://www.gresham.ac.uk/lectures-and-events/pictorial-representation-the-twentieth-century - Pictorial Representation: The Slide Rule, Professor Clive Kilmister,
*Gresham College*(1987).

https://www.gresham.ac.uk/lectures-and-events/pictorial-representation-the-slide-rule - D Robinson, Death of Clive Kilmister,
*hyperspace*(31 May 2010).

https://hyperspace.uni-frankfurt.de/2010/05/31/death-of-clive-kilmister/ - D C Robinson, Gravitation and General Relativity at King's College London,
*The European Physical Journal H***44**(2019), 181-270. - R J Seeger, Review: Men of Physics: Sir Arthur Eddington, by C W Kilmister,
*American Journal of Physics***36**(1968), 71. - J R Silvester, C W Kilmister 1924-2010,
*The Mathematical Gazette***94**(531) (2010), 529-531. - R L Solomon, Review The Nature of the Universe, by C W Kilmister,
*The American Biology Teacher***34**(8) (1972), 483-484. - C Truesdell, Review: Rational Mechanics, by C W Kilmister and J E Reeve,
*Amer. Math. Monthly***74**(6) (1967), 748-749. - A Weinmann, Review: Special Relativity for Physicists, by G Stephenson and C W Kilmister,
*The Mathematical Gazette***44**(348) (1960), 149. - G J Whitrow, Review: Men of Physics: Sir Arthur Eddington, by C W Kilmister,
*The British Journal for the History of Science***4**(1) (1968), 81-82. - W Wilson, Review: Special Relativity for Physicists, by G Stephenson and C W Kilmister,
*Science Progress (1933-)***47**(185) (1959), 140-141. - E Zahar, Review: Eddington's Search for a Fundamental Theory: A Key to the Universe, by C W Kilmister,
*The British Journal for the Philosophy of Science***48**(1) (1997), 132-139.

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Last Update January 2021