# Keith William Morton

### Born: 28 May 1930 in Ipswich, England

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**Bill Morton**'s parents were Keith Harvey Morton (1902-1933) and Muriel Violet Hubbard (1899-1934). Keith and Muriel were married in 1927. Sadly, Keith died in June 1933, shortly after Bill's third birthday, and Muriel died a year later. He was brought up in Hadleigh, Suffolk by his mother's sister Blanche E M Hubbard who was married to Theophilus E Spooner. Later they moved to Colchester, Essex. Bill began his schooling at Hadleigh Bridge Street Primary in 1935. Olive, a sister of his mother, who was married to Donald Ripper, and an older sister Emily Knights, provided some financial support during his schooling and were his official guardians. He spent five years at Hadleigh Bridge Street Primary, completing his studies there in 1940 and entering Sudbury Grammar School in that year. This was an ancient boys' grammar school founded in 1491. It has now amalgamated with other local schools to form Sudbury Upper School.

In 1948, the year when Morton completed his secondary education, national service was compulsory and he spent the year 1948-49 in the Royal Electrical and Mechanical Engineers. This consisted of technicians who maintained the army's equipment. Morton writes [4]:-

After completing his National Service, Morton matriculated at Corpus Christi College, Oxford, where he studied mathematics. At Oxford, Morton attended lectures on quantum mechanics delivered by the South African Jacobus Stephanus de Wet (1913-1995), known to all as Jack. De Wet had a Ph.D. from Princeton in theoretical physics and, after working at the University of Cape Town and the University of Pretoria, was appointed to a senior research fellowship at Balliol College of Oxford University in 1947. John Johnston writes [2]:-Olive and her husband Donald Ripper provided me with a very welcome haven when I was doing my National Service training in radar at Stockport Technical College.

In 1952 Morton married Patricia Mary Pearson; they had two sons and two daughters. Morton graduated with a B.A. in 1952 and began working in the Theoretical Physics Division of the Atomic Energy Research Establishment at Harwell (which was in Berkshire at the time but, following boundary changes in 1974, is now in Oxfordshire). There he worked on Monte Carlo methods for nuclear criticality and published a number of papers in collaboration with John Michael Hammersley who was Principal Scientific Officer at the Atomic Energy Research Establishment at Harwell at the time. These joint papers are:Morton's long-standing inspiration from one of the greats in mathematics, David Hilbert, started when he was first introduced to Hilbert spaces by Jack de Wet whilst studying quantum mechanics as a mathematics undergraduate at Oxford. Hilbert is one of the most influential mathematicians of his time, and his famous address to the International Congress of Mathematicians in Paris in1900, where he announced a number of unsolved problems, was to Morton's mind 'crucial' in its plea that mathematics should always remain a single, undivided subject.

*Transposed branching processes*(1954);

*Poor man's Monte Carlo*(1954);

*The estimation of location and scale parameters from grouped data*(1954); and

*A new Monte Carlo technique: antithetic variates*(1956).

*Poor man's Monte Carlo*, which includes a paper and a discussion, was published by the Royal Statistical Society and reviewed by Alston Householder who writes:-

Alston Householder also reviewed the 1956 paper mentioned above and writes:-This paper and the subsequent discussion relate chiefly to the art of applying Monte Carlo, and no brief summary can do justice to either. The basic thesis can be inferred from the title, that one does not necessarily need high speed machines to use Monte Carlo effectively. The authors first point out that only the name and not the method is new(the discussion brings out that King Solomon was an early practitioner)and then discuss three problems: the critical size of a nuclear reactor, the test of a quantum hypothesis, and self-avoiding walks.

Morton also published the single-authored paper... the paper represents a major contribution to the study of Monte Carlo Methods.

*A generalisation of the antithetic variate technique for evaluating integrals*(1957).

As a consequence of his contributions to this area, Morton was invited by the Courant Institute of Mathematical Sciences in New York to spend some time there. He took sabbatical leave from the Atomic Energy Authority in 1959 and went to the Courant Institute. After spending time there, he was invited by the Courant Institute to undertake graduate studies there. Now at Harwell, Morton [2]:-

He therefore resigned his position at Harwell and, in 1961, began studying for a Ph.D. at the Courant Institute while employed there as a Research Scientist. His thesis advisor was Harold Grad (1923-1986) who had been a student of Richard Courant. Grad was Head of the Magnetohydrodynamics Department at the Courant Institute and was a leading expert on applications of statistical mechanics to magnetohydrodynamics and to plasma physics. Morton was awarded a Ph.D. by New York University in 1964 for his thesis... found it particularly enlightening to work with theoretical physicists, but his role was too much concerned with developing computing, and he wanted to get back to mathematics.

*Finite Amplitude Compression Waves in a Collision-Free Plasma*. After completing his doctoral studies, in 1964 Morton was appointed as Head of Computing and Applied Mathematics at the Culham Laboratory which was operated by the United Kingdom Atomic Energy Authority. The Atomic Energy Authority had been created ten years earlier to undertake nuclear research for the UK government and, in 1960, had opened the purpose-built nuclear fusion laboratory just south of Oxford. Morton worked at Culham until 1972 and during this time published, in collaboration with Robert D Richtmyer, published the book

*Difference methods for initial-value problems*(1967). Astri Sjöberg writes:-

At Culham, as in his earlier position at Harwell, Morton was pleased to work with theoretical physicists but again he felt that he was too involved in computing and wanted to have a larger involvement with mathematics. He was appointed to the Chair of Applied Mathematics at the University of Reading in 1971, taking up the position in the following year. The paperThe book is primarily written for users of difference methods, but it can be highly recommended to everyone interested in the subject.

*Stability and convergence in fluid flow problems. A discussion on numerical analysis of partial differential equations*which he published in 1971 gives both a Culham and a University of Reading address for Morton. This paper, published by the Royal Society of London, is an extremely valuable contribution to the area and we give the beginning of Morton's Introduction where he sets the scene:-

Morton's work in this and many other papers, gained great insight into the flow of fluids. The results of his investigations have influenced a broad range of fields, from weather forecasting to the design of power stations and from the development of aircraft engines to the growth of scientific computing.Of all the partial differential equations which are solved numerically, those arising from fluid flow problems are certainly among the most important. Meteorology and oceanography, engineering flows of liquids and gases, aerodynamics and plasma physics are but some of the fields in which they occur and are being successfully solved. One may indeed expect a rapid expansion of this activity in the next few years as the solution of physically interesting two- and three-dimensional flows becomes a practical and economic proposition.

There is, however, a more pertinent reason for singling out this application area in discussing the numerical analysis of partial differential equations. This is that from the inception of the subject scientists attempting the solution of fluid flow problems have continuously made outstanding contributions to the subject's development. In particular, the detailed understanding of the behaviour of specific difference schemes and of various types of instability owes much to their work.

Each particular field has its own complicating difficulties and the equations necessary to describe physically interesting phenomena are often formidable. It would therefore be inappropriate to work here with complete systems of realistic equations: instead it will be our aim to bring out some of the important points common to the whole class of fluid flow problems by using in each case the simplest model equations adequate for our purpose.

Morton held the chair of Applied Mathematics at Reading from 1972 to 1983 [2]:-

With his colleague Michael Baines, Morton founded the Institute for Computational Fluid Dynamics at the University of Reading. It gained a high international reputation, particularly though organising conferences. In March 1982 the conference 'Numerical methods for fluid dynamics' was organised by Morton and his colleagues at the University of Reading. The conference Proceedings appeared in the same year edited by Morton and Baines. The first paper in the Proceedings is a 32-page paper by Morton... he concentrated on graduate teaching, bringing his wide experience to bear on the MSc courses.

*Generalised Galerkin methods for steady and unsteady problems*. The second conference in this series was held at the University of Reading in April 1985. Again Morton and Baines edited the Proceedings but Morton had left the Chair of Applied Mathematics at Reading before this conference, being appointed as a Professorial Fellow of Balliol College, Oxford University in 1983. He held this position until be retired in 1997 and during this time organised the 'Numerical methods for fluid dynamics' conference at Oxford in March 1988, at Reading in April 1992 and at Oxford in April 1995. After retiring, Morton was made Emeritus Professor at Oxford University, Emeritus Fellow at Balliol College, Oxford, and appointed as a part-time Professor of Mathematics at the University of Bath, 1998-2005.

We should mention two important books he published: (with David F Mayers)

*Numerical Solution of Partial Differential Equations: an introduction*(1994, 2

^{nd}edition 2005); and

*Numerical Solution of Convection-Diffusion Problems*(1996). G W Hedstrom, reviewing the first of these, writes:-

The aim of the second of these books is set out in the Preface by Morton:-This book is a solid introduction to numerical methods for partial differential equations. The methods are primarily based on finite differences, although a brief introduction to finite elements is given. The book includes parabolic, hyperbolic, and elliptic equations, each section starting with an analysis of the behaviour of solutions of the partial differential equations. ... A very desirable feature of the book is that it goes beyond the usual investigation of the heat equation, the wave equation, and Poisson's equation. Numerical methods for linear problems with variable coefficients are discussed, as well as nonlinear problems.

Matin Stynes writes in a review:-The main aim of this book is to try to draw together all these ideas, to see how they overlap and how they differ, and to provide the reader with a useful and wide-ranging source of algorithmic concepts and techniques of analysis.

In July 2010 the London Mathematical Society awarded Morton their De Morgan Medal. It was awarded to:-To a large extent, the book achieves these desirable objectives. It is a nice blend of analysis, numerical results and insightful commentary. A generous number of figures aid the reader's understanding, and the style is clear and elegant. The level of presentation is ideal for anyone with some knowledge of numerical analysis who wishes to learn about the solution of convection-diffusion problems.

The President of the London Mathematical Society, Angus MacIntyre, said:-... Professor Keith William(Bill)Morton of the University of Oxford in recognition of his seminal contributions to the field of numerical analysis of partial differential equations and its applications and for services to his discipline.

Morton, on receiving the De Morgan Medal, replied:-A hallmark of Professor Morton's work is the creation of original, elegant mathematics in the service of real-world applications. The London Mathematical Society is proud to honour a mathematician who has changed the way we look at the numerical analysis of partial differential equations through his world-leading research results, his vision and his dynamic leadership qualities.

Another honour which we should mention was Morton's invitation to deliver the Dame Mary Cartwright Lecture in February 2001. He gave the lectureIt was an immense pleasure to receive the De Morgan Medal and a very rewarding moment in my career. I would like to thank the Prizes Committee, particularly for the award citation, which made me very proud.

*Evolution Operators and Numerical Modelling of Hyperbolic Equations*in the Mathematical Institute, Oxford. To celebrate Morton's 80

^{th}birthday, the conference 'Bill Morton's 80

^{th}Birthday Conference' was held in Oxford University on 29 May 2010.

Morton joined the Society of Industrial and Applied Mathematics in 1963, and was elected the first President of the UK Section when it was formed in 1997. He joined the Institute of Mathematics and its Applications in 1964 and was honoured by serving a period as its vice-president. Together with Michael James David Powell (1936-) he founded the Journal of Numerical Analysis. In addition to his scientific work, Morton lists his interests as reading, real tennis, walking, gardening, and listening to music.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (5 books/articles)

**Mathematicians born in the same country**

**Honours awarded to Bill Morton**

(Click the link below for those honoured in this way)

1. | Lecturer at the EMS | |

2. | IMA Gold Medal | 2002 |

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