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.

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 in 1900, 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.

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.

... the paper represents a major contribution to the study of Monte Carlo Methods.

... 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.

The book is primarily written for users of difference methods, but it can be highly recommended to everyone interested in the subject.

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.

... he concentrated on graduate teaching, bringing his wide experience to bear on the MSc courses.

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.

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.

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.

... 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.

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.

It 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.