**Benjamin Moiseiwitsch**was known as

**Benno**to his friends and colleagues. His parents were Jacob Moiseiwitsch and Chana Kotlerman. Jacob and Chana Moiseiwitsch were Russians and their first child Daniel Moiseiwitsch was born in Russia in 1919. The family moved to England and settled in Romford, Essex. They had two other children, Victoria, and Benjamin, the subject of this biography born in 1927. Let us say a little about Daniel Moiseiwitsch at this point. He became an artist and has several pictures in the V&A Museum, London. In World War II he served with the 1st Battalion of the Loyal Regiment (North Lancashire) in the Italian Campaign and died on 24 February 1944 while fighting in the Battle of Anzio. Victoria was also an artist and she died in 2012. As we will see below, although Benjamin became an applied mathematician, he also had an interest in art, in particular in the connections between art and mathematics.

Benjamin grew up in Romford where he attended the Royal Liberty School, a grammar school in Upper Brentwood Road, founded in 1921. Moiseiwitsch entered the school in 1940 and, after proving to be an outstanding pupil, graduated in 1946. In that year he entered University College London where he studied mathematics and theoretical physics. There he was taught by, among others, Richard Arthur Buckingham (1911-1994) who was a lecturer in mathematics, David Bates who was also a lecturer in mathematics, and Harrie Stewart Wilson Massey (1908-1983), a Australian mathematical physicist who held the Goldschmid Chair of Applied Mathematics. Massey had studied under Ralph Fowler at the University of Cambridge and obtained a doctorate in 1932 with his thesis *The Collision of Material Particles*. Before both Bates and Massey were called for war service, Bates had been a student of Massey's at Queen's University, Belfast, and had moved with him to University College London when Massey was appointed there in 1938. One of Moiseiwitsch's fellow students, also interested in mathematics and theoretical physics, was Alexander Dalgarno (1928-2015). When Moiseiwitsch began his studies at University College London it was only one year after the war had ended and everything was still in a poor state. The intense bombing had destroyed, or partially destroyed, many of the buildings and the Mathematics Department was in temporary dingy accommodation.

Moiseiwitsch was awarded a B.Sc. from University College London in 1949 and continued studying there for a Ph.D. advised by Harrie Massey. Dalgarno was also working towards a Ph.D. advised by Massey and Buckingham. This strong group of researchers were interested in applying mathematics to atomic physics, molecular physics and atmospheric physics.

In 1950 Massey and Moiseiwitsch published *The Scattering of Electrons by Hydrogen Atoms* in the *Physical Review*. This short paper announced results which they stated would be published later in full and, indeed, in August 1950, Massey and Moiseiwitsch submitted the paper *The Application of Variational Methods to Atomic Scattering Problems. I. The Elastic Scattering of Electrons by Hydrogen Atoms* to the Royal Society of London. It was published in the *Proceeding* of that Society in the following year. It begins as follows:-

In 1951 Bates left the University College London group when he was appointed as Professor of Applied Mathematics at Queen's University, Belfast. Ray Flannery writes [1]:-Variational methods have proved to be of the greatest value for the approximate determination of the energies and wave functions for stationary states of various atomic and nuclear systems. In recent years ways have been found for extending such methods to unclosed states(states of the continuous spectrum)which describe collision processes. This makes possible not only the rapid determination of the phase parameters describing the elastic scattering of particles by a centre of force, but also for the first time permits the inclusion of effects due to departure from the single-body approximation - effects such as arise from exchange of particles or from polarization. It therefore opens the way for a re-examination of the theory of the scattering of electrons by atoms which previously only made inadequate allowance for these effects. In this paper we consider the simplest problem of this kind - the elastic scattering of electrons by atomic hydrogen.

[In 1952 Moiseiwitsch graduated from University College London with a Ph.D. awarded for his thesis on quantum theoryBates]created a supportive yet challenging environment at Queen's, and many came from all over the world to carry out research in atomic, molecular and atmospheric physics, under his inspiration and direction. To have built this world-class department within such a short time was no mean achievement. It required great intellectual might and vision, incredible leadership and insight, sustained dedication and loyalty.

*The Application of Variational Methods To Collision Problems.*In the same year he joined Bates as a Lecturer in Applied Mathematics at Queen's University, Belfast.

On 20 June 1953 Moiseiwitsch married Sheelagh McKeon; they had four children: Tanya Moiseiwitsch (born 1954), Lisa Moiseiwitsch, Julian Moiseiwitsch and Nicholas Moiseiwitsch (born 1968). Julian Moiseiwitsch studied dental surgery at University College London and was awarded a Ph.D. from the University of North Carolina at Chapel Hill. He now works in Washington D.C. His wife Françoise Seillier-Moiseiwitsch is a mathematician. Nicholas Moiseiwitsch studied electronic engineering at the University of Southampton and became Head of Engineering Policy at the Institute of Electrical Engineers.

Moiseiwitsch was promoted to Reader in Applied Mathematics at the Queen's University, Belfast in 1962 and Professor in Applied Mathematics and Theoretical Physics in 1968. In 1966 he published his textbook *Variational Principles*. The publisher gives the following description:-

For a version of Moiseiwitsch's Preface to this edition, also his Preface to the 2004 edition and an extract from a review of the 1966 edition, see THIS LINK.This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles(and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities(such as the phase shifts)that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mechanics, and quantum mechanics; field equations; eigenvalue problems; and scattering theory.

In 1977 he published *Integral Equations*. The publisher writes:-

John E G Farina, in the review [6], writes:-Two distinct but related approaches hold the solutions to many mathematical problems - the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem - under suitable conditions - in the form of an infinite series. Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution. The treatment becomes gradually more abstract, with discussions of Hilbert space and linear operators, the resolvent, Fredholm theory, and the Hilbert-Schmidt theory of linear operators in Hilbert space.

Moiseiwitsch was elected to the Royal Irish Academy in 1969. He served as Dean of the Faculty of Science at Queen's University, Belfast, from 1972 to 1975 and head of the Department of Applied Mathematics and Theoretical Physics from 1977 to 1989. He retired in 1993 and, at that time, was made professor emeritus.This book on integral equations is intended for students in the final year of an honours mathematics or mathematical physics course, but might also be useful to engineering students with a strong mathematical background. ... his is a very clearly written book. The author is careful to progress from the concrete to the abstract, so that first a good foundation of computational techniques is laid, followed by the more abstract aspects of the subject. He brings in new concepts gradually, and at the stage when the reader is ready for them. At the end of each chapter there is a set of straightforward, well chosen problems which should fall well within the scope of a reader who has understood the material of the chapter.

Two projects by Moiseiwitsch after he retired are well worth mentioning. The first is his article *Art, Mathematics, Music and the Physical Universe* where he gives a truly fascinating account of the interrelations between the areas mentioned in the title. We give a version of his Introduction to this article at THIS LINK.

The other major project he undertook after he retired was writing his book *How to Solve Applied Mathematical Problems* (2011). The publisher writes on the jacket of the book:-

A version of Moiseiwitsch's Preface is given at THIS LINK.The ability to solve problems in applied mathematics depends upon understanding concepts rather than memorizing formulas or rote learning. This volume bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. The two-part treatment begins with chapters on vector algebra, kinematics, dynamics of a particle, vector field theory, Newtonian gravitation, electricity and magnetism, fluid dynamics, and classical dynamics. The second part examines Fourier series and Fourier and Laplace transforms, integral equations, wave motion, heat conduction, tensor analysis, special and general relativity, quantum theory, and variational principles. The final chapter contains problems associated with many of the preceding chapters and expresses them in terms of the calculus of variations.

He died unexpectedly at the age of 89. His funeral was held at Roselawn Crematorium, Belfast, on Thursday 22 September 2016.

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

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