**Clement Durell**'s mother was Ellen Annie Carlyon and his father was John Vavasor Durell who was rector of the church at Fulbourn. Clement was born in the rectory at Fulbourn, the fifth of his parents sons. He seems to have found having four older brothers rather daunting, and as a result he grew up to be a rather shy person.

Durell was educated at Felsted School and, while still at school, he published his first note in the *Mathematical Gazette*, the journal of the Mathematical Association. The note was *A geometrical method of trisecting any angle with the aid of a rectangular hyperbola* written jointly with W F Beard. Durell joined the Mathematical Association in 1900, the year in which he entered Clare College, Cambridge, to study mathematics. He was a First Class student in the Mathematical Tripos examinations, graduating in 1904. He was appointed as a mathematics teacher at Gresham's School immediately after graduating, and in the following year of 1905 he moved to take up the post of mathematics master at Winchester College.

Soon after taking up this post Durell's first textbook *Elementary Problem Papers* (1906) was published. He was promoted to senior mathematics master at Winchester College in 1910 and began publishing a series of articles in the *Mathematical Gazette*. Before the outbreak of World War I, Durell published *The arithmetic syllabus in secondary schools* (1911) and *Analysis and projective geometry* (1911) in the *Mathematical Gazette*. During World War I, Durell served in the Royal Garrison Artillery as a lieutenant. After the end of the war he returned to Winchester College and began publishing a series of articles in the *Mathematical Gazette* and a remarkable series of textbooks which would make him the best known writer of English school mathematics texts.

As well as writing articles for the *Mathematical Gazette* such as *The use of limits in elementary geometry* (1925) and *The teaching of loci in the elementary geometry course to school certificate stage* (1936), he was also actively involved with the committee work of the Mathematical Association and its report production. He wrote reports *The teaching of geometry in schools* (1925), *Memo from the Girls' Schools' Committee: Mathematics for girls* (1926), and *Questionnaire on the teaching of mathematics in evening continuation schools* (1926). Among the books he wrote around this time were: *Readable relativity* (1926), *A Concise Geometry* (1928), *Matriculation Algebra* (1929), *Arithmetic* (1929), *Advanced Trigonometry* (1930), *A shorter geometry* (1931), *The Teaching of Elementary Algebra* (1931), *Elementary Calculus* (1934), *A School Mechanics* (1935), and *General Arithmetic* (1936). In a catalogue produced by the Mathematical Association's publishers G Bell & Sons in 1934, they listed 20 textbooks by Durell and write:-

There can indeed be few secondary schools in the English-speaking world in which some at least of Mr Durell's books are not now employed in the teaching of mathematics.

Rather than list all the many works that Durell produced, we prefer to take a closer look at two of them. First let us look more closely at *Readable Relativity. A Book For Non-Specialists* which Durell first published with G Bell & Sons in 1926. It is worth noting that the first text in English on relativity was by Eddington in 1923 so Durell's text came very early. The publisher described Durell's book as follows:-

Precise, brief, and practical, this text is the work of a highly respected teacher with years of classroom experience, who sketches the mathematical background essential to a clear understanding of the fundamentals of relativity theory. Each subject - including the velocity of light, the measurement of time and distance, and the properties of mass and momentum - is illustrated with diagrams, formulas, and examples. All chapters conclude with a series of exercises, with solutions at the end of the book. Readers possessing a minor degree of mathematical capacity and a willingness to work out a few numerical examples will find that this text puts Einstein's view of the universe well within their grasp.

In 1960 an American edition of the book was published by Harper & Brothers, New York. This edition of the book contains a Preface written by Freeman J Dyson who was a former pupil of Durell. Dyson, who describes Durell's great abilities as a teacher and writer, says of the book:-

The best layman's introduction to relativity that has ever been written by anybody.

Recently, in 2003, this 1960 edition has been reprinted by reprinted by Dover Publications.

For the second of our more detailed looks at one of Durell's texts let us consider *Advanced Trigonometry* which was also originally published by G Bell & Sons. This work was a collaboration of Durell and Alan Robson who taught at Marlborough College and was a major figure in the Mathematical Association. The publisher writes:-

This volume will provide a welcome resource for teachers seeking an undergraduate text on advanced trigonometry, when few are readily available. Ideal for self-study, this text offers a clear, logical presentation of topics and an extensive selection of problems with answers. Contents include the properties of the triangle and the quadrilateral; equations, sub-multiple angles, and inverse functions; hyperbolic, logarithmic, and exponential functions; and expansions in power-series. Further topics encompass the special hyperbolic functions; projection and finite series; complex numbers; de Moivre's theorem and its applications; one- and many-valued functions of a complex variable; and roots of equations.

We left describing Durell's career with him back at Winchester College after World War I as senior mathematics master. In 1920 be became, in addition, a housemaster at Chernocke House and retained this position for seven years. In contrast to his great success as a teacher and as a textbook writer, Durell did not excel in the role of housemaster. He was not good at personal relationships and his natural shyness with people meant that he did not make much of a success of this position. His relations with the Mathematical Association also became rather cool after he openly criticised one of their reports of 1923 as being elitist and impractical. He kept in contact with the Association, however, and returned to contributing articles to the *Mathematical Gazette* in 1936 after a break of ten years from publishing in the journal. He contributed *The teaching of loci in the elementary geometry course to school certificate stage* (1936), *On differentials* (1936), *Differentials* (1937), *A theorem in solid geometry* (1941), *The transition from school to university mathematics* (1948), and *The nature of main-school geometry* (1949). He also contributed a number of letters and an obituary of Alan Robson in 1952.

Not only did Durell resume writing articles for the journal of the Mathematical Association but he also began to take an active part its work. As secretary to the committee reporting in 1953 on the teaching of geometry in schools, he is described in [3] as:-

... an indefatigable worker, producing numerous drafts, and a courteous though persistent critic of anything he thought loose or inconsistent in the efforts of others.

Price writes [1]:-

On his retirement from Winchester College, Durell moved to73North Lane, East Preston, Sussex, where he was accompanied by a housekeeper, a gardener, and large dogs. Golf was, at one time, a chief recreation, and, in his old age, he escaped from English winters to the climates of Madeira and, latterly, South Africa...

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