# Donald Birkby Eperson

### Born: 22 July 1904 in Gunnersbury, Middlesex, England

Died: 13 May 2001 in Worthing, West Sussex, England

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**Donald Eperson**'s father was Joseph William Eperson, a teacher who was born in July 1876 in Mansfield, Nottinghamshire. He married Anne Jassop Birkby, also a teacher, in October 1901 in Bradford, Yorkshire. She had been born in about 1875 in Bradford, Yorkshire. They had met while both were training to be teachers; Joseph studying at Westminster College and Anne at St Katharine's College. Both were very musical. Joseph William Eperson died in 1966 in Devon, England. Donald had a sister Doreen and, as children growing up in the London suburbs, they had happy times playing croquet. These years, before the start of World War I, were happy times and Donald enjoyed singing in the church choir. He writes in [1]:-

He write of his experiences at Colet Court Preparatory School in [2]:-Every Sunday evening our family made music together: my mother accompanied on the piano the songs and hymns sung by my sister Doreen and myself, and my father would play the violin or join in the singing.

From the preparatory school, Eperson entered selective independent St Paul's School, London, in 1916. This school had been founded in 1509 "to educate boys from all nations and countries regardless of race creed or social background." He had won a £100 a scholarship in 1914 which had covered fees for his final two years at Colet Court Preparatory School and also covered his first two years at the prestigious St Paul's School where he [2]:-... at a preparatory school, my mathematical education was soundly based on books such as 'A School Geometry' by Hall and Stevens, which was a revised version of the authors' 'Text Book of Euclid's Elements', used by my father in Victorian times. Euclid's axioms, definitions and postulates were far above the head of a nine-year old boy, whose enjoyment of mathematical activities was not stimulated by 'homework' consisting of the memorizing of theorems such as the 'Pons Asinorum'Ⓣ.

In his first year at St Paul's, after explaining to his classics teacher why an eclipse of the moon can only occur when the moon is full, he was transferred from the Lower Classical Eighth Form to the Mathematical Eighth Form [2]:-... enjoyed writing Latin and Greek verses. This was probably because they were a kind of word puzzle whose solution depended upon finding words with simple rhythms that fitted into a musical framework of pentameters and hexameters.

We note that Capt H R Pullinger is Henry Robert Pullinger who later became headmaster of the Royal Grammar School Worcester.Here, I worked on books such as Smith's 'Conic Sections' and Askwith's 'Analytical Geometry', whilst also finding an interest in Rouse Ball's 'Mathematical Recreations and Essays'. The form master, Capt H R Pullinger, gave us introductory talks on new topics, and then left us mainly to our own activities. He never moved from his desk during the1^{1}/_{2}hour lessons twice a day. We were also expected to do at least two hours of work at home each weekday evening. I was intrigued by Pascal's Theorem and its dual, Brianchon's Theorem, and spent one summer holiday exploring the Theory of Duality in geometry and trying to find other theorems in which the interchange of the words 'point' and 'line' and the phrases 'lie on' and 'touch' led to pairs of dual theorems.

Eperson took part in other activities at the school too [1]:-

In 1922-23 he sat the University Scholarship Examinations in Mathematics and entered Christ Church, Oxford, in the autumn of 1923 after spending a summer holiday on Jersey with his family [2]:-Each Wednesday afternoon was devoted to sport - cricket in the summer term, and rugger in the other two terms: we had to travel to the playing fields within sight of Wormwood Scrubbs prison. I did not shine in either of these activities, but I enjoyed playing chess, for which I gained two prizes. Only once did I join the school team, playing against another London school, when my young opponent castled on the king's side, and allowed me to mate his king at once. When Sir George Thomas, the national chess champion, came to the school to play simultaneously against about20boys playing black, I was one of the few boys that defeated him.

We note that T W Chaundy mentioned in this quote is Theodore William Chaundy (1889-1966) who was a tutor at Christ Church from 1912 until he retired in 1956. He was the author ofMy tutor, Mr T W Chaundy, was a successor to the lecturer in Mathematics known as Lewis Carroll. With some prize money I acquired a small library of books on the architecture of Oxford and of English Cathedrals. Many visits were made to village churches, cathedrals and abbeys by bicycle. I remember many lectures; in particular some on Cubic Curves, Cubic Surfaces, Professor Love's demonstration of the properties of gyroscopes using a bicycle wheel, and G H Hardy's lecture on Geometry where he covered himself from head to toe with chalk-dust and periodically came out with phrases such as "It is obvious that....". Hardy's book, 'A Mathematician's Apology', has been my mathematical gospel ever since I read it. I share his belief that Mathematics is an Art in its own right, and a source of intellectual delight, closely associated with the beauty to be found in the visual arts and in music.

*The differential calculus*(1935) and (with Bryce McLeod)

*Elementary differential equations*(1969). He was a specialist in the printing of mathematics and was a co-author of a book on that topic. Eperson graduated with a First Class degree from Oxford in 1927 and, in the same year, was appointed as a mathematics master at Sherborne School, Dorset, one of the best schools in England. He wrote [2]:-

As to his approach to teaching, he said [4]:-I trained myself by reading such books as 'The Teaching of Elementary Mathematics' by Godfrey and Siddons. A valuable asset was Boon's 'Companion to Elementary School Mathematics' and I soon began my own collection of notes on recreational topics, such as Magic Squares, Dissections and Number Puzzles. I soon learned the value in the classroom of 'side-tracking' from the appointed syllabus, and exploring topics such as Pythagoras's connection between mathematics and music. In my spare time I organised visits to places of archaeological and architectural interest. I began to study for the General Ordination Examination and, after six months at Ripon Hall Theological College, was ordained Deacon in Salisbury Cathedral in1930.

Eperson had a number of pupils at Sherborne who would become famous, the best known being Alan Turing. Eperson said [4]:-By word and by example, I encouraged boys to investigate puzzles and problems on their own, and to enjoy their mathematical activities.

However, Eperson deserves much credit for his ability to handle a pupil as talented yet unconventional as Turing. In fact, inspired by Eperson, Turing borrowed three books by Lewis Carroll from the School library in November 1930:In one sense he(Turing)was difficult to teach, as he preferred to make his own independent investigations.

*The Game of Logic*,

*Alice in Wonderland*and

*Through the Looking Glass*.

In 1933 Eperson addressed the Annual General Meeting of the Mathematical Association, delivering his talk

*Lewis Carroll - mathematician*.

After he was ordained, Eperson acted as an assistant chaplain to Sherborne School in addition to his mathematics duties. However, in 1938 he left Sherborne School when he accepted an offer from the Bishop of Salisbury, Dr Lovett, to be vicar of Charminster in Dorset and, in addition, to be the chaplain at Herrison Hospital. In September 1939, Eperson married Phyllis M Perrett who had studied mathematics at Cambridge before being appointed to the Sherborne Girl's School. It was their musical interests that had brought them together having met singing madrigals at Sherborne. Epson continued his interest in mathematics and in Dodgson, publishing

*The Lewis Carroll Puzzle Book; containing over*1,000

*posers from Alice in Wonderland and other books by Lewis Carroll*(1948). J C P Miller writes in a review [5]:-

Eperson also produced works on places of interest such asThis consists mainly of a number of "Quizzes" on various subjects - many of the questions, but not all, connected with Lewis Carroll and his works. The mathematical part is short, but interesting: in it are some of Dodgson's "Pillow Problems" and simpler "Armchair Problems". ... The whole collection has an unusual freshness to those not well acquainted with Lewis Carroll's works-perhaps because both Dodgson and compiler are mathematicians.

*The Church of St Mary, Charminster*(1944).

In 1951 he was appointed an Honorary Canon of Salisbury Cathedral but at this stage continued his duties as vicar of Charminster. However, in 1953 he resigned his position in Charminster when he was appointed as Chaplain of Bishop Otter College in Chichester. This gave him the opportunity to teach again, both mathematics and divinity, while his wife became the warden of one of the women's hostels. Bishop Otter College was a teacher training college, so Eperson was now having to show teachers how to teach mathematics. He writes [2]:-

In his attempts to produce material to promote enjoyment and interest in mathematics as well as stimulating pupils, led him to make a number of films, for example... there were few books for the guidance of training college lecturers when devising basic courses in mathematics.[In1956an Inspector]visited and invited the College to organise a supplementary one-year course for teachers who wished to improve their knowledge of mathematics and to teach the subject at secondary school. From1957-1964the course attracted over70men and women teachers. Volunteers on the course assisted me in an investigation into Goldbach's Conjecture that every even number is the sum of two prime numbers, which yielded some interesting discoveries but no proof of the validity of the conjecture.

*Alice in Numberland*,

*The History of Pi*, and

*The History of Calculators*. He continued his love of music, producing works such as

*O mortal man: anthem for five voices*(1956),

*Lord of Mercy. A motet for five voices*(1957) and

*Two lute songs*(1962).

In 1964, when he reached the age of 60, Eperson retired from Bishop Otter College where he had, for some years, been a Principal Lecturer and Dean of Chapel. He taught for a term at a Secondary Modern School at Deal where he used his unpublished 'Mathematics for Pleasure' material. He wrote [4]:-

After the term at Deal, he moved to Canterbury where he was appointed as senior lecturer in mathematics at Christ Church Canterbury, and a minor canon at Canterbury Cathedral. His address in Canterbury was the charming 12 Puckle Lane. In 1969 he officially retired but became even more active in publishing material intended to intrigue, entertain and develop mathematical skills. He now began publishing a section entitled 'Puzzles, Pastimes, Problems' inThis[material]was the outcome of my work with college students suffering from 'mathophobia', for whom I devised activities, based upon traditional and 'modern' mathematics, that would stimulate their interest and convince them that elementary processes and ideas were not beyond their powers of comprehension. My belief is that, at every stage, mathematical activities can be as enjoyable as any other topic in the school curriculum. The material was never published, but the duplicated sheets were in great demand from over500teachers.

*Mathematics in School*, a publication of the Mathematical Association, his first article being published in November 1971. In addition, he published interesting mathematical items in

*The Mathematical Gazette*, and his 'Maths Teasers' were published regularly in the 'Maths Extra' issues of the Times Educational Supplement.

For a few of Eperson's Puzzles, Pastimes and Problems and some of his thoughts about teaching mathematics, see THIS LINK.

In 1988, when he was eighty four years old, Eperson published a book entitled

*Patterns in Mathematics*which ran to five editions. This book, wrote Eperson, emphasised [2]:-

He was still living in Canterbury in 1998 but with increasing frailty, both of himself and of his wife, they moved to Sussex, living at Hillrise, 12 Tennyson Road, Worthing, West Sussex. By the year 2000, he was ninety-six years old but still writing articles. He completed writing his autobiography... mathematics as a form of art which can be enjoyed by young and old alike, and containing hundreds of original puzzles and pastimes. Just as Rhythm is the basic element in all forms of Music, Pattern is the basic element in Mathematics that can give pleasure to everyone.

*Music and Mathematics*in March 2001 but he did not live to see it published in the following year. His final article on Lewis Carroll was

*No Ear for Music?*which was, in fact on Lewis Carroll and Sir Arthur Sullivan. It was published in the Spring issue of

*The Carrollian,*the journal of The Lewis Carroll Society, at around the time of Eperson's death.

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

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