Dame Kathleen Mary Ollerenshaw (1912-2014), mathematician, educationalist, and politician, was an honorary member of the Manchester Literary and Philosophical Society. In her 101 years she published extensively and played a prominent part in the political and intellectual life of modern Manchester during the twentieth century. She was a very proud Mancunian.
Kathleen was born into the Timpson shoe dynasty. Her paternal grandfather William Timpson founded shops in Manchester in 1865, and this developed into a large shoe empire. He married Elizabeth Farey, his first cousin, and their second son born in 1881, was Kathleen’s father. Her father was a respected local magistrate and president of the local Liberal Association, and the family home in Didsbury was a solidly middle-class household. It was a place where Liberal politics was the norm. C. P. Scott, a Liberal MP and editor of the Manchester Guardian, was a hero to her mother and through his progressive ideals she held a strong belief in the value of a sound education. Brought up in a non-conformist culture, Sunday attendance at the Manchester Wesleyan chapel was an added feature of Kathleen’s early life.
From the age of six Kathleen was educated at the Lady Barn House School in Withington, a suburb bordering on Didsbury in south Manchester. At eight years a combination of a viral infection and a family history of otosclerosis left her almost completely deaf. She became expert in lip-reading and remarkably enjoyed music through the school’s connection with ‘Dalcroze eurythmics’, a Swiss educational theory which advocated the importance of musical movement.
The adage of the connection between mathematics and music was certainly true in Kathleen’s case. As a child she felt at one with mathematics. The hearing affliction did not hamper her, and she later wrote: ‘The deafness was a hindrance to be battled with, but also a spur to effort; the mathematics has been the icing on the cake. I was also blessed from the start in having a passion for numbers. Numbers are fun and contain an infinity of mysteries.’ When the Rubik’s cube craze took hold in the 1980s, she joined in and proved a worthy exponent, though it cost her a repetitive strain injury requiring surgery for tendonitis.
At thirteen she transferred to St Leonard’s, a private boarding school in St Andrews Scotland, where her love of mathematics became a fully-fledged passion; she recognised that it was the ‘one subject in which I was at no disadvantage’. Back home in Manchester she took herself down to the university, explaining to the head of mathematics, Louis Mordell, a need to be brought up to speed in the subject for the purpose of gaining entrance to Oxbridge. He passed her on to J. M. Child who coached her for the entrance examinations, and in the process widened her knowledge of mathematics and its history.
In 1931 she went to Somerville College Oxford and immersed herself in student life. Shortly after entering she became engaged to Robert Ollerenshaw, a trainee surgeon who she had known since primary school. She attended the lectures of W. L. Ferrar and T. W. Chaundy, becoming friendly with both. She gained much from Ferrar, an algebraist, and from Chaundy who would later supervise her doctoral studies. In 1934 she graduated with a first-class honours degree. Outside of academic work she gained a hockey Blue and, after Oxford, represented Lancashire and the North of England. She became a proficient ice skater and took part in national championships.
It was said that four M’s defined Kathleen’s life: mathematics, music, mountains, and Manchester. Mathematics flowed through Kathleen’s life and was perhaps the most precious ‘M’ of all. It became a constant in her life, no less than an intellectual companion, and she later reflected: ‘Mathematics is a living activity with a living language, always developing to convey new concepts and new techniques for solving problems’, and this excited her.
The summers of 1933-39 were spent with Robert and his widowed father (a distinguished orthopaedic surgeon) near Salzburg, where she was among the mountains and where she had the enjoyment of hiking and climbing. Indeed, she used to say there was a strong connection between mountains and mathematics. In the first attempt of the ascent of a mountain, she noted: ‘the struggle is to find any route’ but once on top: ‘other possible routes up may be discerned and safer or shorter may be chosen for the descent or for subsequent ascents. Finding a result in mathematics could be compared with this, but whereas a mountain was clearly there to be scaled, for mathematicians she perceived an additional challenge: ‘we do not always know that there is a result, or if the proposition (to be proved) is only a figment of the imagination, let alone whether a proof can be found.’
After leaving Oxford she took up statistical forecasting while working for the Shirley Institute in Manchester, an organisation specialising in textile research. This familiarity with Statistics was invaluable when it came to analysing data in her later role as an educationalist, and later she served as president of the Manchester Statistical Society in 1981-1983.
At the onset of war in September 1939, she and Robert married after their eight-year engagement. In Manchester, Mordell suggested she meet Kurt Mahler, a German emigree who had come to the city in 1938. By any measure Mahler was a brilliant mathematician. Self-taught, he was interested in number theory and geometry and importantly the close links between the two fields. To Kathleen he mentioned an unsolved problem in ‘critical lattices’ which she described as ‘right up her street’. Within a short time she had solved it and using it as a launchpad, she undertook further exploration of the topic. Audaciously she obtained government permission (required during the war years) to study for a DPhil at Oxford. She enrolled at Somerville with Chaundy as supervisor and for five papers published in notable British research journals, she was awarded the doctoral degree in 1945.
As to her love of Music, another of the M’s, she never missed a Hallé concert when she was in Manchester. With her hearing disability, her way of appreciating music was by closely following the musical scores and watching the movement of the musicians. Later she became involved in the establishment of the Royal Northern College of Music in 1973. Her enjoyment of music was enhanced by the advent of hearing aids around 1950, and at the age of thirty-seven her life was transformed.
In the 1950s she was drawn into politics and quickly took to the education brief as a co-opted member of the local council. Her first quest, backed up by statistical analysis, was directed to the practical needs of schools and the buildings they occupied. Two years after co-option she became an elected member, a status which gave her greater authority in the battles ahead. From 1956 she was elected to represent Rusholme as a Conservative on the City Council, and she served in this capacity until 1981. In the controversial introduction of comprehensive schools in the 1960s she was of the old guard fiercely defending grammar schools, a system which retained some of the advantages she had enjoyed in her own school education. But she recognised this was designed for an elite, and that politically change was coming.
While a member of the Conservative party, and one who prided herself on the virtues of a private school education, it is notable that Kathleen found an ally in Eric Robinson, vice president of the Socialist Education Association from 1965 until his death in 2011. A man who was who became a revolutionary pioneer of the polytechnic movement of the 1960s, he also acted as advisor to the Labour government. Robinson’s own training as a mathematician helped their relationship and they jointly argued that primary school teachers must have a basic ‘Ordinary level’ qualification in mathematics for entrance to teacher training programs.
During her ‘political period’ post 1950, she accumulated many civic honours. She was made Dame Commander of the British Empire in 1971 for services to education and served as Lord Mayor of Manchester in 1975–76. The one position she prized above all, ‘Freedom of the City of Manchester’, was granted in 1984. Mathematics was always there and in 1978-1979 she served as President of the Institute of Mathematics and its Applications, in the list of its presidents following Prince Philip in that role.
Kathleen’s interest in ‘magic squares’ began in the 1980s. This vast area of mathematical activity is rooted in ancient cultures, first signs taking place in China before the Christian era. It poses many unsolved problems which continue to attract widespread attention today.
The simplest example of a magic square is one with three rows and three columns. This is a 3×3 square filled in with different whole numbers:
| 8 | 1 | 6 |
| 3 | 5 | 7 |
| 4 | 9 | 2 |
This is ‘magic’ because filled in with numbers 1 to 9, the sums of each row, each column, and each diagonal add to the same number, here 15 (called the square’s magic number). Apart from swapping rows and columns and rotations, this is the only 3×3 magic square which is possible. Looking at 4×4 squares, the situation is quite different and with them the whole subject opens. Such a 4×4 square was displayed by the artist Albrecht Dürer in 1514 with magic number 34, but in the seventeenth century the French mathematician Bernard Frénicle de Bessy conducted an exhaustive search and listed 880 essentially different 4×4 magic squares. Kathleen and Sir Hermann Bondi, a famous mathematical cosmologist, joined forces and through analysis confirmed Frénicle’s work and published their result in the Philosophical Transactions of the Royal Society (1982). They referred to the ‘mysterious properties of these fascinating squares’ and with this mystery Kathleen became captivated by the subject.
Kathleen worked on pandiagonal magic squares, those with the extra requirement that ‘broken diagonals’ should also add to the magic number. With still more properties required, there are also ‘most perfect pandiagonal magic squares’. This research occupied her for some eight years. By a happy accident she teamed up with her Didsbury tenant lodger David Brée, who was Professor of Artificial Intelligence at the University of Manchester from 1990 to July 2006. He brought the necessary computer skills to the task and became her co-author, and they published their Most-Perfect Pandiagonal Magic Squares: Their Construction and Enumeration (1998). With this she commented: ‘Only now, with the work complete, is it possible for me to look back and see the process as it developed, savouring in retrospect the challenge presented when proof was first attempted, and recalling each step of the astonishing mathematical adventure that it has been.’
In her late seventies she took up the study of Astronomy, and typically, with the very determined streak in her personality, there were no half-measures. An amateur she may have been, but she took the study seriously and found guidance from Sir Patrick Moore, presenter of the BBC’s The Sky at Night, and Sir Bernard Lovell, who established the Jodrell Bank Observatory (about twenty miles south of Manchester) and oversaw construction of what became the famous Lovell Telescope. She acquired a powerful telescope herself and joined the Manchester Astronomical Society where she made many friends. In her later years she spent time travelling the globe chasing eclipses of the sun. She also embarked on an autobiography, To talk of many things (2004) and launched into the writing challenge. In gratitude she inscribed a copy to her professional indexer Martin Hargreaves:
Continuing with mathematics, some new and different challenges arrived in her later years. In her nineties a worsening eyesight added to her deafness, but she merely brushed this off ‘as a maddening frustration—a double whammy’. Her response was to go to classes to learn Braille. Being long-lived she also endured personal grief with her husband, daughter and son predeceasing her.
In old age, she retained her sharp wit, punctuated with an infectious sense of humour. Scores of Manchester’s children remembered her for the Speech Days she attended, held at the Free Trade Hall or at schools spread throughout the city. She took a real interest in the students she met and remembered them too; years later they might have been surprised to receive a congratulatory note for their passing of a mathematical examination. She was ever present in the sphere of higher education in the north-west of England, often in the formal positions she occupied: vice president of UMIST, pro-chancellor of Salford University, deputy pro-chancellor of Lancaster University, and chairperson of Manchester Polytechnic (which became Manchester Metropolitan University).
As a Freeman of the City, she never refused an invitation to a civic function and always dressed herself immaculately for such occasions. An annual highlight for her was the Remembrance Service held at the cenotaph in St Peter’s Square in the autumn. In her nineties she insisted on processing to and from the Town Hall, frequently on the arm of Sir Bobby Charlton (a Freeman elected in 2008) to the approval of those who lined the route. In her last days she was a familiar figure around Didsbury in south Manchester where she lived most of her life. In the daily round she would regularly stop and chat to people during her walks in the company of her fluffy dogs Tom and Jerry. She was completely at home in the neighbourhood in the city she always called ‘her beloved Manchester’.
Tony Crilly, member of Manchester Lit & Phil
Images: Wikimedia Commons (Sim0n), The University of Manchester
