Dame Kathleen -- who published her autobiography at 93 -- wrote that maths was "the one subject in which I was at no disadvantage. Nearly all equations are found in textbooks or shown on the blackboard as the teacher speaks. Mathematics is a way of thinking. It requires no tools or instruments or laboratories. It may be convenient to have a pen and paper, a ruler and a compass, but it is not essential: Archimedes managed very well with a stretch of smooth sand and a stick."
An Oxford hockey blue and champion skater in her youth, she was also a keen astronomer -- Lancaster University named its observatory after her.
As an adviser to Margaret Thatcher , she was a trenchant supporter of independent schools . Her warnings in the 1970s about falling standards in state schools were taken up by James Callaghan when he launched his "great debate" on the issue.
Throughout her career she was supported by her husband, Robert Ollerenshaw, whom she had met at school when she was six. In the sixth form Robert gave her his slide rule: "He had made a leather case for it and I counted this as the mark of true love." They married in 1939 and had two children, both of whom she outlived. Robert Ollerenshaw became a distinguished military surgeon before going into academia.
Kathleen Mary Timpson was born on October 1 1912, a granddaughter of the founder of Timpson Shoes. In 1921 a viral infection and inherited otosclerosis left her almost deaf, and she learned to lip-read. At St Leonard's School, St Andrews, she was told she could not take maths in the sixth form as she had not attended applied maths classes; she threatened to leave, then achieved outstanding grades.
Having spent a year studying higher algebra and geometry with JM Child at Manchester University, Kathleen won a scholarship to Somerville College, Oxford, graduating in 1934 .
In 1937 she went to the Shirley Institute, which undertook research for the cotton industry, but soon met the German mathematician Kurt Mahler, who had come to Manchester University. He mentioned an unsolved problem on critical lattices, an aspect of number theory and geometry, and she solved it within days. Mahler suggested she return to Oxford for a DPhil; she produced five original papers which qualified her without the need to submit a thesis. After Robert was demobilised, she lectured at Manchester University.
Kathleen Ollerenshaw was co-opted on to Manchester education committee in 1954, and two years later elected a councillor, serving almost continuously until 1980. After telling the National Council of Women of the poor state of Manchester s older schools, she was asked for a detailed report, which found that 750,000 British children used schools built before 1870; this led to the government releasing extra funds for school buildings. In 1958 she published a Conservative Political Centre pamphlet, Education for Girls, which insisted on more than "a diluted or merely modified version of the traditional education provided for boys". Girls, she wrote, must be educated for work as well as marriage, with greater encouragement to study maths and sciences. She became chairman of Manchester's education committee when the Conservatives took control in 1967, serving for three years before Labour regained it. She was appointed DBE in 1971.
When Stanford University published research showing that attainment in maths by Japanese children was far higher than elsewhere, Kathleen Ollerenshaw persuaded the British Council to send her to Japan to ascertain why. She found class sizes much larger than in Britain, but a high standard of discipline and an expectation of success.
Dame Kathleen was Manchester's lord mayor in 1975-76, and during her term of office wrote a children's book, The Lord Mayor's Party, as well as First Citizen, in which she told how she would play Frisbee with her secretary in the main hall . She dispensed with the lord mayor's dining room, because "My husband and I have no time for entertaining". She led the council's Conservative opposition from 1977 to 1979 .
In 1978 she succeeded the Duke of Edinburgh as president of the Institute of Mathematics and its Applications, which she had helped found. Under her leadership it conducted the first national tests in basic maths, and she was appalled by the results: fewer than nine per cent of children obtained anywhere near full marks on an extremely simple paper, and 15-year-olds in inner London were a year behind those in Cleveland.
One of the first mathematicians to solve the Rubik's Cube (her efforts resulted in her having to undergo an operation for "cubist's thumb"), Dame Kathleen published her Rubik's Cube paper in 1980. To solve the puzzle in 80 moves, she said, you did the bottom face first, then the top corners, then the middle slice edges and finally the top edges.
She went on to study the theory of magic squares -- in which the numbers 1 to 16 are arranged in a 4×4 array so that the sum of each row, each column and the two diagonals add to the same. With the cosmologist Herman Bondi she verified 17th-century calculations that there were exactly 800 different such squares, and in 2006 she published Constructing Magic Squares of Arbitrarily Large Size.
In 2004 Dame Kathleen brought out a memoir, To Talk of Many Things. In 2008, Sir Peter Maxwell Davies dedicated his Naxos Quartet No 9 to her.
Among her many posts, Dame Kathleen Ollerenshaw was a Pro-Chancellor of Salford and Lancaster Universities; and chairman of the courts of the Royal Northern College of Music, Manchester College of Commerce and its successor, Manchester Polytechnic, and Manchester University.
She was president of Manchester Statistical Society and Manchester Technology Association; vice-president of Manchester Astronomical Society and of the British Association for Commercial and Industrial Education and the City and Guilds; and chairman of the Association of Governing Bodies of Girls' Public Schools and the St John Ambulance Council for Greater Manchester. She was appointed a Deputy Lieutenant for Greater Manchester in 1987.
Robert Ollerenshaw died in 1986, and both their children predeceased her.
Dame Kathleen Ollerenshaw, born October 1 1912, died August 10 2014
3 August 2014 © Telegraph