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Centenarian Dame Kathleen Ollerenshaw—Conqueror of Magic Squares, Rubik's Cube and Mauna Kea

Born in 1912, mathematician, amateur astronomer, politician, wife and mother Ollerenshaw is still as sharp as ever



University of Salford

A quintessential moment in Dame Kathleen Ollerenshaw's 2004 autobiography occurs as she scrambles up Hawaii's Mauna Kea volcano for a better view of an eclipse in 1991. This is her third trip to see an eclipse and her second in under a year. Clouds had thwarted both previous attempts, and she is determined not to let rising clouds foil her yet again. Her bus was stopped at a barrier. She wrote, "I had a fixation that I must get as high as possible. I grabbed my tripod and camera and clambered up a steep, bracken-covered slope until at last I came to a level spot and set up my gear." After watching the drizzle in dismay from this perch, the moment of the total eclipse was almost biblical. As she described it: "Lo, there appeared a patch of pale blue sky. There was a great shout. At the crucial moment of the onset of totality the clear patch coincided with the sun and moon." This was no ordinary 79-year-old.

Ollerenshaw will celebrate her 100th birthday on October 1. Born in Manchester, England, in 1912, Ollerenshaw has lived almost her entire life in that city. She earned her doctorate in mathematics from the University of Oxford in 1945, worked as a part-time math instructor for several years, served in local government, including as Lord Mayor of Manchester, and became a dedicated amateur astronomer after her husband died. In some ways, her life serves as a counterexample to recent articles questioning whether women can have it all. In other ways, her experience is completely foreign to young women in the early 21st century who are trying to balance career, family and hobbies. She was unavailable for an interview, so her autobiography To Talk of Many Things (Manchester University Press, 2004) is the source of all of her quotes in this article.

Ollerenshaw's most famous contribution to mathematics is her book Most-Perfect Pandiagonal Magic Squares, published by the Institute of Mathematics and its Applications (IMA) in 1998 with David Brée, a computer scientist who rented one of her rooms for several years. Magic squares are arrays of numbers in which the sums along the rows, columns and diagonals are all equal. They were able to enumerate and describe an infinite family of magic squares. She was also involved with the IMA in the U.K. and published one of the first solutions to the Rubik's cube in the IMA Bulletin (now the journal Mathematics Today). The Rubik's cube story illustrates her relentless perseverance on any problem she faced: She damaged the tendons in her left thumb so badly with repeated turning of the cube that she required surgery.

In addition to perseverance, Ollerenshaw clearly has an incredible mathematical mind. It is not unlikely that she would be considered a mathematical savant today. In boarding school she developed a technique she calls subliminal learning: She would think about a problem before going to sleep, tracing important aspects of it out with her fingers, and the answer would be "written" on a wall or the ceiling in the morning. (She wrote that she also applied this technique to skating and skiing, two of the many sports she loved.) Terry Edwards met Ollerenshaw in 2001 when he interviewed her in honor of her 90th birthday while working as an administrator for the IMA, and they have developed a friendship since then.* "I regard her as a 'natural' mathematician. It is what she was born to do," he wrote in an e-mail. As an example, he uses her research on magic squares. "When she looks at an incomplete square, she 'sees' the missing numbers without needing to compute them," he wrote. This ability transferred over to Sudoku puzzles when they became popular. Edwards wrote that Ollerenshaw doesn't consider herself particularly clever, but a very hard worker.

Ollerenshaw was a product of her time, not a deliberate breaker of barriers. But she sometimes ended up flouting conventional notions of her role in society. At age eight, she went deaf. Otosclerosis, an abnormal bone growth in the middle ear, ran in her family, and an infection precipitated her deafness. She learned to read lips and went to a small school that was able to give her the attention and accommodations she needed to cope with her impairment. She believes that her deafness made mathematics an appealing subject: understanding it relied much less on hearing than other subjects did, and she benefited from good teachers who encouraged her natural mathematical curiosity. But at that time people assumed that teaching was the only appropriate mathematical career for a woman and that a deaf person could never become a teacher. The school tried to keep her out of higher math classes at age 16, but Ollerenshaw threw a fit and convinced the administration to let her continue studying math.

After graduating, Ollerenshaw gained admittance and a scholarship to Oxford, in part because her interviewers did not know she was deaf—her lipreading skill was good enough to conceal her handicap. (She had had trouble reading lips at her interview with the University of Cambridge, however, and mentioned her difficulty to an interviewer. They were much less enthusiastic about having her.) She became engaged in 1931 during her first term to childhood friend Robert Ollerenshaw, a medical student, and "envisaged a life as Robert's wife, he a practicing surgeon, myself playing the role of the supporting wife and, hopefully, mother." She wrote that her domestic ambitions and interest in sports kept her from paying as much attention to her studies as she might have. "I spent too much time playing hockey and going with Robert to dances," she wrote.

Had it not been for the interruption of everyday life by World War II, she may have continued along her planned domestic path and never fully realized her mathematical potential. The couple married hastily in 1939, just after war broke out in Europe. As she explains, "I took it for granted that Robert would be posted abroad immediately—and be slaughtered in northern France as had happened to so many soldiers. I dreaded being left unmarried after so long betrothed."

Robert was not immediately deployed, and he survived many close calls during the war. The couple had a son, Charles, in 1941, and the next year, Robert was finally sent to the field. Ollerenshaw wrote the shock was so great that she had a miscarriage. "I cried nonstop for three days and then picked myself up and took the tramcar to the university to see how I could best use my mathematics (notwithstanding being deaf) to help the war effort." She returned to earn her PhD at Oxford while tutoring "emergency" mathematics courses.

After her husband returned from the war, Ollerenshaw taught math part-time at the University of Manchester while raising their two children. (A daughter, Florence, was born in 1946.) In 1954, a few years after her first hearing aid allowed her to participate more fully in conversations, she began her political career. "To serve on the Manchester education committee seemed an ideal way of giving the public service that I had been brought up to believe should be a main objective for those not obliged to earn their own living," she wrote. Her long political career took her to the city council and numerous national education committees, including stints in Margaret Thatcher's administration in the 1980s. In 1971 she was knighted for services to education, earning the title Dame. In 1975–76 she served one term as Lord Mayor of Manchester, the "first citizen" who represented Manchester on formal and ceremonial occasions.

Ollerenshaw and her husband Robert bought a cottage 160 kilometers from Manchester just before she got involved in politics. Hodge Close was her haven, an escape from committees and duties, and the location where she performed most of her mathematics. "Every path, every steep hillside and grassy slope, every familiar rutted road has its memories of moments of insight when the solution, or at least a way forward for some problem that had been holding things up, suddenly became clear," she wrote. Mathematics was also a comfort during tragic times. In 1972 Ollerenshaw's daughter died after an 18-month battle with cancer. Her husband passed away in 1986, their son in 1999. "When I have needed solace and I have had to depend on my own resources, the mathematics has been there. I am grateful." But, as Edwards wrote, "she doesn't 'do' mathematics to escape from life. She does it because it is her greatest joy."

Although Ollerenshaw did not have a typical research career by today's standards, mathematics has always permeated her life. It is the way she approaches the world. "Every true mathematician sees mathematics everywhere—in a child's swing or a pendulum, in the outline shape of a tree and that of its leaves, in the clouds," she wrote. Both asking the right questions and finding the answers always excited her. "When I found a good mathematical result, I jumped around in glee with Charles, then about four. If we then went out for a walk, he would stop people we knew with a proud announcement: 'Mother's got a sum right, mother's got a sum right,'" she wrote.

In 1990 Ollerenshaw plunged into her hobby of astronomy with typical fervor. She purchased a telescope and created an observatory at Hodge Close. She learned everything she could about astronomy and carefully arranged to observe eclipses and comets, either on trips or from her cottage. During the next few years she upgraded her telescopes several times, eventually donating one to Lancaster University. In 2002 the university named their rebuilt observatory after Ollerenshaw. Astronomy, like mathematics, gave her the joy of discovery and helped her cultivate many friendships.

Ollerenshaw's path in life would not have been possible without her having been born into a well-off family or without her husband's income, which provided amply for their family and meant that she did not have to work herself. One can't help but wonder how her career and life would have been different if she had been born 50 or 70 years later. Her deafness could have been treated earlier, and her mathematical abilities might have been nurtured much more actively at all levels of her education. She probably would have been encouraged to pursue a research career as a professor of pure or applied mathematics. But, Edwards wrote, "the main point about Dame Kathleen is that she did not have one career, she has had many." Today's typical research career may actually have been limiting for her. "I do not think that Dame Kathleen would have been suited to become an industrial mathematician or hold a university post. Had she been born much later, I think her life might have been channeled down a narrow route—like the rest of us."

Today Ollerenshaw is somewhat limited by her declining vision and hearing. But Edwards wrote that she is still remarkably active for someone her age, and her mind is as bright as ever. (She occasionally chides him for ignorance of an event in the news.) She leads the Remembrance Day parade in Manchester every year (observed on November 11, the U.K. holiday is similar to Veterans' Day or Memorial Day), attends the annual Dame Kathleen Ollerenshaw Lectures at the University of Manchester and even attended the Summer Olympics in London for a day. She is still working on several research projects that interest her, including the statistics of social change and another paper on magic squares. Edwards wrote that the projects may not be completed due to age-related challenges but, "certainly it won't be for a lack of mental abilities, because her mind is as sharp as anybody's I know." 

For her birthday, Edwards wrote that Dame Kathleen will be having a party for friends and neighbors in her garden.

*Correction (9/18/12): This sentence was edited after posting to correct the year Ollerenshaw met Terry Edwards.

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