Eleanor Pairman was an outstanding mathematician whose potential was never realised, largely due to the expectations of women in her times.
Eleanor (or Nora, as she was known by her family and friends) was born at 142 Polton Road, Lasswade on 8 June 1896, the fourth and youngest daughter of Helen Pairman and her husband John, a solicitor at the Supreme Court. Sadly, Eleanor was unlikely to have had any firm memories of her father as he died of pneumonia and peritonitis when she was three and a half years old, leaving Helen with four daughters of 11 and under to bring up on her own.
After attending Lasswade Higher Grade School, Eleanor followed her older sisters, Maxwell (Maxie), Margaret (Madge) and Adelina (Aline) to George Watson’s Ladies’ College when she was 12. She excelled at school, gaining a George Watson School Bursary which entitled her to free education for session 1912-13 and an allowance of £10. She sat the Scottish Leaving Certificate examinations, passing Lower Dynamics and Lower Science, with Higher passes in English, French, Latin, Mathematics, and Analytical Geometry. Eleanor also won the George Watson Higher Bursary of £80 and the Special Prize for Mathematics. She was the Dux of the School for 1914.
Like several of her peers, Eleanor moved on from GWLC to Edinburgh University where, having won a John Welsh Mathematical Bursary, she studied mathematics, natural philosophy, chemistry, and logic in her first year. By the end of that year she had become the first woman ever to top the mathematics class at Edinburgh. Two years later in 1917, she graduated with first class honours in mathematics and natural philosophy and, following a competitive examination, was awarded a three-year Vans Dunlop scholarship which could be used for study at any university. After another year at Edinburgh, during which she gave two papers at meetings of the Edinburgh Mathematical Society, Eleanor spent a year in the Department of Applied Statistics at University College London as a “computer”. At this time, computers were human beings, not machines.
The head of the department was Karl Pearson. He is a controversial figure in the mathematical and scientific history of the early twentieth century due to his eugenicist theories, but he is also widely regarded as the founder of modern statistics. Eleanor Pairman published a paper with him in the journal Biometrika in November 1919 and Pearson paid tribute to Eleanor’s skill as a mathematician by asking her to review and correct a previous article. He noted “As the problem is an exceedingly important one, the writer asked Miss Eleanor Pairman to revise his work. . . . This she has done with certain additions and expansions”. That same year, Eleanor also produced the first volume of tables in the Tracts for Computers series. There is no evidence that Eleanor’s association with Pearson implicated her in the development of his eugenicist thinking.
Radcliffe College was the women's college associated with Harvard University in Cambridge Massachusetts and it was here that Eleanor gained a place to study for her PhD. In 1918 her tutor at Edinburgh University, Cargill Knott had written a reference for her to the Dean at Radcliffe:
Throughout her career as an undergraduate Miss Pairman's exceptional mathematical abilities were in strong evidence. Although her natural inclinations were towards Pure Mathematics, she easily mastered the Principles and Methods of Applied Mathematics, and gained the Medal in both my Honours Classes in Dynamics and Hydrodynamics, and this among a group of students of marked ability. Miss Pairman also attended a short course I give on Hamiltonian Quaternions with Physical Applications, and there I was impressed with her capacity for appreciating the theoretical foundations of the calculus. Very rarely indeed have we had the good fortune of teaching a student with such a strong predilection for mathematical study as Miss Pairman undoubtedly possesses. With fitting opportunity she has every promise of a distinguished and useful career.
Despite a delay in securing permission to travel to the United States, by October 1919 Eleanor had arrived at Radcliffe. Her thesis Expansion Theorems for Solution of a Fredholm's Linear Homogeneous Integral Equation of the Second Kind with Kernel of Special Non-Symmetric Type was submitted in time for her to be awarded her Ph.D. in June 1922. She was the third of only nine women to receive a doctorate in mathematics from Radcliffe before 1940.
Eleanor returned to Scotland briefly and married an American, Bancroft Huntington Brown, in a ceremony at her family home, Roselea in Bonnyrigg on 10 August 1922. Bancroft had been studying at Harvard and had also been awarded a Ph.D.in mathematics that year. On their marriage certificate they are both described as ‘University Lecturers’. However, on their return to the States, it was Bancroft who joined the faculty of Dartmouth College, an Ivy League College in Hanover, New Hampshire. In those days it was for men only and had an all-male teaching staff and so there was no possibility that Eleanor might join him in teaching there.
And Eleanor was already pregnant. The Browns’ ‘honeymoon baby’, John, was born on 16 May 1923 and would always be known as ‘Jock’, perhaps in a nod to his mother’s Scottish origins. A daughter, Barbara, was born two years later. However, in what must have been a break from toddler-wrangling and the domestic duties of a wife of a busy academic, Eleanor published a mathematics paper On a class of integral equations with discontinuous kernels with a friend, Rudolph E Langer in 1927.
Eleanor had two more daughters, Joanna born in 1935 who died as a baby, and Margaret who was born in 1937. Bancroft would stay at Dartmouth his entire career and family life took on a predictable rhythm. His parents would come and stay in Hanover for four months every year. Holidays were spent at the in-laws’ small cottage at Martha’s Vineyard, which, as neither Bancroft or Eleanor could drive, must have been quite an expedition to reach. Eleanor took her two eldest children, Jock and Barbara, to visit her family back in Bonnyrigg in the summers of 1929 and 1934. She and Barbara also visited Bermuda in 1936. In the springtime of several years, Eleanor would take the train to Boston to see a flower show and stay overnight before returning to Hanover.
It seems that Eleanor began to learn Braille in about the late 1940s or early 1950s. After learning standard Braille, she then learned the Nemeth Code for mathematical notation and began ‘transcribing’ mathematical texts so that blind students could use them. Here, as her daughter Margaret remembers, her ingenuity came to the fore.
Geometry was a particular problem, because you really need diagrams. ... So she rounded up all kinds of household implements like pinking shears and pastry wheels and such and created diagrams that could be felt with the fingers, like the Braille symbols. Apparently nobody had ever done this before.
A graduate student at Harvard was blind and needed a particular book put into Braille, and it was full of mathematical symbols. What to do? The sewing machine, of course. She had written down the math and had it beside the machine. She put a piece of Braille paper under the foot and proceeded to reproduce the symbols by guiding the paper under the needle. It had to be the mirror image of what she had written.
But, as Margaret also observed,
For all the satisfaction that she got from these [Braille] projects, the only time I saw her truly happy was when she was teaching. And she had precious little opportunity to do that, being obviously ahead of her time and also stuck in a males-only college community and in a world where it was well-nigh impossible for married ladies to function professionally.
By the mid 1950s, a few women were employed amongst the teaching staff at Dartmouth College and once Eleanor’s youngest daughter had left for university, she became a part-time Instructor in Mathematics there for four years.
Of the Pairman sisters, only Eleanor married and had children. Maxie, Madge and Aline remained unmarried, part of the generation whose potential husbands had been killed during the First World War. Eleanor, the youngest of the girls, would move to another continent, marry and have a family. But despite her prodigious mathematical capabilities and her determination to give blind people access to mathematical texts, society’s expectations still limited her opportunities. In that, Eleanor Pairman’s story reflects the experience of many of her female contemporaries.
Eleanor Brown (nee Pairman) died of breast cancer in Vermont in 1973, aged 77.