**Eleanor Pairman**was born in Lasswade, which is about six miles south-east of the centre of the city of Edinburgh. Broomieknowe is an area of Lasswade. Her parents were John Pairman, a solicitor at the Supreme Courts of Scotland, and Helen Dunlop. Eleanor, called Nora by her family, was the youngest of her parents' four children, having three older sisters, Maxwell, Margaret and Adeline. John Pairman died before Eleanor was five years old. She began her schooling at Lasswade Higher Grade School in 1903, remaining there for five years. Then in 1908 she entered George Watson's Ladies' College in Edinburgh. Her performance at the school was outstanding and, in 1912, she won a George Watson School Bursary entitling her to free education for session 1912-13 and an allowance of £10.

Pairman sat the Scottish Leaving Certificate examinations passing Lower Dynamics and Lower Science, with Higher passes in English, French, Latin, Mathematics, and Analytical Geometry. In July 1914 she became dux of George Watson's Ladies College. She also won the George Watson Higher Bursary of £80 and the Special Prize for Mathematics. She matriculated at the University of Edinburgh, beginning her studies in session 1914-15 after winning a John Welsh Mathematical Bursary.

In her first year at Edinburgh University she studied Mathematics, Natural Philosophy, Chemistry, and Logic. The First Year Chemistry Course was taught by James Walker, and Pairman did well, but not brilliantly, being ranked Second Class. Similarly in the Laboratory Chemistry course taught by Leonard Dobbin she was ranked Second Class. However, her performance in mathematics was outstanding. In July 1915 she was awarded the Newton Bursary in Mathematics (placed equal with Samuel Allen). In the Second Ordinary Class in mathematics, taught by Lester R Ford, she was placed second to Samuel Allen and was awarded a class medal. She continued her studies taking honours in Mathematics and Natural Philosophy and was awarded an M.A. with First Class Honours in July 1917. She was also awarded a Vans Dunlop Scholarship in Mathematics which was a three year scholarship to study at the university of her choice. Supported by the scholarship, Pairman spent the academic year 1917-18 undertaking graduate studies at the University of Edinburgh. She hoped to continue graduate studies at Radcliffe College, a women's college associated with Harvard University, in Massachusetts and Cargill Knott wrote to the dean at Radcliffe:-

Leaving Edinburgh, Pairman went to London where she worked for a year for Karl Pearson in the Department of Applied Statistics at University College London as a computer (at this time computers were people and not machines!). It was a highly productive year for not only did she produce a substantial joint publication with Karl PearsonThroughout 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.

*On corrections for the moment-coefficients of limited range frequency distributions when there are finite or infinite ordinates and any slopes at the terminals of the range*which appeared in

*Biometrika*(November 1919), but she also wrote

*Tracts for Computers*which was published by

*Cambridge University Press*(1 January 1920).

From London, Pairman went to the United States to undertake research at Radcliffe College arriving in New York on 12 October 1919. Her thesis advisor was George Birkhoff and after submitting 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* she was awarded a Ph.D. in 1922.

Pairman joined the Edinburgh Mathematical Society in January 1917, and read the paper *On a difference equation due to Stirling* to the meeting of the Society on 11 January 1918, and the paper *A new form of the remainder in Newton's interpolation formula* to the next meeting of the Society on 8 February. After about five years she informed the Society that her name was now Mrs Eleanor Pairman Brown. She remained a member for around 16 years. In fact Pairman had met Bancroft Huntington Brown when both were graduate students and they had both been awarded a Ph.D. in mathematics in June 1922. The two then went to Scotland where they were married in Broomieknowe on 10 August 1922. They returned to the United States, moving to Hanover, New Hampshire where Bancroft Brown had a position at Dartmouth College. The College was founded in 1769 as a men's College with an all male teaching staff and when Bancroft Brown was appointed this was still the case so there was no possibility that Eleanor could teach at the College. He remained at the College throughout his whole career.

Eleanor and Bancroft Brown had four children, a son John Pairman born in 1923, a daughter Barbara in 1925, a second daughter Joanna in 1935 who died as an infant, and a third daughter Margaret Wylde in 1937. In 1927 she published a joint mathematics paper *On a class of integral equations with discontinuous kernels* with Rudolph E Langer, who was a friend who graduated from Harvard in a June 1922 ceremony as Eleanor Pairman and Bancroft Brown and, like Eleanor, had George Birkhoff as his thesis advisor. Langer taught at Dartmouth College during 1922-25. However, Eleanor Brown later undertook task to help students who were blind. The authors of [3] write:-

Her daughter Margaret explained:-Eleanor Brown began to learn Braille in about1950and later learned the Nemeth Code for mathematical notation. She made transcriptions using household items and her sewing machine to create geometric diagrams and mathematical symbols. Examples of her work included a freshman mathematics text and a reference book on group theory.

Eleanor Brown's son-in-law Thomas Streeter wrote:-Geometry was a particular problem, because you really need diagrams. Braille is done on paper like thin cardstock. 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.

Although she had not been employed as a mathematician after being awarded her doctorate, Eleanor Brown did take up an appointment as a part-time Instructor in Mathematics at Dartmouth College in September 1955 and taught there for the next four academic years. At this time her husband was B P Cheney professor at Dartmouth. John Kemeny, who was appointed to the Mathematics Department at Dartmouth in 1953, became chairman of the Department at the same time that Eleanor Brown began her teaching post at the College. Her daughter Margaret wrote:-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.

She died after a long battle with breast cancer in a nursing home in White River Junction; her husband died one year later.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.

Finally let us comment on the careers of Eleanor Brown's three children. Her son John Pairman Brown studied mathematics and classics at Dartmouth College and then went to Union Theological Seminary in New York City where he obtained a doctorate. Eleanor Brown's eldest daughter Barbara was awarded a doctorate in languages and literature from Rutgers University and became a university lecturer of English. Eleanor Brown's youngest daughter Margaret graduated from Brown University and became a medical editor.

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

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