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  • Writer's pictureDale DeBakcsy

The Englishwoman in America: Charlotte Angas Scott and the Development of American Mathematics

In 1885, when you heard the term ‘mathematical epicentre’ one of the last places that would have been brought to mind was the United States. Sure, it had a handful of locally distinguished minds to its credit by that point – figures on the order of Thomas Godfrey (1704–1749), Nathaniel Bowditch (1773–1838), Theodore Strong (1790–1869), Benjamin Peirce (1809–1880), George William Hill (1838–1914) and Henry Fine (1858–1928), but a half dozen notables strung out over the course of a century hardly a robust intellectual tradition makes, and by the late nineteenth century, the situation was getting frankly embarrassing. Fortunately, that is when there came to the US an Englishwoman who brought with her not only connections to the wider world of European mathematics but a zest for teaching, gift for original research, and know-how for building up national scientific institutions that soon turned America from a mathematical backwater to a bustling community.


That woman, Charlotte Angas Scott (1858–1931) was, like the astronomer Maria Mitchell a generation before her and an ocean away, the beneficiary of her family’s particular religious beliefs. Just as Mitchell’s upbringing among Quakers brought her opportunities to educate herself and pursue a career in science not generally available to most young American women of her era, so was Scott’s family’s non-conformist Congregationalism the gateway for young Charlotte to whatever academic pursuits she found herself wishing to pursue. Her father, Reverend Caleb Scott, was a Congregationalist minister who was known for urging his parishioners to let their daughters ‘not be all repressed and stifled in the iron mould of any conventionalism’.


Upon becoming the principal of Lancashire Independent College in 1865, Caleb had access to a bristling array of bright young minds whom he hired to provide Charlotte with tutoring in whatever fields excited her interest. On the strength of her mind and her private lessons, she won a Goldsmiths’ Company scholarship in 1876 to attend Girton College, which had been established in 1869 under the name College for Women, at Benslow House (more popularly known as Hitchin College), but upon the college’s move from Hitchin to Girton in 1872 to be nearer Cambridge, the institution changed its name. (Some sources say that Scott matriculated at Hitchin College, but by that point the name change had been in place for at least three years.)


Scott was one of eleven students entering that year, a positive explosion in attendance from the 1869 entering class of five individuals. At the time, Girton students were allowed to take classes at neighbouring Cambridge if granted permission by the class’s professor, permission generally denied by about a third of the college’s faculty, and often only extended under the proviso that the woman attendees would secrete themselves behind a screen so as not to be a distraction to the male students’ delicate sensibilities. Girton students could also apply for permission to take the famous Tripos exam, though they could not be ranked among the male Tripos participants, nor receive a degree from Cambridge for their performance. Women before Scott had taken the Tripos, but Scott was the first to receive a score on the fifty-hour, nine-day examination that placed her among the top ten male performers. Her score entitled her to the title of Eighth Wrangler, but university rules prohibited her both from receiving that title, and from even attending the ceremony where the placements were announced and the titles awarded.


But then, something magical and rare happened. For those whose ideas about the maturity of British college men in the nineteenth century is based upon the stories of their appalling, self-serving, and brutish behaviour towards the Edinburgh Seven from 1869 to 1873 (for more on which, see Volume 1 of this series), the outcome of the 1880 Tripos ceremony will doubtless come as a profound surprise. As the Tripos placements were being read, everything proceeded as was traditional until the Eighth Wrangler position was called out, and the halls resounded with undergraduates yelling out ‘Scott of Girton’, drowning out the name of the man who had scored beneath her but was nonetheless receiving her title. Back at Girton, meanwhile, a special ceremony was arranged for Scott’s accomplishment, wherein she was led between lines of Girton students, while they sang ‘See the Conquering Hero Comes’, and then seated on a dais, where they crowned her head with laurels and recited odes composed in honour of her victory.


Scott’s feat made the English papers, and spurred the creation of a petition to let women sit the Tripos exam regularly, without the need to apply for special permission, a right which was granted in 1881. Though she had triumphed, Scott did not receive a degree for her work (Cambridge would not start awarding degrees to women until 1948), but thanks to the efforts of Sophia Jex-Blake, the leader of the afore-mentioned Edinburgh Seven, in 1876 England passed a law allowing (but not compelling) universities to award women degrees. Scott took advantage of the new law to receive her bachelor’s degree with first-class honours from the University of London in 1882, and her PhD in 1885.


Meanwhile, Girton’s hero student returned to her alma-mater as a lecturer in mathematics, serving in that capacity from 1880 to 1884, when she received an invitation from M. Carey Thomas to join the faculty of Bryn Mawr as an associate professor, one of the university’s eight starting faculties, and one of only two women. There was a special sense of continuity for Scott at Bryn Mawr, as it was a college established by Quakers, who had a similar devotion to women’s education to that of the Congregationalists of Scott’s youth. With the founding of Bryn Mawr in 1885, they created the first American university offering graduate education for women, and Scott was happy to switch from the Girton-Cambridge atmosphere of intensive examination paranoia to the less student-mauling approach of America.


While at Bryn Mawr, she developed a reputation as an advocate for students who were applying themselves but faced various adversities, including an incident where she went to the absolute mats for a student who had done a great deal of fine work, but who the university was contemplating refusing to award a degree to after she caught tuberculosis. While in America, Scott picked up golf and added it to her love of lawn tennis, activities which, while not strictly proper to conservative circles, she nonetheless thoroughly enjoyed, even as most other aspects of life in America left her feeling somewhat isolated and depressed, causing her to return to England at every opportunity to reconnect with colleagues and with her cultural roots.


Beginning in 1892, Scott published a series of papers on algebraic geometry that continued at the rate of one or two a year for the next decade and a half and which cemented her international reputation as a mathematician of note. She focused her work on plane curves of degree greater than two (i.e. equations in x and y featuring highest powers of three and greater), and in particular kept returning to the subject of singularities, which are technically defined as locations where curves behave, like, super badly. These include cusps, points where graphs cross over each other, and isolated points that sit glumly by themselves away from the rest of the graph. Scott’s work focused on characterising higher singularities, and in investigating the intersections of plane curves, through her own brilliant and individual sense of geometric objects and how to corral them within different structures that compel them to reveal their internal relationships.


In 1894, she published the textbook An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry, in which, employing her clear writing style and gift for creating new ways to consider spaces and the objects inside of them, she was able to communicate some of her time’s newest ideas about projective geometry, invariance and absolute conics in a manner that required virtually no revisions upon the text’s re-publication three decades later. This was also the era when she was employing her experience as a member of some of Europe’s most important mathematical associations to improve the cohesion of American mathematical life, joining the New York Mathematical Society (founded 1888) in 1891 and acting as one of the guiding forces behind its expansion into the American Mathematical Society in 1894, serving on its council for most of the 1890s, and acting as vice president in 1905–06.


When she first arrived at Bryn Mawr, it was on the understanding that, as the years went on, her teaching and grading load would be reduced so that she would have more time for research and administrative work. This did not ultimately happen, and Scott’s frustration with the amount of time taken up by grading led her to explore the possibility of national standards for mathematical testing, taking up the role of Chief Examiner in Mathematics for the College Entrance Examination Board in 1902 and 1903. (Today the CEEB is known simply as The College Board, an institution equalled perhaps only by Pearson as a caustic, generally reviled dead weight at the centre of American educational practices, but in Scott’s era it was seen as an organisation that was helping to increase access to higher education for high school students.)


Scott was also central to improving the general mathematical expectations of the US college system. At a time when Harvard was not even particularly concerned whether its students entirely knew how to multiply, Scott was establishing at Bryn Mawr standards for general mathematical literacy to be met by all students, as well as expected competencies for mathematicsmajors, that are now commonplace in university curricula.


In 1906, Scott’s publication career came to an abrupt end when she was diagnosed with rheumatoid arthritis, and advised by her doctors to spend more time engaging in outdoor exercise and gardening, and less time hunched over mathematical proofs. This, along with the serious advancement of a deafness that had begun during her Girton days, made teaching increasingly difficult for Scott, who by her retirement in 1924 was effectively entirely deaf. She returned to England in 1926, where she spent time happily among her relatives, and even returned to research with a paper on higher singularities that ranks among the most influential of any she wrote during her career.


Charlotte Scott died on 10 November 1931 in Cambridge, and was buried in grave 4C52 beneath a headstone that does not mention her career as an internationally respected mathematician. That is unfortunate, but in truth she did not need a graveyard inscription to ensure the continuation of her memory, for her legacy lay elsewhere, in a Bryn Mawr mathematics department that grew on her watch to be a trailblazer in more rigorous undergraduate curricula, in her crystal-clear exposition of the lives and secrets of plane curves, and in the living testament to her example carried on by her seven PhD students, including the likes of future luminaries Ruth Gentry, Ada Maddison, and Marguerite Lehr. She helped bring a nation into the global mathematical community, and the memory and gratitude for that will last long past any mere etching in stone.


FURTHER READING: Charlotte Scott is a figure you must find in pieces, here and there. For the content of her mathematical work, the best source by far is F.S. Macaulay’s 1932 obituary piece in the Journal of the London Mathematical Society, an appreciation which that august institution will let you look at for forty-eight hours online if you pay them $12, and will let you actually print out for yourself if you pay them $49.


Forty … nine … dollars. For an obituary … from 1932.


Absolutely scandalous, but if you’re a big Scott fan, and pretty familiar with algebraic geometry, it is definitely worth a look. Her 1894 book, An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry is available in a nice amply-sized reprint from the Leopold Classic Library, and it is a pretty fun trip which keeps challenging you to think of familiar objects in new ways. For her life and professional impact, both MC Bradbook’s 1969 That Infidel Place: A Short History of Girton College, and the ever-indispensable Women of Mathematics edited by Grinstein and Campbell are useful, while you can glimpse more of Scott and the system she put in place in books about Bryn Mawr, and particularly about its influential and controversial second president, M. Carey Thomas, including Edith Finch’s Carey Thomas of Bryn Mawr (1947) and Helen Horowitz’s The Power and Passion of M. Carey Thomas (1999).


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