This biography, written by J J O’Connor and E F Robertson, has been republished with permission from the School of Mathematics and Statistics at the University of St Andrews, Scotland.
Born: 13 August 1866, United States
Died: 14 April 1948
Country most active: United States
Also known as: NA
Clara Bacon was the daughter of Larkin Crouch Bacon (1818-1877) and Louisa Latimer (1831-1914). Larkin Bacon had been born 2 March 1818 in Jonesborough, Tennessee. He became a farmer and married Honor Durbin (1825-1864) on 26 December 1941 in Handcock, Illinois. They had four children: Mary Ann Bacon (1843-1936), George W Bacon (1848-1867), Joseph Barnes Bacon (1854-1936) and Fannie Bacon (1864-1864). Honor died as a result of childbirth, the child Fannie dying two days after her mother. Larkin Bacon married his second wife Louisa Latimer on 20 October 1864 in McDonough, Illinois. For Louisa it was also her second marriage. She had married Joseph Meek on 13 November 1849 in Knox, Illinois and they had several children before Joseph died on 23 October 1863. Larkin and Louisa Bacon had four children, Clara Latimer Bacon (1866-1948), the subject of this biography, Nancy Bacon (1867-1880), Willie Larkin Bacon (1871-1880) and Agnes Latimer Bacon (1874-1930). Although Clara was the oldest of her parents four children, she had quite a number of half-siblings. For example, at the 1870 US census, Clara is three years old and five older half-siblings are living at the same home, namely Eugene, Joseph B, James H, Harvey M and Louie.
The Bacon family lived in Hills Grove, a small town where early settlers lived. It was near the Hancock County border in Tennessee Township, but the town eventually vanished. At the time Clara was growing up it had a primary school, which she attended. On 24 October 1877 Larkin Bacon died in Hills Grove and soon after that Clara’s mother Louisa moved to Abingdon, Knox County, Illinois. Certainly by the time of the 1880 US census, Louisa and the four children from her marriage with Larkin, were living in Abingdon. This town, like Hills Grove, was a town set up by early settlers but unlike Hills Grove, Abingdon has survived. Clara began her secondary education at North Abingdon High School. This school was a brick building which had been built in 1868. After graduating from this school, she studied at Hedding College in Abingdon. This college had begun life as Hedding Collegiate Seminary, founded in 1855 and named after the Methodist Bishop, Elizah Hedding. In 1857 it had became known as the Hedding Seminary and Central Illinois Female College, then changed its name to Hedding College in 1875. Clara was awarded the degree of PhB (Bachelor of Philosophy), an undergraduate bachelor’s degree.
After the award of her PhB degree, Bacon taught for the school year 1886-87 at a private school in Dover, Kansas. In the autumn of 1887 she entered Wellesley College, a private women’s college in Wellesley, Massachusetts, and studied for a second bachelor’s degree and she was awarded a B.A. in 1890. One of her mathematics lecturers at Wellesley College was Ellen Hayes who had been appointed in 1879, only four years after the College opened. It was remarkable for a women’s college in the United States since it was the first to have scientific laboratories. Bacon was particularly influenced by Ellen Hayes who became a professor and Head of the Mathematics Department in 1888 while Bacon was studying there. Later in her Ph.D. thesis, Bacon gave special thanks to Ellen Hayes for her help while she was at Wellesley College.
After graduating from Wellesley College, Bacon was appointed as a teacher in a private school in Litchfield, Kentucky. This was the first of four different schools she taught in over the next seven years. After one year, 1890-91, at the school in Litchfield, she was appointed to teach at Hedding College in Abingdon, where she herself had studied. For the two years 1891-93 she taught mathematics and German at the College and, in addition, served as librarian. Remaining in Abingdon, she spent the next two years, 1893-95, as the principal of North Abingdon High School, again being at a school where she had been a pupil. Her final school for this seven year period was at the Grand Prairie Seminary, a secondary school in Onarga, Illinois. Onarga was a small town which, like Hills Grove and Abingdon, had been settled in the first half of the 19th century. Although a small town there were two schools, a public school and the private co-educational Grand Prairie Seminary which was a boarding school that had been established in 1864. The pupils had to have well off parents to be able to afford the fees but the education it offered was outstanding.
In 1897 Bacon was appointed as an instructor at the Woman’s College of Baltimore which was renamed Goucher College in 1910. Up to this time she had never spent more than two years in one job, but things now changed and she spent the rest of her career at this College, working there until she retired in 1934. When she was appointed, there was only one other mathematician at the College, her head of department William Henry Maltbie. He had been born in Toledo, Ohio in 1867, served as Professor of Mathematics at Hedding College in 1890-91, then studied for his Ph.D. at Johns Hopkins, being awarded the degree in 1895. He had been appointed as an instructor at the Woman’s College of Baltimore in 1895, being promoted to associate professor later in the same year. Agnes Latimer Bacon, Clara’s sister, had studied for an A.B. in physics at Wellesley College, and she moved to Baltimore City where Clara, her mother and her sister Agnes set up home together. At the time of the 1900 US census, the three of them are living at 2316 Calvert Street in Baltimore City with both Clara and Agnes giving their occupation as “teacher’. They also have a coloured servant, Ida Lindsay, who was working as their cook.
Clara Bacon now began to study for more advanced degrees and, while continuing to work full time at the Woman’s College, she studied each summer from 1901 to 1904 at the University of Chicago for a Master’s Degree. She took the following courses: Solid Analytics and Determinants (taught by James Harrington Boyd); Differential Equations (taught by Herbert Ellsworth Slaught); Definite Integrals (taught by Arthur Constant Lunn); Analytic Mechanics (taught by Arthur Constant Lunn); Pure Projective Geometry (taught by Leonard Eugene Dickson); Modern Analytic Geometry (taught by Leonard Eugene Dickson); Higher Plane Curves (taught by Heinrich Maschke); Theory of Functions of a Complex Variable (taught by Leonard Eugene Dickson); and Theory of Invariants (taught by Oskar Bolza). Her dissertation, which she submitted in in 1903, was The determination and investigation of the real chords of two conics which intersect fewer than four real points and she was awarded an A.M. in September 1904.
After she retired, Bacon wrote to Oskar Bolza on 23 April 1936. John W Boyer writes:-
The quality of teaching on the graduate and undergraduate levels seems to have been generally high, and many former students looked back on their association with senior faculty with pleasure and nostalgia. Writing to Oskar Bolza, one of the founders of the Department of Mathematics, a former MA student, Clara Latimer Bacon, recalled, “Your zest for the subject and your careful preparation for each class and the clearness and elegance of your lectures as well as your personal interest in your students have been an inspiration to me as a teacher ever since. Among the pleasantest memories of my life at the University of Chicago are the Sunday evenings in your home where you and Mrs Bolza made your students so welcome.”
The award of her Master’s Degree did not stop Bacon’s summer visits to the Mathematics Department in Chicago, for she was there in 1907 and 1908. In fact she had applied to Johns Hopkins in September 1907 for graduate studies there. This was prompted by the decision by the trustees of Johns Hopkins who had decided to allow women to be admitted to graduate study. In fact Christine Ladd-Franklin had been admitted in 1878 as a “special student,” on the condition that her name would not appear in the catalogue and her case would not set any precedents. Margaret Rossiter writes:-
It was not until 1907, thirty-one years after the university had opened, that … Johns Hopkins President … Ira Remsen could finally admit the women officially. Remsen defended the new policy … as “a simple act of justice” that merely recognised what was fast becoming standard university practice. He also softened the blow for coeducation’s diehard opponents by reserving the right to refuse women students if they wished. Women were admitted to all classes provided there was “no objection on the part of the instructor concerned.”
One of the courses Bacon took in 1908-09 was on symbolic logic, taught by Christine Ladd-Franklin. Bacon was a Johns Hopkins’ fellow in 1909-11, and in 1910-11 she held a fellowship from the Baltimore Association for the Promotion of the University Education of Women. This Association had been founded in 1897, partly through the efforts of Ladd-Franklin, and had worked to persuade Johns Hopkins to open its graduate school to women:-
During this period Bacon’s sister Agnes was a physics student at Johns Hopkins, and in 1914 she was a mathematics student at the University of Chicago. Agnes Bacon worked at the Johns Hopkins School of Hygiene and Public Health and published several articles in the field of biometrics during the early 1920s.
Bacon was awarded a Ph.D. in 1911 for her thesis The Cartesian oval and the elliptic functions ℘ and σ. The main results appeared in a paper with the same title in the American Journal of Mathematics. It has the following Introduction (we have removed the page numbers in the given references):-
The object of this paper is to show that the leading properties of the Cartesian oval, as developed in such texts at Williamson’s “Differential Calculus,” Salmon’s “Higher Plane Curves” or Loria’s “Spezielle Algebraische und Transcendente Ebene Kurven (Special Algebraic and Transcendental Plane Curves),” may be readily deduced from the Weierstrass elliptic functions ℘ and σ, and that they give a geometric interpretation to the standard formulae of these functions.
Greenhill has used these functions in connection with the Cartesian oval (Proc. London Math. Soc., 1886, and also his treatise on “Elliptic Functions,”) and has deduced the relations between the focal radii, though we have give a more symmetric form to these relations by the introduction of the triple focus.
Professor Frank Morley published a note on the subject some years ago in the Haverford Studies. (See also Harkness and Morley, “Treatise on the Theory of Functions.”)
When the u-plane is mapped to the x-plane by means of the equation du=dx√Qdu = largefrac{dx}{√Q}normalsizedu=√Qdx, where Q is a quartic in x, to lines in the u-plane parallel to the real or imaginary axis, correspond in the x-plane bicircular quartics whose real foci are the zeros of Q, provided these zeros are concylic or anticyclic. (Greenhill, Camb. Phil. Proc.; Fabian Franklin, American Journal of Mathematics, Vol XI and Vol XII.)
The problem of reducing this form to the Weierstrass form which we use, where one focus is at infinity, is analogous to the reduction of the bicircular quartic to the Cartesian. (Salmon, “Higher Plane Curves.”)
On being awarded her Ph.D. in 1911, Clara Bacon became the first woman to be awarded a doctorate in mathematics from Johns Hopkins University. Christine Ladd-Franklin had completed her doctoral thesis at Johns Hopkins and published it in 1883 but although she had published several papers in the American Journal of Mathematics while she undertook research, she was not awarded a Ph.D. because she was a woman, and only in 1926 did Johns Hopkins award her the degree.
Bacon was promoted to professor at Goucher College in 1914 and continued to teach there until she retired in 1934. She was very highly regarded as a teacher and for her concern for her students, whether they were highly talented or were less able. For example, a student wrote:-
Miss Clara Bacon was one of the best teachers I ever had in the clearness with which she presented mathematics, her understanding of the student’s point of view, and her patience. I do not know adequate superlative adjectives to express the wonderful spirit she embodied.
Another student wrote:-
She believed in us so simply and so deeply that we could not disappoint her. When she felt that circumstances prevented us from doing all she hoped, she tried to change the circumstances. It was her support that made graduate study possible for me. Her patience and understanding as a teacher opened up the beauty of mathematics. For many years her faith in all of us made life seem so good.
One of Bacon’s favourite ways to relax was to travel with her sister Agnes with whom she lived until Agnes’s death in 1929. For example in the summer of 1926 they were in Bermuda, returning from Hamilton, Bermuda to New York on the SS Fort St George in September of that year. After Clara retired in 1934 she set out on a fifteen month trip in June 1934, travelling first to England then going to Scotland, Italy, Egypt, and Palestine before returning to Baltimore in October 1935 sailing from Hamburg, Germany, to Baltimore on the SS City of Norfolk.
This was not her last travelling abroad, for in the summer of 1936 she was in Mexico, returning in July from Vera Cruz to New York on the SS Yucatan.
Bacon continued to live at 2316 Calvert Street with her servant Ida Lindsay, who was far more than a servant, being also a companion and friend. She continued to live there after she become ill in 1947, and died in her home in April 1948. Her funeral service was held in the First Methodist Church, which was near her house on Calvert Street, and she was buried in Cherry Grove Cemetery near Abingdon, Illinois. In 1958 Goucher College renamed North House, “Bacon House” in her honour. There is also a Clara and Agnes Bacon endowed scholarship at Goucher.