# Mildred Leonora Sanderson

### Quick Info

Born
12 May 1889
Waltham, Massachusetts, USA
Died
15 October 1914
East Bridgewater, Massachusetts, USA

Summary
Mildred Sanderson was L E Dickson's first female Ph.D. student and was described by him as "my most gifted pupil." Tragically, she died in the year following the award of her doctorate.

### Biography

Mildred Sanderson was the daughter of Horace M Sanderson (1856-1937) and Edna E Pratt (1862-1933)). Horace Sanderson, the son of the farmer Nathan Sanderson and his wife Adeline Wellington, was born in Waltham, Middlesex, Massachusetts. Many generations of the Sanderson family had lived and farmed in Waltham for over 200 years. Horace followed the tradition and became a farmer. He married Edna Pratt on 16 May 1883 in Waltham. Edna Pratt had been born in Hadley, Hampshire, Massachusetts to the farmer Edwin E Pratt and his wife Harriet Augusta Hemenway. Horace and Edna Sanderson had five children: May Evelyn Sanderson (1884-1941); Alice Gertrude Sanderson (1886-1956), known as Gertrude; Mildred Leonora Sanderson (1889-1914), the subject of this biography; Amelia Hemenway Sanderson (1894-1897); and Ralph Hemenway Sanderson (1898-1979).

At the time of the 1900 US census, Horace Sanderson's occupation is given as florist and market gardener, the three oldest children are at school, while the youngest Ralph is only one year old. There are only four children since Amelia died in 1897 aged two. Living with them are two servants, Thomas Garrity, a farm labourer who emigrated from Ireland to the USA, and Celia Daly, employed by the family to do general housework, who also emigrated from Ireland to the USA. At the time of the 1910 US census, Horace Sanderson's occupation is given as market gardener and florist. All four children are still living at home, May and Gertrude are both teachers in a public school while Mildred's occupation is recorded as 'none'. Also living with them is Horace's brother Edmund L Sanderson, a proprietor and Waltham machine worker, and Horace's sister Ella O Sanderson. In the same house are two hired farm hands, both of whom had emigrated from Italy to the USA.

Mildred Sanderson attended the North Grammar School and Waltham High School, two public schools in Waltham which were closely linked. Waltham High School had been founded in 1832 with the construction of a building on the corner of Lexington Street and School Street. Until 1849, when the town administrative officials moved from this building to the City Hall, this building was shared by the administrators, the Grammar School, and the High School. Waltham High School became a separate school in 1869 with the joint construction of North Grammar School and a new High School building at the corner of Church Street and School Street. Sanderson graduated from the North Grammar School in 1902 before being a highly successful pupil at Waltham High School from which she graduated in 1906 as valedictorian. One of her teachers at Waltham High School wrote (see [7]):-
Miss Sanderson was gentle-mannered, of brilliant intellect, an exact student, broad-minded, self-reliant, and courageous.
Entering Mount Holyoke College in 1906, she received "Sophomore Honors" in June 1908, for general scholarship, and graduated with a Bachelor of Arts degree with "Senior Honors" in mathematics in 1910. Let us say a little about this famous College. Founded in 1837 in South Hadley, Massachusetts, as Mount Holyoke Female Seminary by the chemist Mary Lyon, it was the first of the Seven Sisters women's colleges. Originally having a three year course, this was extended to four years in 1861. Its seminary curriculum was phased out in 1893 and it changed its name to Mount Holyoke College at this time. It had an excellent reputation for teaching academic subjects and provided Sanderson with a high quality education.

Sanderson was awarded a Bardwell Memorial Fellowship for 1910 and 1911. This Fellowship was awarded by the Alumnae Association of Mount Holyoke College to outstanding students. The recipient was not restricted in the subject of study, nor in the place of study, and Sanderson chose to take graduate studies in mathematics at the University of Chicago. The University had an outstanding collection of professors of mathematics at this time including Eliakim Hastings Moore, Leonard Eugene Dickson, Herbert Ellsworth Slaught and Gilbert Ames Bliss.

At the University of Chicago, Sanderson was advised by L E Dickson and began studying for her Master's Degree. She was awarded the A.M. degree in 1911 having written the dissertation Generalizations in the Theory of Numbers and Theory of Linear Groups. Not many people have written a Master's dissertation in one year which is of such a standard that it leads to a publication in the Annals of Mathematics, but this is exactly what Sanderson achieved. L E Dickson writes [7]:-
Of this original and valuable thesis a very brief extract was printed in the 'Annals of Mathematics', Series 2, Volume 13, 1911, pages 36-39. This work might well have served for her doctor's thesis; but she was quite willing to undertake a new investigation in a wholly different field.
The four page paper has the following Introduction:-
The term function is here used to denote a rational integral function of y with integral coefficients. Employing a fixed integer m and a fixed function P(y), we shall say that two functions are congruent modulis m and P(y) if their difference can be given the form mq(y) + P(y)Q(y); also that f(y) has an inverse $f_{1}(y)$ if $f(y).f_{1}(y)$ is congruent to unity modulo m, P(y). Then f(y) and f(y) + k(y)P(y) have the same inverse, so that we may restrict attention to functions of degree less than the degree r of P(y). We proceed to prove the
Theorem.
If P(y) is of degree r and is irreducible with respect to each prime factor of m, a function R(y) of degree < r has an inverse modulis m and P(y) if and only if the greatest common divisor d of the coefficients of R(y) is prime to m.
In 1913 she was awarded a Ph.D. having submitted the thesis Formal Modular Invariants with Applications to Binary Modular Covariants. The main results of the thesis were published in the paper [10] published in the Transactions of the American Mathematical Society. L E Dickson writes that her thesis [7]:-
... was entitled "Formal Modular Invariants with Applications to Binary Modular Covariants," and appeared in the 'Transactions' of the American Mathematical Society, Volume 14, 1913, pages 489-500. This paper is a highly important contribution to this new field of work; its importance lies partly in the fact that it establishes a correspondence between modular and formal invariants. Her main theorem has already been frequently quoted on account of its fundamental character. Her proof is a remarkable piece of mathematics.
E T Bell wrote in [1]:-
Miss Sanderson's single contribution (1913) to modular invariants has been rated by competent judges as one of the classics of the subject.
Sanderson writes in the paper:-
We see clearly just how the difference in the definitions of formal and modular invariants affects the actual computations. Dickson has given a very simple and elegant theory of modular invariants. No theory has been developed for formal invariants. However, there exists between the two subjects an interesting and important relation, which I shall develop in what follows. I take this opportunity to express my gratitude to Professor Dickson for his interest and many helpful suggestions, in particular for the present formulation of this introductory section.
In the 30 page thesis there is the following Vita:-
MILDRED SANDERSON was born in 1889 in Waltham, Massachusetts, where she received her secondary school education. She took the degree of Bachelor of Arts at Mount Holyoke College in 1910, the degrees of Master of Science (1911) and Doctor of Philosophy (1913) at the University of Chicago, doing her major work in mathematics, and her minor work in astronomy.
We note that Forest Ray Moulton and Ernest Julius Wilczynski had taught astronomy courses which Sanderson had studied as part of her minor subject.

After the award of her doctorate, Sanderson was appointed as an Instructor in Mathematics at the University of Wisconsin. The authors of [4] write:-
Sanderson was an instructor at the University of Wisconsin during the first semester 1913-14 but left in February 1914 when she became ill with pulmonary tuberculosis. She died at age twenty-five in a hospital in East Bridgewater, Massachusetts, the following October. Services were conducted in her family's home in Waltham by a pastor of the First Baptist Church, and she was buried in Mt Feake cemetery in Waltham.
L E Dickson writes [7]:-
The remarkable mathematical ability and originality shown by Miss Sanderson in her master's and doctor's theses and the very unusual ease with which she assimilated ideas in all branches of pure and applied mathematics, combined with her enthusiasm for that science, gave full promise of a highly successful career for her in research. Her death on October 15, 1914, only a year after completing her graduate studies, was not only a distinct loss to progress in mathematical research in America, but was a very keen blow to her fellow students, to all of whom she had endeared herself by her most lovable personality. ... If I may be permitted to add my personal tribute to the universally expressed tribute to her remarkable ability, it would be to say that she was my most gifted pupil.
We note that Mount Holyoke College established the Mildred L Sanderson Prize for Mathematics in 1939.

### References (show)

1. E T Bell, Fifty Years of Algebra in America, 1888-1938, in Semicentennial Addresses of the American Mathematical Society (American Mathematical Society, Providence, R.I., 1988).
2. Funeral of Miss Sanderson, Waltham Evening News (16 October 1914).
3. J Green and J LaDuke, Sanderson, Mildred Leonora, Pioneering Women in American Mathematics (American Mathematical Society, Providence, Rhode Island, 2009).
4. J Green and J LaDuke, Sanderson, Mildred Leonora, Supplementary Material for Pioneering Women in American Mathematics: The Pre-1940 PhDs, American Mathematical Society (6 October 2015).
https://www.ams.org/publications/authors/books/postpub/hmath-34-PioneeringWomen.pdf
5. G Kass-Simon and P Farnes, Sanderson, Mildred Leonora, in G Kass-Simon and P Farnes (eds.), Women of Science: Righting the Record (Indiana University Press, 1990).
6. Miss Mildred L Sanderson (Obituary), Waltham Daily Free Press-Tribune (16 October 1914).
7. L E Dickson, A Tribute to Mildred Lenora Sanderson, Amer. Math. Monthly 22 (8) (1915), 264.
8. L E Dickson, A Tribute to Mildred Lenora Sanderson, Association for Women in Mathematics Newsletter 4 (5) (1974), 9-10.
9. L E Dickson, A Tribute to Mildred Lenora Sanderson, Association for Women in Mathematics Newsletter 14 (4) (1984), 16.
10. L Riddle, Mildred Leonora Sanderson, Biographies of Women Mathematicians, Agnes Scott College (2016).
https://www.agnesscott.edu/lriddle/women/sander.htm
11. M Sanderson, Formal Modular Invariants with Application to Binary Modular Covariants, Transactions of the American Mathematical Society 14 (4) (1913), 489-500.
12. M Sanderson, Generalizations in the Theory of Numbers and Theory of Linear Groups, Annals of Mathematics (2) 13 (1/4) (1911-1912), 36-39.
13. The University of Chicago Magazine 7 (University of Chicago Alumni Association, 1914), 24.

Written by J J O'Connor and E F Robertson
Last Update December 2021