Mildred Sanderson

Sanderson was born in Waltham, Massachusetts, in 1889 and was the valedictorian of her class at the Waltham High School.[1] She graduated from Mount Holyoke College in 1910, winning Senior Honors in Mathematics.[1] She obtained her Ph.D degree from the University of Chicago in 1913,[3] publishing the thesis (Sanderson 1913) in which she set forth her mathematical theorem. She was Leonard Eugene Dickson's first female doctoral student.[1][3]

After completing her Ph.D., Sanderson briefly taught at the University of Wisconsin before her untimely death in 1914 due to tuberculosis.[1][4]

Sanderson family grave at Mount Feake Cemetery, Waltham, Massachusetts. The grave of Mildred Sanderson is behind the main marker.

Sanderson's theorem (Sanderson 1913, p.490) states: "To any modular invariant ${\displaystyle i}$ of a system of forms under any group ${\displaystyle G}$ of linear transformations with coefficients in the field ${\displaystyle {\rm {GF}}[p^{n}]}$, there corresponds a formal invariant ${\displaystyle I}$ under ${\displaystyle G}$ such that ${\displaystyle I=i}$ for all sets of values in the field of the coefficients of the system of forms."

Leonard Eugene Dickson (she was his first female doctoral student[1][3]) wrote of her thesis, "This paper is a highly important contribution to this 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."[1]

Eric Temple Bell wrote, "Miss Sanderson's single contribution (1913) to modular invariants has been rated by competent judges as one of the classics of the subject."[1]

A Mildred L. Sanderson prize for excellence in mathematics was established in her honor in 1939 at Mount Holyoke College.[4]

She is mentioned in the 2008 book Pioneering women in American mathematics: the pre-1940 PhD's, by Judy Green and Jeanne LaDuke.[4]

• Rutherford, Daniel Edwin (2007) [1932], Modular invariants, Cambridge Tracts in Mathematics and Mathematical Physics, No. 27, Ramsay Press, ISBN 978-1-4067-3850-6, MR 0186665
• Sanderson, Mildred (1913), "Formal Modular Invariants with Application to Binary Modular Covariants", Transactions of the American Mathematical Society, Providence, R.I.: American Mathematical Society, 14 (4): 489–500, doi:10.2307/1988702, ISSN 0002-9947, JSTOR 1988702