Mildred Sanderson

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Mildred Sanderson (1889-1914) was an American mathematician, best known for her mathematical theorem concerning modular invariants.[1][2]


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 PhD 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] Dickson later 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] E.T. 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] After completing her Ph.D., Sanderson briefly taught at the University of Wisconsin before her untimely death in 1914 due to tuberculosis.[1][4] She is mentioned in the book Pioneering women in American mathematics: the pre-1940 PhD's, by Judy Green and Jeanne LaDuke.[5] A Mildred L. Sanderson prize for excellence in mathematics was established in her honor in 1939 at Mount Holyoke College.[5]

Sanderson's theorem[edit]

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