Mildred Sanderson

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

Life

Sanderson was born in Waltham, Massachusetts, in 1889 and was the valedictorian of her class at the Waltham High School. She graduated from Mount Holyoke College in 1910, winning Senior Honors in Mathematics. She obtained her PhD from the University of Chicago in 1913, publishing the thesis (Sanderson 1913) in which she set forth her mathematical theorem. She was Leonard Eugene Dickson's first female doctoral student. 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." 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." After completing her Ph.D., Sanderson briefly taught at the University of Wisconsin before her untimely death in 1914 due to tuberculosis. She is mentioned in the book Pioneering women in American mathematics: the pre-1940 PhD's, by Judy Green and Jeanne LaDuke. A Mildred L. Sanderson prize for excellence in mathematics was established in her honor in 1939 at Mount Holyoke College.

Sanderson's theorem

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."