Reilly was born on February 14, 1895, in
Chicago, to Agnes Finn Reilly and Michael Reilly. Her birth name was Margaret Reilly. Her mother was a homemaker, and her father was a public works employee. She had two siblings. She graduated from
Mother of Mercy High School in Cincinnati in June 1914, and immediately entered the congregation of the Religious Sisters of Mercy of Cincinnati. Some sources say
Our Lady of Mercy High School (Ohio), but Mother of Mercy seems more likely because it was run by the Sisters of Mercy. She was perpetually vowed in August 1917. She was a teacher in Cincinnati before and during college, teaching music and English in all grades from 1914 to 1928 at St. Edward School, St. Andrew School, Our Lady of Mercy Academy, Elder High School and Mother of Mercy Academy. During this period she earned a B. A. on June 18, 1923, from St. Xavier College (now
Xavier University) in Cincinnati, Ohio, and an M. A. in 1925 with a major in sociology and a minor in philosophy. Although Xavier was a Jesuit college for men, she and other sisters from a number of regional congregations were allowed to attend special classes at nights and on weekends. She earned a PhD in 1936 from the
Catholic University of America in Washington, DC. She was in residence in Washington off and on, sometimes both studying and teaching at the Teachers' College of the
Athenaeum of Ohio. Her dissertation was
Self-Symmetric Quadrilaterals In-and-Circumscribed to the Plane Rational Quartic Curve with a Line of Symmetry, directed by
Dr. Aubrey E. Landry. In it she cites the mathematic work of other nuns, including Sister Felice Vaudreuil, Sister Helen Sullivan, Sister Laetitia Hill, Sister
Domitilla Thuener, Sister Leonarda Burke, and Sister
Mary Nicholas Arnoldy. Their inclusion at the opening of the thesis makes it clear she thought of their work as interconnected, and this could form the basis of more research on these sister-mathematicians. == Mathematics career ==