Hayes conducted significant research in mathematical astronomy, including the calculation of the orbital elements of the newly discovered asteroid
267 Tirza, completed during her studies at the
Leander McCormick Observatory at the
University of Virginia. Orbit determination in the late nineteenth century required extensive manual computation and advanced mathematical training, making such work notable at a time when women rarely had access to advanced scientific institutions. In addition to her astronomical work, Hayes authored several mathematical textbooks and instructional materials used in collegiate education. Her teaching career at
Wellesley College spanned several decades, during which she contributed to the development of mathematical curricula for women in higher education. Her career represents an early example of sustained female participation in professional mathematics in the United States. As a mathematics professor, she was described as controversial. She questioned the truth of the
Bible in front of students. A history of Wellesley College reads: ==Women in math==