Martha Elizabeth Peterson was born June 22, 1916 near Jamestown, Kansas to Anton Romeo Peterson (1890-1952) and Osey Gail French (1891-1982), who were married November 14, 1914. In 1933 Peterson graduated from Salina High School, Salina, Kansas, and went on to attend the University of Kansas (KU), earning both her B.A. (1937) and M.A. (1943) in mathematics.

Peterson taught math in high schools in Stockton and Ellinwood, KS from 1937-1942 before joining the KU Department of Mathematics as an instructor in 1942. As she worked towards a Ph.D. in educational psychology, which she completed in 1959, Peterson served as assistant dean of women at KU from 1947-1952, and as dean of women from 1952-1956. She is credited with installing the dormitory system for freshmen women while at KU.

In 1956 Peterson left KU to become dean of women at the University of Wisconsin-Madison; she remained in this position until 1963, when she was named University Dean of Affairs.

In 1967, Peterson became the president of Barnard College, where she navigated the student body through the Vietnam War years. She also developed the college's relationship with Columbia University, which lead to a successful course exchange program between the two schools.

Peterson left Barnard in 1975 to become the first woman president at Wisconsin's Beloit College, where she remained until her retirement in 1981. Peterson's tenure at Beloit saw her enact drastic budget cuts in an effort to restore fiscal stability to the institution at a time when both enrollment and endowment funding were down.

Peterson became the first woman to sit on the board of Exxon in 1975. She would also become the first woman to sit on the boards for both Metropolitan Life Insurance Company and Dry Stock Savings Bank.

During her retirement Peterson continued serving on a number of boards, including the Board of Trustees for the University of Notre Dame. She and her longtime companion, Dr. Maxine Bennett, divided their time among residences in Wisconsin and Florida, and traveled extensively.

Peterson was inducted into KU's Women's Hall of Fame in 1972 and received KU's highest honor, the Distinguished Service Citation, in 1968. She also received the KU School of Education's Apple Award in 1993. At the time of her death on July 14, 2006, Peterson had received over 20 honorary degrees from different institutes of higher learning.