Baker's father was Richard Philip Baker, a British-born mathematician, mathematical model maker, and college administrator. Her mother, Katherine Riedelbauch Baker, was a music teacher and chamber musician. Baker was born on December 19, 1902, in
Anna, Illinois, and was home-schooled until high school, where she attended a public school in
Iowa City, Iowa. She became valedictorian of her school, graduating in 1919. At the
University of Iowa, where her father had become a mathematics professor, she studied classics and mathematics, graduating
magna cum laude and
Phi Beta Kappa in 1923. She continued on as a graduate student, working with her father in mathematics and completing a master's degree in 1925. After completing her master's degree, Baker became head of the mathematics and physics department at
Tabor College in Iowa in 1925, but the college closed in 1927. After briefly teaching at Jefferson City Junior College in Missouri, she earned a teaching certificate from the University of Iowa in 1928, and took courses at the
University of Chicago beginning in 1929. She entered the university as a full-time student in 1931, and completed her Ph.D. in 1934. Her dissertation,
A Contribution to the Waring Problem for Cubic Functions, concerned a variation of
Waring's problem in
number theory, on representing integers as sums of the values of a
cubic polynomial; it was supervised by
Leonard Eugene Dickson. Both Dickson and Richard Baker, in turn, had been students of the same
doctoral advisor,
E. H. Moore. ==Later life and career==