[1] Branner studied mathematics and physics at Aarhus University, where mathematician Svend Bundgaard was one of her mentors, and in 1967 earned a master's degree (the highest degree then available) under the supervision of Leif Kristensen.
She had intended to travel to the U.S. for a doctorate, but her husband, a chemist, took an industry job in Copenhagen.
Branner could not get a job as a high school teacher because she did not have a teaching qualification, but Bundgaard found her a position as a faculty assistant for Frederik Fabricius-Bjerre at the Technical University of Denmark.
[1] European Women in Mathematics was founded as an organization in 1986 by Branner, Caroline Series, Gudrun Kalmbach, Marie-Françoise Roy, and Dona Strauss, inspired by the activities of the Association for Women in Mathematics in the USA.
[1] A symposium in honor of Branner's 60th birthday was held in Holbæk in 2003, and published as a festschrift in 2006.