Braun studied botany and geology at the University of Cincinnati. She earned a bachelor's degree in 1910, a master's degree in geology in 1912, and a PhD in botany in 1914. In 1912, she studied with Henry C. Cowles; Harris M. Benedict was her dissertation adviser, with additional advice from Nevin M. Fenneman. She became the sixth woman to earn a PhD from that institution; her sister was the first. Braun's teaching and research career at the University of Cincinnati began as an assistant in geology (1910–1913). She taught as an assistant in botany from 1914 to 1917, then advanced through the titles of instructor, assistant professor, and associate professor. She achieved full professorship as a professor of plant ecology in 1946, two years before her retirement. She held the title of professor emeritus of plant ecology from 1948 until her death in 1971.