nugel was the fourth of six children of a musician, friedrich arthur nugel. she was born on 18 june 1884 in cottbus. she studied at the mädchen-mittelschule (girl's middle school) there until 1901, then began studies at the höhere mädchenschule (girl's high school) until 1906. shortly after, she completed the state teaching examination in berlin. returning to cottbus, she worked as a private tutor for the von werdeck family, before taking the final level of german mathematics exams under the tutelage of rudolf tiemannn.