[2] Thus she belonged to a small group of talented young women in Germany at the beginning of the 20th century who were allowed to take the Abitur externally at boys' schools.
Since Prussia began to allow women to formally attend university only from the winter semester of 1908–09, Löbenstein and her friend Margarete Kahn first attended the universities of Berlin and Göttingen as guest students.
[3] Hilbert's sixteenth problem concerned the topology of algebraic curves in the complex projective plane; as a difficult special case in his formulation of the problem Hilbert proposed that there are no algebraic curves of degree 6 consisting of 11 separate ovals.
Löbenstein obtained a doctorate in 1910 under David Hilbert in Göttingen, with a dissertation titled Über den Satz, daß eine ebene, algebraische Kurve 6.
Ordnung mit 11 sich einander ausschließenden Ovalen nicht existiert [On the proposition that no plane algebraic curve of degree 6 with 11 mutually exclusive ovals exists], and was therefore one of the first German women to obtain a doctorate in mathematics (the mathematics division was part of the faculty of philosophy then).