Five years after the untimely death of his wife Johanne, their father married her younger sister Julie (1860–1934), with whom he had a daughter, Margarethe's half-sister Martha (1888–1942).

Thus she belonged to the small elite of young women in Germany at the beginning of the 20th century who were allowed to take the Abitur externally at boys' schools.

At the University of Göttingen she attended lectures given by, among others, David Hilbert, Felix Klein, Woldemar Voigt, and Georg Elias Müller; in Berlin she attended lectures by Hermann Amandus Schwarz and Paul Drude at the Royal Prussian Academy of Sciences.

Against opposition in particular from the Berlin faculty, but supported by the University of Göttingen and Felix Klein, Kahn obtained a doctorate in 1909 under David Hilbert in Göttingen, with a dissertation titled Eine allgemeine Methode zur Untersuchung der Gestalten algebraischer Kurven [A general method to investigate the shapes of algebraic curves] 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).

[7] On 13 September 2008, a Stolperstein was laid at 127 Rudolstädter Straße in Wilmersdorf in memory of Margarethe Kahn, as well as on 26 May 2010 in front of her parents' former house at Stad 29 in Eschwege, where additionally a commemorative plaque was attached on 13 December 2017.