Noether was certified to teach English and French in schools for girls in 1900, but she instead chose to study mathematics at the University of Erlangen (now University of Erlangen-Nürnberg). At that time, women were only allowed to audit classes with the permission of the instructor. She spent the winter of 1903–04 auditing classes at the University of Göttingen taught by mathematicians David Hilbert, Felix Klein, and Hermann Minkowski and astronomer Karl Schwarzschild. She returned to Erlangen in 1904 when women were allowed to be full students there. She received a Ph.D. degree from Erlangen in 1907, with a dissertation on algebraic invariants. She remained at Erlangen, where she worked without pay on her own research and assisting her father, mathematician Max Noether (1844–1921).