After returning to Erlangen (they had started officially accepting female students) she worked under Paul Gordan, a family friend whom she had known since she was young. His nickname was "The King of Invariant Theory." Emmy was his only doctorate student he ever mentored.
PhD in Mathematics, thesis on Algebraic Invariants - Suma Cum Laude
Despite being held in HIGH ESTEEM by the mathematics community and having published numerous influential and well-received papers in her field, she was not given an official position until 1919 (Privatdozent, which recognized her PhD and gave her the right to lecture and advise students but not a professorship - and was not paid). Initially she worked under her father at the University of Elerangen and later was invited to Göttingen and lectured under Hilbert's name because the University would not give her an official position with permission to teach (until 1919).
Noether's Thoerem (symmetry and conservation) - a basic tenant of modern physics.
Worked with the best mathematicians at the time as a PEER but did not receive pay until 1923.
1920: Concerning Moduli in Non-Commutative Fields Particularly in Differential and Difference Terms
Worked on Commutative Algebra, 1920-1926
1925: Greta Hermann completed her PhD - under the mentorship of Emmy Noether
Presented at the International Mathematical Congress, 1928 & 1932
German Mathematical Annual
Her mathematical colleagues continually tried to petition for greater recognition (in terms of POSITION at the University) for Emmy - despite her low "rank" - she was considered a Leader in the Mathematics community.
Lost her position when the Nazi party passed laws effectively prohibiting Jews from holding civil positions
Albert Einstein's letter about Emmy Noether was published in The New York Times in which he called her the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians.