She completed her dissertation entitled "On Complete Systems of Invariants for Ternary Biquadratic Forms," receiving her Ph.D., summa cum laude, on July 2, 1908.
Noether worked without pay at the Mathematical Institute of Erlangen from 1908 until 1915, where her university duties included research, serving as a dissertation adviser for two students, and occasionally delivering lectures for her ailing father. In addition, Noether began to work with Ernst Otto Fischer, an algebraist who directed her toward the broader theoretical style characteristic of Hilbert. Noether not only published her thesis on ternary biquadratics, but she was also elected to membership in the Circolo Matematico di Palermo in 1908. The following year, Noether was invited to join the German Mathematical Society (Deutsche Mathematiker Vereinigung); she addressed the Society's 1909 meeting in Salzburg and its 1913 meeting in Vienna.
Formulates the Mathematics of Relativity
In 1915, Klein and Hilbert invited Noether to join them at the Mathematical Institute in Göttingen. They were working on the mathematics of the newly announced general theory of relativity, and they believed Noether's expertise would be helpful. Albert Einstein later wrote an article for the 1955 Grolier Encyclopedia, characterizing the theory of relativity by the basic question, "how must the laws of nature be constituted so that they are valid in the same form relative to arbitrary systems of co-ordinates (postulate of the invariance of the laws of nature relative to an arbitrary transformation of space and time)"" It was precisely this type of invariance under transformation on which Noether focused her mathematical research.
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