This chapter sketches the contents of Noether’s 1918 article, ‘Invariante Variationsprobleme’, as it may be seen against the background of the work of her predecessors and in the context of the debate on the conservation of energy that had arisen in the general theory of relativity.

Emmy Noether received notification of dismissal from her university post in Göttingen in April 1933 and had to look for a position outside of Germany to continue her mathematical research. By the end of the year, she moved to Bryn Mawr College in the United States and started to give guest lectures at the Institute for Advanced Study, Princeton. in February 1934. Her move was successful, but Noether initially considered going to Moscow and Oxford. She was enthusiastic about both options and even accepted an offer from Somerville College, Oxford. This chapter recovers the documents left in the Weston Library and Somerville College, the University of Oxford and Bryn Mawr College and recounts the effort of Pavel Sergeyevich Alexandroff and Helen Darbishire, who wished to help Noether and her academic career when she was forced to leave Göttingen.

In approaching ‘Invariante Variationsprobleme’ as a contribution to mathematical physics (which it undeniably was), one might easily regard it as a singularity within Noether’s corpus of collected works. This impression quickly dissipates, however, if one shifts the focus to the mathematical methods she employed. Beyond Lie’s theory of differential equations, Noether also made use of formal methods in the calculus of variations, ideas first set forth by Riemann and Lipschitz. This chapter shows the importance of these methods for understanding Noether’s broader agenda in 1917-18. It highlights two competing approaches to the study of differential invariants before, during, and after the advent of Einstein’s general theory of relativity. Noether’s expertise in invariant theory made her an ideal assistant to Felix Klein in his explorations of older literature relating to the mathematical foundations of special and general relativity. Klein argued that Christoffel’s purely algebraic methods for deriving differential invariants were essentially inferior to those based on formal variational methods. The former-as championed by Ricci and later taken up by Grossmann and Einstein-thus stood in opposition to Noether’s work from this period.