OK, this is not new. This arXiv manuscript was uploaded way back in 1998. But I was looking for some reference for someone else regarding the historical development of Noether's theorem, and stumbled upon this. It gives that, and also the significance of Noether's amazing insight. In fact, if you have not been aware of the importance of symmetries and how they reflect the conservation laws that we have, this is a good paper to read.
Abstract: Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract algebra, it is of some historical interest to examine how she came to make these discoveries. The present paper is an historical account of the circumstances in which she discovered and proved these theorems which physicists refer to collectively as Noether's Theorem. The work was done soon after Hilbert's discovery of the variational principle which gives the field equations of general relativity. The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein. Noether's theorems solved this problem. With her characteristically deep insight and thorough analysis, in solving that problem she discovered very general theorems that have profoundly influenced modern physics.