"Noether showed that the symmetries of general relativity — its invariance under transformations between different reference frames — ensure that energy is always conserved."

This isn't quite right. Energy isn't conserved in General Relativity. There is a conservation law involving the stress-energy tensor, but as the name implies, it's not energy alone that's being conserved.

But more generally, Noether's theorem, which leads to this conservation law, is probably the most beautiful theorem in physics: https://en.wikipedia.org/wiki/Noether%27s_theorem. Given that, what's amazing is that Emmy Noether only worked on physics for a relatively short time. She was asked by David Hilbert to work on the problem of invariants in General Relativity, came up with one of the most important theorems in physics, and then moved on to other (extremely important) mathematical work.