A wonderful article at arstechnica tells of the work of a woman Jew in the early 20th century. She lived in Germany in the years leading up to WWII. She had to leave, and came to America. Some of her best work is on Einstein‘s General Theory of Relativity.
Science kind of takes some symmetries for granted. For example, you should be able to perform the same experiment a year later and get the same result. Or you should be able to do it in two places and get the same result. But one of the main laws of physics — conservation of energy — seems to be broken by general relativity. It is possible for a machine to emit gravity waves, and gain energy instead of losing it.
It turns out that with general relativity, you may get different results depending on where you are when you perform your experiments. Here on earth, the experiments all happen in very similar circumstances. But in a strong gravitational field, the curvature of space is different, and you can get different measurements. This strange effect is predicted by Einstein’s theories, and Neother’s theorem provides the connection.