Last week's In Our Time on Radio 4, presented by Lord Bragg of Wigton, is about the mathematician and physicist Emmy Noether. Understanding the mathematics of Noether's Theorem is one of my lasting ambitions. She proved that the fact that doing the same experiment tomorrow and getting the same results, showing symmetry in time, is a consequence of Conservation of Energy; that doing the same experiment in different places and getting the same result, showing symmetry in space, is a consequence of Conservation of Momentum. For me, the best bit is in the epilogue on the podcast, where the difference between global symmetry and local symmetry is explained.
https://www.bbc.co.uk/programmes/m00025bw