Today's Google Doodle celebrates the 133rd anniversary of the birth of Emmy Noether (https://www.google.com/doodles/emmy-noethers-133rd-birthday), who I think is responsible for the most remarkable theory in all of mathematical physics: Noether's theorem (https://en.wikipedia.org/wiki/Noether%27s_theorem), that every symmetry law has a related conservation law. That's way oversimplified, but expresses the flavor of it -- I haven't the math to explain in detail.
For example, the law of conservation of energy is a consequence of actions being symmetric under time -- i.e., all other things being equal, it doesn't matter when you perform an action, you get the same result from an experiment done on Tuesday morning as you do on Wednesday afternoon.
Invariance under translation (movement in space -- all other things being equal, it doesn't matter where you do something) leads to conservation of momentum. Invariance under rotation (it doesn't matter which way you're looking) leads to conservation of angular momentum.
This just blows my mind. It's my favorite theorem in all of mathematical physics because it's so unexpected. Go out and read up a little bit, I think it's an amazing concept to try to get your brain around.