Physics at its core uses a lot of math, both for calculations and for finding fundamental principles. Concentrating on the connection makes you a mathematical physicist. I can argue that the greatest one in the past 100 years was Emmy Noether in Germany… and, after the Nazis took over, at Bryn Mawr College in the US.
The math in the famous general theory of relativity is exquisite and mind-bending, even for Einstein, its originator. He was deeply puzzled why the treasured principle of conservation of energy didn’t show up in general relativity. He tried a ‘quick’ fix. Emmy Noether saw the subtle math error and corrected it, delving deeply into the symmetries of the Universe.
Much further, Noether showed that those treasured principles of conservation of momentum, of angular momentum, and of energy all arise not as postulates as Newton had it. They come from the symmetries: respectively: move left, right, up down in space and physics looks the same; rotate in space and physics is the same; shift in time, ditto.
This last symmetry says that energy is conserved….but not exactly in a Universe filled with matter and also expanding. We can plan spacecraft trajectories essentially ignoring this twist but it shows up in light from the early Universe becoming low-energy microwaves. Cool!
This has been an outreach activity of the Las Cruces Academy, viewable at GreatSchools.org.
Source: Veritassium podcast, Derek Muller, May 2025; https://www.youtube.com/watch?v=lcjdwSY2AzM
