One theorem proved why energy is conserved — using pure symmetry

In 1918, mathematician Emmy Noether proved that every continuous symmetry in a physical system corresponds to a conserved quantity: symmetry in time gives conservation of energy, symmetry in space gives conservation of momentum. Einstein and Hilbert had struggled with the problem; Noether solved it despite being barred from a paid professorship for being a woman. Physicists now call it one of the most important theorems in modern physics.

— Emmy Noether, Invariante Variationsprobleme — Göttinger Nachrichten, 1918