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@@ -2724,7 +2724,7 @@ Duality of time and frequency, space and momentum. Every signal decomposes into
$$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx$$ $$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx$$
**41. Noether's Theorem** — Emmy Noether (1915) **41. Noether's Theorem** — Emmy Noether (1918)
Every continuous symmetry corresponds to a conserved quantity. Time symmetry → energy conservation. Spatial symmetry → momentum conservation. Rotational symmetry → angular momentum conservation. Symmetry is conservation. Every continuous symmetry corresponds to a conserved quantity. Time symmetry → energy conservation. Spatial symmetry → momentum conservation. Rotational symmetry → angular momentum conservation. Symmetry is conservation.
**42. Gauss's Theorema Egregium** — Carl Friedrich Gauss (1827) **42. Gauss's Theorema Egregium** — Carl Friedrich Gauss (1827)