Beautiful Theorems and what constitutes as beautiful [closed]

Solution 1:

$$\int_M d\omega = \int_{\partial M}\omega $$

Solution 2:

$$\mathcal G(n)=\int_0^\infty e^{-x^n}dx\qquad=>\qquad n!=\mathcal G\bigg(\dfrac1n\bigg)$$ In particular, the Gaussian integral $$\int_{-\infty}^\infty e^{-x^2}dx=\sqrt\pi$$