Navier-Stokes (incompressible):

$$\rho \left( \frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f}$$

Einstein field equations:

$$R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$

Schrödinger equation (time-dependent):

$$i\hbar \frac{\partial}{\partial t} | \Psi(\mathbf{r},t) \rangle = \left[ -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r},t) \right] | \Psi(\mathbf{r},t) \rangle$$

Riemann zeta function:

$$\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \prod_{p \text{ prime}} \frac{1}{1 - p^{-s}}$$

Path integral (QFT):

$$\mathcal{Z} = \int \mathcal{D}[\phi] \, \exp\left( i \int d^4x \, \mathcal{L}(\phi, \partial_\mu\phi) \right)$$

Fourier transform:

$$\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i x \xi} \, dx \quad \Longleftrightarrow \quad f(x) = \int_{-\infty}^{\infty} \hat{f}(\xi) \, e^{2\pi i x \xi} \, d\xi$$