The quadratic formula: x = − b ± b 2 − 4 a c 2 a {\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
The Pythagorean theorem: a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}}
Einstein's famous equation of mass-energy equivalence: E = m c 2 {\displaystyle E=mc^{2}}
The Navier-Stokes equation for fluid dynamics: ∂ u ∂ t + ( u ⋅ ∇ ) u = − 1 ρ ∇ p + ν ∇ 2 u {\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}+(\mathbf {u} \cdot \nabla )\mathbf {u} =-{\frac {1}{\rho }}\nabla p+\nu \nabla ^{2}\mathbf {u} }
The Schrödinger equation for quantum mechanics: i ℏ ∂ ψ ∂ t = H ^ ψ {\displaystyle i\hbar {\frac {\partial \psi }{\partial t}}={\hat {H}}\psi }
Maxwell's equations for electromagnetism: ∇ ⋅ E = ρ ϵ 0 ∇ ⋅ B = 0 ∇ × E = − ∂ B ∂ t ∇ × B = μ 0 J + μ 0 ϵ 0 ∂ E ∂ t {\displaystyle {\begin{aligned}\nabla \cdot \mathbf {E} &={\frac {\rho }{\epsilon _{0}}}\\\nabla \cdot \mathbf {B} &=0\\\nabla \times \mathbf {E} &=-{\frac {\partial \mathbf {B} }{\partial t}}\\\nabla \times \mathbf {B} &=\mu _{0}\mathbf {J} +\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\end{aligned}}}
