| No. | Equation                                      | Description                                                                 |
|-----|----------------------------------------------|-----------------------------------------------------------------------------|
| 1.  | $e^{i\pi} + 1 = 0$                           | Connects five fundamental constants (e, i, π, 1, 0), revealing the profound relationship between exponential functions and trigonometry. |
| 2.  | $a^2 + b^2 = c^2$                             | In right triangles, the hypotenuse squared equals the sum of the squares of the other sides. Cornerstone of geometry with applications in navigation and architecture. |
| 3.  | $\int_a^b f(x) \, dx = F(b) - F(a)$          | Establishes that differentiation and integration are inverse operations. If F is an antiderivative of f, the definite integral equals F(b) - F(a). Revolutionized mathematical problem-solving. |
| 4.  | $\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$ | Unified electricity and magnetism as manifestations of the same force. Describes electromagnetic field behavior, predicting waves traveling at light speed. Enabled technologies from radio to smartphones. |
|     | $\nabla \cdot \mathbf{B} = 0$               |                                                                             |
|     | $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$ |                                                                             |
|     | $\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$ |                                                                             |