Johann Carl Friedrich Gauss

1. Fundamental Theorem of Algebra

Gauss gave the first rigorous proof in 1799, helping legitimize complex numbers within mainstream mathematics.

$$ p(z) = 0 \quad \text{has at least one complex root} $$

2. Gaussian Integral

This result appeared in Gauss’s early 19th-century work on probability and error theory tied to astronomical observations.

$$ \int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi} $$

3. Gauss’s Law (Electrostatics)

Developed in the 1830s, this law became foundational to electromagnetism decades before Maxwell unified the field.

$$ \oint_{\partial V} \mathbf{E}\cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} $$

4. Quadratic Reciprocity Law

Gauss proved this in 1801 and famously called it the “golden theorem” of number theory.

$$ \left(\frac{p}{q}\right)\left(\frac{q}{p}\right) = (-1)^{\frac{(p-1)(q-1)}{4}} $$