Isaac Newton

1. Newton’s Second Law

Published in Principia (1687), this equation mathematically formalized motion in a way that dominated physics for over two centuries.

$$ \mathbf{F} = m\mathbf{a} $$

2. Law of Universal Gravitation

Newton introduced this in 1687, unifying celestial and terrestrial mechanics under a single mathematical law.

$$ F = G\frac{m_1 m_2}{r^2} $$

3. Binomial Series

Developed in the 1660s, this expansion was part of Newton’s broader creation of infinite series methods before calculus was formalized.

$$ (1+x)^n = \sum_{k=0}^{\infty} \binom{n}{k} x^k $$

4. Newton–Leibniz Calculus (Fluxions)

Newton devised fluxions in the mid-1660s, though publication delays fueled the famous priority dispute with Leibniz.

$$ \frac{dy}{dx} $$