Newton & Leibniz — The Calculus
Two independent inventions that changed the course of science forever
12.1 Newton's Fluxions
Isaac Newton (1643–1727) developed his method of fluxions in 1665–1666 during the annus mirabilis. He used calculus to derive Kepler's laws of planetary motion in his Principia Mathematica (1687) — but was notoriously reluctant to publish.
12.2 Leibniz's Calculus
Gottfried Wilhelm Leibniz (1646–1716) independently developed calculus in the 1670s. His notation — dx, dy, ∫ — was far more elegant than Newton's and is the notation we use today. He conceived of calculus as a formal symbolic system, anticipating modern computer science.
12.3 The Priority Dispute
The bitter controversy over who invented calculus first consumed the scientific world for decades. Modern historians agree both men developed it independently. The dispute had real consequences: British mathematicians fell behind Continental peers who used Leibniz's superior notation.