Isaac Newton & Gottfried Wilhelm Leibniz

Newton: 1643–1727
Leibniz: 1646–1716
Title: Inventors of Calculus

The Giants Who Understood the Laws of the Universe

Isaac Newton

The Giant Who Perceived Universal Laws

In 1665, the plague broke out in London, and Cambridge University closed. The 22-year-old Newton returned to his rural home to escape the plague. During those lonely 18 months (called the "Year of Wonders"), he invented calculus, discovered universal gravitation, and studied optics.

Core Theory: Method of Fluxions (Calculus)

Newton needed a mathematical tool to describe changes in an object's velocity (acceleration) and planetary trajectories. The mathematics of the time couldn't handle the concepts of "instantaneous" and "infinitesimal," so he invented calculus.

Core Idea: He viewed variables as quantities that flow continuously over time (Fluents), with rates of change called fluxions.

Masterpiece: Principia Mathematica

The Mathematical Principles of Natural Philosophy is one of the greatest works in the history of science, establishing the laws of motion and universal gravitation.

Gottfried Wilhelm Leibniz

Master of Symbols and Logic

Leibniz independently invented calculus. If Newton did it to solve physical problems, Leibniz did it out of an obsession with philosophy and logical symbols.

Core Contribution: Excellent Calculus Notation

Newton's notation (like $\dot{x}$ ) was less intuitive and mainly used in Britain.

Leibniz's notation ( $dx$ , $dy$ , $\int$ ) was extremely intuitive and elegant, and is still used worldwide today. The integral symbol $\int$ comes from the elongated Latin letter S (from Summa, meaning sum), and $d$ represents Difference.

Fundamental Theorem of Calculus

He clearly articulated that differentiation (finding tangents) and integration (finding areas) are inverse operations.

The Historical Controversy: The Calculus Priority Dispute

Newton and Leibniz's supporters argued for decades over "who invented calculus first." In reality, Newton discovered it first (about 10 years earlier), but Leibniz published first.

This dispute caused British mathematics to break off from continental Europe for nearly a century, causing British mathematics to stagnate during that period.

Legacy

Together, Newton and Leibniz gave humanity the ultimate tool for handling change—calculus. This super tool enabled the explosive development of mathematics, physics, and engineering in the following centuries.