The Invention of Calculus
Invented by Newton in the 1660s (pub. 1687) and independently by Leibniz in the 1680s (pub. 1684). Both built on Galileo’s popularizing the idea of the infinitesimal.
Calculus, the mathematical study of continuous change, introduced the concepts of differentiation and integration, providing tools to model and analyze motion, growth, and the infinitesimal. Newton, working primarily in England, utilized calculus to formulate his laws of motion and gravitation, fundamentally altering our understanding of the physical universe. Simultaneously, Leibniz developed a similar set of mathematical tools, contributing a notation system that remains in use to this day. He introduced the integral sign (∫) and the differential operator (d), foundational in calculus for representing integration and infinitesimal changes, respectively. His “dy/dx” notation for derivatives elegantly describes rates of change, all of which remain central to calculus today.
Calculus didn’t just describe change—it revealed it. By giving us tools to track motion, acceleration, force, and continuous processes, Newton and Leibniz unlocked the language physics had been waiting for. Modern physics stands on the shoulders of this idea.
Calculus is the bridge between motion we can see and the mathematics needed to describe it. Physics had always wrestled with continuous change—falling objects, curving trajectories, accelerating planets—but before calculus, these ideas lived in a fog of geometric approximations and clever guesses. By turning infinitesimal changes into something calculable, Newton and Leibniz gave physicists a toolkit to measure the very things nature refuses to present in still frames. Suddenly, motion wasn’t a mystery; it was a function.
And this connection changed everything. Newton built his three laws of motion directly on top of calculus, using derivatives to describe acceleration and integrals to reconstruct motion from forces. From that point forward, physics became a calculus-driven enterprise. Electromagnetism, thermodynamics, general relativity, quantum mechanics—all of them rely on derivatives and integrals as the grammar of physical law. In a real sense, calculus didn’t just support physics; it created the form of physics we recognize today.
Michael Alan Prestwood
Author & Natural Philosopher
Prestwood writes on science-first philosophy, with particular attention to the convergence of disciplines. Drawing on his TST Framework, his work emphasizes rational inquiry grounded in empirical observation while engaging questions at the edges of established knowledge. With TouchstoneTruth positioned as a living touchstone, this work aims to contribute reliable analysis in an emerging AI era where the credibility of information is increasingly contested.
