Gottfried Leibniz Calculus Quotes

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

as is always the case with scientific geniuses, Einstein’s theories would exist even if he had not. Special relativity, general relativity, and the photon model of light might not have been developed by the same individual, but someone would have sussed them out. Henri Poincaré, Hendrik Lorentz and others worked out much of relativity before 1905, just as Gottfried Leibniz independently worked out the calculus in parallel with Newton, and Alfred Russel Wallace developed natural selection in isolation from Charles Darwin. Historians of science once subscribed to a ‘Great Man’ theory, but we now know that transformative ideas emerge from the work of many talented individuals, instead of emerging ex nihilo from one brilliant mind.

The world had become Newton’s family, with a few notable exceptions. Having laid Robert Hooke to rest, literally, Newton had become involved in an all-out feud with a German philosopher named Gottfried Wilhelm Leibniz, who had claimed credit for discovering the calculus. (See “Between a Rock and a Hard Life.”)

The immediate catalyst for the emergence of the Enlightenment in the eighteenth century was the scientific revolution of the sixteenth and seventeenth centuries, which included three momentous discoveries in astronomy: Johannes Kepler delineated the rules that govern the movement of the planets, Galileo Galilei placed the sun at the center of the universe, and Isaac Newton discovered the force of gravity, invented calculus (Gottfried Wilhelm Leibniz independently discovered it at the same time), and used it to describe the three laws of motion. In so doing, Newton joined physics and astronomy and illustrated that even the deepest truths in the universe could be revealed by the methods of science. These contributions were celebrated in 1660 with the formation of the first scientific society in the world: the Royal Society of London for Improving Natural Knowledge, which elected Isaac Newton as its president in 1703. The founders of the Royal Society thought of God as a mathematician who had designed the universe to function according to logical and mathematical principles. The role of the scientist—the natural philosopher—was to employ the scientific method to discover the physical principles underlying the universe and thereby decipher the codebook that God had used in creating the cosmos. Success in the realm of science led eighteenth-century thinkers to assume that other aspects of human action, including political behavior, creativity, and art, could be improved by the application of reason, leading ultimately to an improved society and better conditions for all humankind. This confidence in reason and science affected all aspects of political and social life in Europe and soon spread to the North American colonies. There, the Enlightenment ideas that society can be improved through reason and that rational people have a natural right to the pursuit of happiness are thought to have contributed to the Jeffersonian democracy that we enjoy today in the United States.