Newton and Leibniz
Before Newton and Leibniz, the word “calculus” was a general term used to refer to any body of mathematics, but in the following years, "calculus" became a popular term for a field of mathematics based upon their insights. The purpose of this section is to examine Newton and Leibniz’s investigations into the developing field of infinitesimal calculus. Specific importance will be put on the justification and descriptive terms which they used in an attempt to understand calculus as they themselves conceived it.
By the middle of the seventeenth century, European mathematics had changed its primary repository of knowledge. In comparison to the last century which maintained Hellenistic mathematics as the starting point for research, Newton, Leibniz and their contemporaries increasingly looked towards the works of more modern thinkers. Europe had become home to a burgeoning mathematical community and with the advent of enhanced institutional and organizational bases a new level of organization and academic integration was being achieved. Importantly, however, the community lacked formalism; instead it consisted of a disordered mass of various methods, techniques, notations, theories, and paradoxes.
Newton came to calculus as part of his investigations in physics and geometry. He viewed calculus as the scientific description of the generation of motion and magnitudes. In comparison, Leibniz focused on the tangent problem and came to believe that calculus was a metaphysical explanation of change. Importantly, the core of their insight was the formalization of the inverse properties between the integral and the differential. This insight had been anticipated by their predecessors, but they were the first to conceive calculus as a system in which new rhetoric and descriptive terms were created. Their unique discoveries lay not only in their imagination, but also in their ability to synthesize the insights around them into a universal algorithmic process, thereby forming a new mathematical system.
See also: Leibniz–Newton calculus controversyRead more about this topic: History Of Calculus
Famous quotes containing the words newton and/or leibniz:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“Navarette, a Chinese missionary, agrees with Leibniz and says that “It is the special providence of God that the Chinese did not know what was done in Christendom; for if they did, there would be never a man among them, but would spit in our faces.””
—Matthew Tindal (1653–1733)