Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Gottfried Wilhelm Leibniz was a German polymath active as a mathematician, philosopher, scientist and diplomat who invented calculus in addition to many other branches of mathematics and statistics. Leibniz has been called the "last universal genius" due to his knowledge and skills in different fields and because such people became less common during the Industrial Revolution and spread of specialized labor after his lifetime. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science by devising a cataloguing system whilst working at the Herzog August Library in Wolfenbüttel, Germany, that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.
Sir Isaac Newton was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher. He was a key figure in the Scientific Revolution and the Enlightenment that followed. His pioneering book Philosophiæ Naturalis Principia Mathematica, first published in 1687, consolidated many previous results and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus, though he developed calculus years before Leibniz.
Method of Fluxions is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736.
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educating Leonhard Euler in the pupil's youth.
The System of the World is a novel by Neal Stephenson and the third and final volume in The Baroque Cycle. The title alludes to the third volume of Isaac Newton's Philosophiae Naturalis Principia Mathematica, which bears the same name.
In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively.
The year 1703 in science and technology involved some significant events.
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Infinitesimal calculus was developed in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz independently of each other. An argument over priority led to the Leibniz–Newton calculus controversy which continued until the death of Leibniz in 1716. The development of calculus and its uses within the sciences have continued to the present.
Nicolas Fatio de Duillier was a mathematician, natural philosopher, astronomer, inventor, and religious campaigner. Born in Basel, Switzerland, Fatio mostly grew up in the then-independent Republic of Geneva, of which he was a citizen, before spending much of his adult life in England and Holland. Fatio is known for his collaboration with Giovanni Domenico Cassini on the correct explanation of the astronomical phenomenon of zodiacal light, for inventing the "push" or "shadow" theory of gravitation, for his close association with both Christiaan Huygens and Isaac Newton, and for his role in the Leibniz–Newton calculus controversy. He also invented and developed the first method for fabricating jewel bearings for mechanical watches and clocks.
Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet was a French natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749.
Pierre Varignon was a French mathematician. He was educated at the Jesuit College and the University of Caen, where he received his M.A. in 1682. He took Holy Orders the following year.
René-François Walter de Sluse was a Walloon mathematician and churchman who served as the canon of Liège and abbot of Amay.
In the history of calculus, the calculus controversy was an argument between the mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first invented calculus. The question was a major intellectual controversy, which began simmering in 1699 and broke out in full force in 1711. Leibniz had published his work first, but Newton's supporters accused Leibniz of plagiarizing Newton's unpublished ideas. Leibniz died in 1716, shortly after the Royal Society, of which Newton was a member, found in Newton's favor. The modern consensus is that the two men developed their ideas independently.
Acta Eruditorum was the first scientific journal of the German-speaking lands of Europe, published from 1682 to 1782.
The concept of multiple discovery is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors. The concept of multiple discovery opposes a traditional view—the "heroic theory" of invention and discovery. Multiple discovery is analogous to convergent evolution in biological evolution.
"Nova Methodus pro Maximis et Minimis" is the first published work on the subject of calculus. It was published by Gottfried Leibniz in the Acta Eruditorum in October 1684. It is considered to be the birth of infinitesimal calculus.
A fluxion is the instantaneous rate of change, or gradient, of a fluent at a given point. Fluxions were introduced by Isaac Newton to describe his form of a time derivative. Newton introduced the concept in 1665 and detailed them in his mathematical treatise, Method of Fluxions. Fluxions and fluents made up Newton's early calculus.