Many of the most influential advances in mathematics during the 18th century involved the elaboration of the calculus, a branch of mathematical analysis which describes properties of functions (curves) associated with a limit process. Although the evolution of the techniques included in the calculus spanned the history of mathematics, calculus was formally developed during the last decades of the 17th century by English mathematician and physicist Sir Isaac Newton (1643-1727) and, independently, by German mathematician Gottfried Wilhelm von Leibniz (1646-1716). Although the logical underpinnings of calculus were hotly debated, the techniques of calculus were immediately applied to a variety of problems in physics, astronomy, and engineering. By the end of the 18th century, calculus had proved a powerful tool that allowed mathematicians and scientists to construct accurate mathematical models of physical phenomena ranging from orbital mechanics to particle dynamics.
Although it is clear that Newton made his discoveries regarding calculus years before Leibniz, most historians of mathematics assert that Leibniz independently developed the techniques, symbolism, and nomenclature reflected in his preemptory publications of the calculus in 1684 and 1686. The controversy regarding credit for the origin of calculus quickly became more than a simple dispute between mathematicians. Supporters of Newton and Leibniz often arguing along bitter and blatantly nationalistic lines and the feud itself had a profound influence on the subsequent development of calculus and other branches of mathematical analysis in England and in Continental Europe. more