Gottfried Wilhelm Leibniz is credited as the inventor of differential and integral calculus, though historically, questions arose about his precedent over Sir isaac newton, who discovered differential and integral calculus independently. Current opinion favors the German mathematician over the Englishman. Leibniz also invented a mechanical calculator that represented a major improvement over blaise pascal’s calculator design. Leibniz is also recognized for his contributions to philosophical thought.
Leibniz was born on July 1, 1646, in Leipzig, Germany. His mother was Katherina Schmuck, and his father, Friedrich Leibniz, was a professor of moral philosophy at the University of Leipzig who died when Leibniz was only six years old. The next year, he entered the Nicolai School and augmented his classical studies there by installing himself in his late father’s extensive library, reading voraciously. In 1661, at the age of 15, he entered the University of Leipzig to study jurisprudence and philosophy. Two years later, he earned his bachelor’s degree on the strength of his baccalaureate thesis, De Principio Individui ("On the Principle of the Individual").
Leibniz spent the summer term of 1663 at the University of Jena studying Euclidian geometry under Erhard Weigel and then returned to Leipzig to earn his master’s degree in philosophy with a dissertation combining philosophy, law, and mathematics. The University of Leipzig refused to grant him a doctorate in law, purportedly due to his youth. Impatiently, Leibniz proceeded to the University of Altdorf, where he earned his doctor of law degree in 1667 for his thesis, De Casibus Per-plexis ("On Perplexing Cases").
Leibniz turned down a chair at Altdorf, serving instead as secretary to the Nuremberg alchemical society until he met Baron Johann Christian von Boyneburg, who employed him as a secretary, librarian, lawyer, and adviser in Frankfurt starting in November 1667. During this time, he started work on his calculating machine, capable of multiplying, dividing, and extracting roots (by mechanically adding or subtracting repeatedly), representing a significant improvement over Blaise Pascal’s calculator. Pierre de Carvaci, the royal librarian in Paris, requested a prototype in 1671, though Leibniz did not complete its construction until 1672.
That year, Leibniz and his patron traveled to Paris on a political mission, though Leibniz focused his attention on studying Cartesianism with christiaan huygens. In December 1672, Boyneburg died; bereft of employment, Leibniz accepted a political mission to London in January 1673, though again he focused more attention on his scientific career than on his assignment, as he gained induction into the Royal Society and met Isaac Barrow and Sir Isaac Newton.
Leibniz spent the years between 1673 and 1676 in Paris, vainly trying to secure a salary from the Academie des Sciences. In 1676, Johann Friedrich, the duke of Brunswick-Luneberg, secured Leibniz’s services as adviser, librarian, and genealogist. He also conducted scientific work on hydraulic presses, windmills, lamps, submarines, clocks, carriages, water pumps, and the binary number system.
In 1684, Leibniz published a paper explaining his differential calculus, "Nova Methodus pro Maximus et Minimis" ("New Method for the Greatest and the Least"), in the Leipzig journal Acta Eruditorium (its lack of proofs prompted Jacob Bernoulli to call it more of an enigma than an explanation). Two years later, he introduced his integral calculus in the same journal, complete with notation. It was not until the next year that Newton published his Principia; his calculus of fluxions, which he devised sometime between 1665 and 1671, was not published until an English edition appeared in 1736. This lag time between conception and publication complicated the issue of precedence.
In later years, Leibniz readily admitted Newton’s influence on his own research on tangents and quadratures, the genesis of his discovery of differential and integral calculus. In 1699, Fatio de Duiller, a Swiss mathematician and fellow of the Royal Society, questioned the originality of Leibniz’s discovery, and a dozen years later, the Royal Society endorsed Newton as the father of differential and integral calculus. However, evidence strongly suggests that Leibniz devised his calculus independent of Newton, despite the fact that he developed his calculus after meeting Newton. Leibniz considered himself and Newton "contemporaries in these discoveries."
In 1700, Leibniz helped found the Berlin Academy, which named him president for life. In 1712, Peter the Great of Russia appointed him a privy councilor, as did the Viennese court from 1712 through 1714 (though he had been seeking this position for years). However, these were minor victories for Leibniz, who sunk into relative obscurity later in his life. He developed a case of gout in about 1714 and died on November 14, 1716, in Hannover, Germany. Both the Royal Society and the Berlin Academy overlooked his death, and it was not until much later that his name was resurrected, and he was credited as the thinker who most clearly expressed the fundamentals of calculus.
