The German mathematician, logician, political adviser, and philosopher Gottfried Wilhelm Leibniz, who was credited with his independent invention of integral and differential calculus, was born in Leipzig on July 1, 1646. It was a tumultuous time, in the last years of the Thirty Years’ War. He was raised a Lutheran. In 1652, Gottfried’s father died. He left his family a substantial library of books, which the young learner consumed with gusto. He spent a lot of time in the library, learning much from his own studies. Gottfried was also enrolled at the Nicolai School.
Gottfried was accepted at the University of Leipzig as a law student. There, he was introduced to the ideas of Francis Bacon, René Descartes, Galileo Galilee, and Thomas Hobbes. He was denied his application for the degree of doctor of law in 1666 because he was underage.
In May 1663, Gottfried completed his baccalaureate thesis, entitled De Principio Individui (On the Principle of the Individual). In this treatise, which was inspired by Lutheran nominalism, Leibniz argued on the significance of an individual’s existential value, which is founded on the person’s entitate tota, or whole being. Three years later, in 1666, in De Arte Combinatoria (On the Art of Combination), he presented a theoretical model that can be considered a predecessor of the modern ideas that made the existence of computers possible.
Leibniz continued with his academic pursuits at Nürnberg. He left Leipzig for Altdorf, where he pursued his doctor of law degree. His dissertation was entitled, De Casibus Perplexis (On Perplexing Cases).
Involvement in Politics
Leibniz denied a professor’s chair for the opportunity to advise Johann Philipp von Schönborn, the Archbishop of Mainz on political and legal matters. He was introduced to the court of the Prince Elector by his friend, the distinguished statesman, Johann Christian, Freiherr von Boyneburg.
During this time, Leibniz worked on the Hypothesis Physica Nova (New Physical Hypothesis), which was published in 1671, in the effort to promote the reunion of the church and divert the attention of King Louis XIV of France, who was becoming a significant threat to the German Holy Roman Empire. Leibniz conducted extensive research while working on the Demonstrationes Catholicae, and developed the idea that “nothing occurs without sufficient reason,” along with important arguments on issues relating to space, optics, and movement. One of his key arguments was that movement depends on the action of God, in accordance with the theory of his compatriot Johannes Kepler, the celebrated astronomer.
Leibniz was sent to Paris in 1672 on a mission where he met with controversial Jansenist theologian Antoine Arnauld to help him work on ideas to promote reunion of the church. Upon the deaths of his benefactors in the latter part of 1672 and in early 1673, he decided to focus on science and sought financial backing for his projects. In his first journey to London, England in 1673, he presented a calculating machine that he invented to the Royal Society.
The Founding of Dynamics
In the latter part of 1675, Leibniz has already constructed the basic arguments that served as the foundations for dynamics, which he would then use to expand into the foundations of differential and integral calculus. He developed ideas based on the notion that the discovering the basic laws of motion requires delving beyond studies of their nature, and instead contains an imaginary element. He posited that the world is a “well-related dream,” contrary to the ideas presented by Descartes before him. His ideas were critical of Cartesian mechanics, and suggested that visible movement must be resulting from a force. These ideas formed the foundations of dynamics, a new formulation that expounded on the concept of kinetic energy in place of conservation of movement.
In 1676, Leibniz was employed as librarian by the Duke of Braunschweig-Lüneburg, John Frederick. A year after his employment, Leibniz applied for the duke for the position of councilor, which was granted to him in 1678. In 1679, he completed his work on the binary system of numeration and set down the foundations of a branch of mathematics known as general topology.
Leibniz's Mechanical Devices and Other Preoccupations
Gottfried Leibniz worked on theoretical formulations and mathematical concepts, but he also invented various mechanical devices with practical usage. He occupied himself with the development of clocks, lamps, water pumps, windmills, hydraulic presses, carriages, and even submarines.
In 1680, Duke John Frederick and was succeeded by Ernest Augustus I. From 1680 -1685, Leibniz worked as an engineer in the Harz Mountains, working on mines and making geological observations. It was during this time that he posited that the earth started out as a molten mass. He is now considered one of the pioneers of the geological sciences.
In 1681, Leibniz still continued with his work in mathematics and in metaphysical systems. In the same year, while the German Empire was in a state of chaos amid the French invasion of Strasbourg and Alsace, the Turkish advance, and the Hungarian revolt, he became more deeply involved in political matters as adviser to the prince. He recommended methods for water desalination for boosting linen production. He also wrote a pamphlet in Latin and French in violent protest against King Louis XIV of France.
From 1690 onward, while serving as historian, he expanded his scope to studies on the history of the Earth, explored the migrations and origins of peoples, and directed his efforts in studying universal history. He managed to formulate new ideas, which became very influential, although he was unable write a comprehensive treatise. Leibniz became the librarian at Wolfenbüttel in 1691 and from then onward he continued to publish in scientific journals.
Leibniz was made a member of the Academy of Sciences of Paris in 1700. By this time, he was already considered an important thinker and philosopher in Europe. In 1714, Leibniz became a Baron and promoted to the post “Adviser to the Empire” by the Emperor.
The Calculus Controversy
The rivalry between Sir Isaac Newton and Gottfried Leibniz revolved around the creation of Calculus, a branch of mathematics. Newton invented calculus around 1666 in order to solve the problems he was working on in geometry and physics. Meanwhile, Leibniz started his own studies on calculus around 1675 when he became interested in the tangent line problem. Newton came upon the discovery of the principles of calculus before Leibniz, but it is common contention that Leibniz’s notations are far more extensive than Newton’s. The approach used by the two men is also very different. While Leibniz devoted his time on the abstract and infinite aspects Newton focused on the concrete reality and limits of calculus.
In the end, a verdict of plagiarism was handed down to Gottfried Leibniz by the Royal Society. Nevertheless, Newton and Leibniz worked on calculus separately, using different methods. Newton started working on derivatives. Meanwhile, Leibniz focused on the problem of integration first. It is highly unlikely that Leibniz copied from Newton because Newton first published his work in 1693, while Leibniz published his paper in 1684. Today, both men are credited for their independent discovery, and the dx/dt notation for derivatives devised by Leibniz is not favored over Newton’s “dot” notation.
Publications and Final Years
In 1684, Leibniz published an exposition of differential calculus, which is the Nova Methodus pro Maximis et Minimis (New Method for the Greatest and the Least). Meanwhile, in his work entitled, Meditationes de Cognitione, Veritate et Ideis (Reflections on Knowledge, Truth, and Ideas), Leibniz expounded on his own ontological argument for the existence of God, and discussed the relation between man’s and God’s ideas.
In 1685, he served as court adviser and historian for the House of Brunswick. His main task was to determine the origins of the princely house of Hanover in relation to the Italian House of Este to support its rightful claim to the ninth electorate.
In 1686, he published Discours de Métaphysique (Discourse on Metaphysics), where he explained the principle of the identity of indiscernibles, and Brevis Demonstratio Erroris Memorabilis Cartesii et Aliorum Circa Legem Naturae (Brief Demonstration of the Memorable Error of Descartes and Others About the Law of Nature) where he expounded on his ideas on dynamics. He also worked on the movement of celestial bodies, publishing essays while traveling to Italy in 1687.
In 1695, he published Système Nouveau (New System) where he discussed part of his dynamic theory of motion. In 1697, he presented a cosmological argument on the existence of God on De Rerum Originatione (On the Ultimate Origin of Things). In 1710, he published Théodicée (Theodicy), where he discussed divine justice. In 1714, he wrote “Principes de la nature et de la Grâce fondés en raison,” and “The Monadologia.”
After meeting with Russia’s Peter the Great one last time in 1716, he spent most of his time in bed suffering from gout. Leibniz died on November 14, 1916. His funeral was unattended by royalty and other members of the court, for being out of favor because he was unable to complete the history of the Brunswick family, and for his loss against Sir Isaac Newton in the calculus priority dispute. His grave was unmarked for more than half a century.