Gottfried Leibniz was born in 1646, the son of Friedrich Leibniz, a professor of moral philosophy at Leipzig. His father died when Leibniz was only six years old, and he was brought up by his mother (who was his father's third wife). His early years were informed by the moral and religious values of his mother that would play a significant role in his life and philosophy. He entered the Nicolai School in Leipzig at the age of seven, where he was taught Latin, though he advanced his own studies in the field, including some Greek, and becoming proficient by the age of 12. His penchant for teaching himself from his father's library led to studies in theology and metaphysics, embellishing his formal schooling in the logical systems of Aristotle that he was interested in improving. Due to his own scholastic drive, he entered the University of Leipzig at the age of fourteen in 1661. He studied philosophy, mathematics, rhetoric, Latin, Greek and Hebrew and graduated with a bachelor's degree in 1663 with a thesis De Principio Individui (On the Principle of the Individual) in which he introduced his notion of "monad". He spent the following summer in Jena, where he met Erhard Weigel, a philosopher and mathematician who believed that the number was the fundamental concept of the universe. By October 1663 Leibniz was awarded his Master's Degree in philosophy for a dissertation that combined aspects of philosophy and law, studying relations in these subjects with mathematical ideas that he had learnt from Weigel. Shortly after Leibniz presented his dissertation, his mother died.
Leibniz set out to write his habilitation in philosophy that was to be published in 1666 as Dissertatio de arte combinatoria (Dissertation on the combinatorial art). In this work Leibniz aimed to reduce all reasoning and discovery to a combination of basic elements such as numbers, letters, sounds and colors. Unfortunately the paper failed to procure his doctorate in law at Leipzig. He transferred to the University at Altdorf and succeeded to receive his doctorate in law the following year for his dissertation De Casibus Perplexis (On Perplexing Cases). Leibniz declined the promise of a chair at Altdorf because he had other aspirations. He served as secretary to the Nuremberg alchemical society; he then met Baron Johann Christian von Boineburg. By November 1667 Leibniz had moved to Frankfurt, employed by Boineburg. During the next few years Leibniz undertook a variety of different projects, scientific, literary and political. Leibniz thus put his thoughts to the possibilities of a peace within the Holy Roman (German) Empire and with its neighbors, especially the French king Louis XIV — a peace based on a new Christian theology, which would allow Catholics and Protestants to come together on a new theological plane. He drafted a number of monographs on religious topics. He also continued his law career taking up residence at the courts of Mainz from 1667 to 1672. One of his ambitions, undertaken for the Elector of Mainz, was to improve the Roman civil law code for Mainz. He saw his work on Roman civil law as part of one of his lifelong aims to collate all human knowledge.
One particular area of interest for Leibniz was motion, beginning with abstract notions of motion, although he also had in mind the problem of explaining the results of Wren and Huygens on elastic collisions. In 1671 he completed and published Hypothesis Physica Nova (New Physical Hypothesis), claiming that movement depends on the action of a spirit. He communicated with Oldenburg, the secretary of the Royal Society of London, and dedicated some of his scientific works to The Royal Society and the Paris Academy.
In a war-torn Europe in which the Catholics and Protestants and other monarchies such as in Germany, France, Spain vied for power and control, Leibniz placed his faith in the system of clear human reasoning to elevate beyond such violence and struggle. Mathematics could structure theological and political thought so as to bring the chaos of Europe into a fully reasoned existence. Such a vision runs throughout his life. He sought to invent a universal language based not on geometry but on calculus perfected down to the level of logic that would provide a common mathematical, philosophical, logical and scientific foundation for all thought; in Leibniz's ideal system all such disputes could be resolved reasonably by systems of rigorous calculations.
For example, Leibniz formed a political plan to persuade the French to drive the Turks out of Egypt, in a ploy to divert the French from attacking German areas. He went to Paris in 1672, on behalf of Boineburg, though his advice was not taken. He remained in Paris for four years, where he met the "natural philosophers" Huygens, Malbranche, and Arnauld. Hyugens introduced him to his own theories on the nature of light that were in opposition to Newton's. Leibniz' own theories contrasted with Newton's, he in turn impressed upon Arnauld the workings of his own metaphysical system. He also prided his ability to recite poetry, claiming to be able to recite the majority of Virgil's "Aenid" by heart, earning him the friendship of the Royal Librarian, Carcavi, in Paris.
Leibniz accepted the position of librarian and Court Councilor by invitation of the Duke of Hanover. Leaving Paris in 1676, he took the opportunity to travel through London and Holland, where he spent a month visiting Spinoza in Amsterdam. He spent the rest of his life in Hanover, taking many opportunities to travel and visit friends and colleagues. He also took on diverse projects, including one that involved the draining of water from the mines in the Harz mountains. He proposed to use wind and water power to operate pumps. Though the project failed, his time on the project led to important discoveries in the field of geography, including the theory that the earth was once molten. During these years he also developed a binary number system, as well as a series of key components to a discipline of symbolic logic. He also returned his focus on his own philosophy, completing works on metaphysics and systematic philosophy during the 1680's and 90's.
Leibniz was known for a wide range of ideas about fundamental concepts and principles: on truth, necessary and contingent truths, the principle of sufficient reason (nothing occurs without a logical explanation), the principle of an a priori harmony in the world (God's universe is such that corresponding mental and physical events occur simultaneously) and the principle of non-contradiction (a proposition cannot be said to be true if a contradiction can be derived from it). Leibniz published Meditationes de Cognitione, Veritate et Ideis (Reflections on Knowledge, Truth, and Ideas) which clarified his theory of knowledge. In February 1686, Leibniz published his Discours de métaphysique (Discourse on Metaphysics).
Leibniz's key works are the Essais de Theodicee (1710; Eng. trans., 1951), in which much of his central concepts are found, and the Monadology (1714; trans. as The Monadology and other Philosophical Writings, 1898), in which he conceives his theory of the monad. Leibniz strongly disagreed with the Newtonian cosmology of absolute matter, space and time. Newton's theory of material substance, founded on the atom and its placement and movements, was opposed by Leibniz' monads as the foundation of all reality. Leibniz' monads had no materiality in time and space, no velocity or direction of movement. His monads functioned as what we currently would define as potential energy — each monad distinct in its potentiality and a part of a larger "colony" of monads which, through the directives of God, combined in distinct ways to form the observable elements of our universe. Monads are not Newtonian in the sense of each having specific and distinct role within the functioning of a totality of the universe, but rather are each tiny mirrorings of the entire universe. Each monad has the capacity or potential to express the fullness of the universe through the relationship of all the monads with each other. And yet each monad represents only a single view or perspective — the view from where it sits in relationship to the whole of the universe. God alone has the capacity to see the universe in its entirety, from all perspectives simultaneously, and the capacity to choose which of these views or mirrorings will be the one that comes into actual being, through an "unfolding" of the potential of the multiplicity of monads into the harmonious actuality of their behavior as designed by God.

In 1700 the Brandenburg Society (Berlin Academy of Science) was founded at Leibniz's prompting. He worked on founding an institutional framework for the sciences in central Europe and Russia. He met with Peter the Great a number of times, offering recommendations for educational reforms for Russia, and he proposed what would eventually be the Saint Petersburg Academy of Science. He lived privately during the last years of his life, harassed by the controversy of whether it was he or Isaac Newton who should claim the rights as the first inventor of the calculus. Much of his work, like the studies on symbolic logic, remained unknown during his lifetime, and was only discovered in the twentieth century. He is an important figure of German idealism and the Enlightenment. He died on November 14, 1716.