Gottfried Wilhelm Leibniz began with legal and diplomatic work before a mission to Paris in 1672 opened a formative period of mathematical study. Contact with Christiaan Huygens and other scholars helped him develop new techniques. He constructed a calculating machine and was elected to the Royal Society in 1673. During the 1670s he developed differential and integral calculus independently of Newton, introducing notation that proved especially effective for later mathematical work.

From 1676 Leibniz served the rulers of Brunswick-Lüneburg at Hanover as librarian, adviser, and historian. His responsibilities included dynastic research, legal and political projects, and technical schemes such as work on mining. He maintained an enormous correspondence, linking scholars across Europe and pursuing cooperation between institutions and religious communities. He helped establish the Berlin scientific society in 1700, an important part of his effort to organize research beyond individual achievement.

Leibniz published an account of differential calculus in 1684 and later work on integration. A bitter priority dispute with Newton and their supporters damaged relations between British and continental mathematicians. The evidence supports independent development, even though the controversy was long framed through allegations of plagiarism. His broader scientific work included binary arithmetic and arguments concerning force and motion, while many proposed projects remained incomplete or impractical.

In philosophy Leibniz developed principles concerning sufficient reason, identity, and the relation between individual substances and the world. Theodicy in 1710 defended divine justice in a world containing evil, while the short work later called Monadology in 1714 summarized aspects of his metaphysics. Much of his philosophical writing appeared only after his death or survived in correspondence, complicating attempts to identify one final system. His standing at Hanover declined, particularly after the elector became George I of Britain, and he died there in 1716. His career joined court service with mathematical invention, philosophy, history, and institutional planning. Its breadth should not obscure the specific successes and failures of each project, but the enduring notation of calculus and the questions posed by his metaphysics show how work developed under dynastic patronage could reshape international intellectual life.