History of calculus

The history of calculus traces the development of methods for studying continuous change and accumulation, from ancient geometry to modern mathematical analysis.

Exhaustion method: An ancient Greek method for finding areas and volumes by bounding figures with successively closer approximations. It established a rigorous geometric route toward integral reasoning.
Isaac Newton: An English mathematician and natural philosopher who formulated a method of fluxions for changing quantities. His calculus linked rates of change to motion and gravitation.
Infinitesimal: A quantity smaller in magnitude than every positive real number, interpreted differently across mathematical frameworks. Early calculus relied on infinitesimal quantities whose foundations remained disputed.
Calculus of variations: A field that finds functions optimizing quantities defined by integrals. It extended calculus from choosing numbers to choosing entire paths and functions.
Newton–Leibniz calculus controversy: A dispute over priority for the independent invention of calculus by Newton and Leibniz. The controversy exposed national rivalries and complicated recognition of calculus's origins.
Method of indivisibles: A seventeenth-century approach that treated figures as collections of infinitely thin lines or planes. It revived area calculations that helped prepare the way for integral calculus.
Gottfried Wilhelm Leibniz: A German philosopher and mathematician who independently developed calculus and introduced much of its lasting notation. His symbols for differentials and integrals became the standard language of calculus.
Limit (mathematics): A value that a function or sequence approaches as its input approaches a specified point or grows without bound. The limit concept eventually supplied a precise foundation for derivatives and integrals.
Ordinary differential equation: An equation relating an unknown function of one variable to its derivatives. Differential equations turned calculus into a tool for modeling changing physical systems.
Riemann integral: An integral defined through limits of sums over partitions of an interval. It formalized integration differently from the early infinitesimal approaches.

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