Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher, mathematician, and diplomat who independently developed calculus and advanced logic, metaphysics, and mechanical computation.

Infinitesimal calculus: A branch of mathematics that studies change and accumulation using derivatives and integrals. Leibniz independently developed its methods and notation.
Leibniz notation: The differential and integral symbols commonly used in calculus, including dy/dx and ∫. His notation made calculus operations compact and helped establish their modern form.
Isaac Newton: An English mathematician and natural philosopher who developed a form of calculus independently of Leibniz. Their rival claims over calculus priority became a prolonged controversy.
Calculus controversy: The dispute over whether Newton or Leibniz first invented calculus and whose notation should be adopted. The priority dispute divided British and continental mathematicians for generations.
Leibniz–Clarke correspondence: A published exchange between Leibniz and Samuel Clarke on space, time, God, and Newtonian physics. It exposes competing accounts of the universe and divine action.
Binary number system: A numeral system that represents numbers using only the digits zero and one. Leibniz explored binary arithmetic and linked it to his account of creation.
Leibniz integral rule: A rule for differentiating an integral whose limits or integrand depend on a variable. It applies his differential methods to integrals with changing bounds.
Jakob Bernoulli: A Swiss mathematician who helped develop and apply early calculus. He adopted Leibnizian methods and helped spread them across continental Europe.
Computer science: The study of computation, algorithms, and information-processing systems. Leibniz's binary arithmetic and calculating-machine designs became landmarks in its prehistory.
Leibniz's philosophy of mind: Leibniz's account of perception, consciousness, and mental representation within his metaphysics. His distinction between perception and apperception raises questions about consciousness.

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