Mathematics

Gottfried Leibniz

German polymath · 1646–1716

The calculus, the dream of a universal logic, and a calculating reason.

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Lessons

The Invention of the Calculus

How Leibniz, independently of Newton, discovered the calculus - a method for handling the infinitely small, taming the twin problems of tangents and areas with a single symbolic machinery.

Notation as Thought: dx and the Integral Sign

Why Leibniz’s symbols for the calculus - the differential d and the elongated S of the integral - were not mere decoration but a deliberate design that made the mathematics think for you.

Binary Arithmetic: Counting with 0 and 1

How Leibniz developed the base-two number system - every number written with only 0 and 1 - finding in it a metaphysical image of creation and laying, unknowingly, the arithmetical foundation of the digital age.

The Universal Characteristic and the Calculus of Reason

Leibniz’s most audacious dream: a universal symbolic language (the characteristica universalis ) and a calculus of reasoning (the calculus ratiocinator ) that would let all thought be carried out, and all disputes…

Sufficient Reason and the Best of All Possible Worlds

Leibniz the metaphysician: the principle of sufficient reason, the monads as the true atoms of reality, and the famous and much-mocked claim that ours is the best of all possible worlds - the optimisation logic of a mat…

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