Knowra John Wallis John Wallis John Wallis (1616–1703) was an English mathematician and cryptographer whose work on infinite series, algebra, and infinitesimals helped shape calculus. He introduced ∞ as a symbol for infinity.
Infinite series : A sum of infinitely many terms, studied through its partial sums and convergence. Wallis used infinite expansions and products to extract numerical results.
Wallis product : An infinite product expressing π/2 as the product of ratios of even and odd integers. Wallis derived this formula by comparing integrals of powers of sine.
Oxford University : A collegiate research university in Oxford, England, with origins in the late eleventh century. Wallis studied and later taught at Oxford, holding the Savilian Chair of Geometry.
Isaac Newton : An English mathematician and physicist who formulated the laws of motion and universal gravitation. Newton credited Wallis’s mathematical work as an influence on his own methods.
Calculus : The branch of mathematics concerned with change, accumulation, derivatives, and integrals. Wallis’s work on quadratures and infinite series supplied methods later incorporated into calculus.
Indivisibles : A geometric method that treats figures as composed of infinitely many lower-dimensional elements. Wallis used indivisibles to calculate areas and volumes before integral calculus.
Arithmetica Infinitorum : A 1656 mathematical work by Wallis on arithmetic, powers, and infinite processes. Its interpolation methods led to the product now bearing Wallis’s name.
English Civil War : A series of armed conflicts in England, Scotland, and Ireland from 1642 to 1651. Wallis’s parliamentary sympathies and cryptographic work arose during this conflict.
Gottfried Wilhelm Leibniz : A German polymath who independently developed calculus and introduced its enduring differential notation. Leibniz engaged with Wallis’s work on infinite series and mathematical analysis.
Infinity : A concept describing something without bound or larger than every finite quantity. Wallis helped make ∞ a standard written symbol for this concept.
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