The shape of the sideways figure eight "∞", now used to denote "infinity", has a long pedigree. It appears in the cross of Saint Boniface, wrapped around the bars of a Latin cross; in algebraic geometry the shape of the symbol is called a lemniscate; it is also a symbol in modern mysticism. However, the English mathematician John Wallis is credited with introducing it as the infinity symbol with its mathematical meaning in 1655, in his "De sectionibus conicis."

John Wallis (1616 – 1703), an English clergyman and mathematician, was a contemporary of Newton and one of the greatest intellectuals of the early renaissance of mathematics. He has been given partial credit for the development of calculus. From 1643 to 1689 he served as chief cryptographer for Parliament and the royal court.

Wallis did not explain his choice of the symbol "∞" to represent infinity, but it taken to be a variant form of a Roman numeral for 1,000 (originally CIƆ, also CƆ, sometimes used to mean "many"), or a variant of the last letter in the Greek alphabet “ω” (“omega”). Wallis similarly used 1/∞ for an infinitesimal. The infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large towards infinity—rather than actually taking an infinite value.

Leonhard Euler (1707 – 1783) used a similar-looking “open” variant of the symbol to denote infinity, but this symbol is no longer used.

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